1360 lines
36 KiB
Rust
1360 lines
36 KiB
Rust
use std::cell::RefCell;
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use std::collections::hash_map::Entry;
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use std::collections::{BTreeSet, HashMap, HashSet};
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use std::rc::Rc;
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use petgraph::visit::{ EdgeCount, EdgeRef, GraphBase, IntoEdgeReferences,
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IntoEdges, IntoNeighborsDirected, IntoNodeIdentifiers,
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IntoNodeReferences, NodeCount };
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use petgraph::Direction::{Incoming, Outgoing};
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// -----------------------------------------------------------------------------
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// Helper Functions
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// -----------------------------------------------------------------------------
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#[inline(always)]
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fn equal_vectors<T>(a: &Vec<T>, b: &Vec<T>) -> bool
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where
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T: PartialEq
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{
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for el in a {
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if !b.contains(el) {
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return false;
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}
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}
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for el in b {
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if !a.contains(el) {
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return false;
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}
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}
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true
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}
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// -----------------------------------------------------------------------------
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// Bisimilarity
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// -----------------------------------------------------------------------------
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// -----------------------------------------------------------------------------
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// Bisimilarity by Kanellakis and Smolka from The algorithmics of bisimilarity
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// by Luca Aceto, Anna Ingolfsdottir and Jirí Srba; pages 105 to 110
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// https://doi.org/10.1017/CBO9780511792588.004
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// -----------------------------------------------------------------------------
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struct GraphPartition<'a, G>
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where
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G: GraphBase,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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{
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pub node_to_block: HashMap<(usize, G::NodeId), u32>,
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pub block_to_node: HashMap<u32, Vec<(usize, G::NodeId)>>,
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pub graphs: [&'a G; 2],
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last_block: u32,
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blocks: BTreeSet<u32>
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}
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impl<'a, G> GraphPartition<'a, G>
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where
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G: GraphBase,
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G::NodeId: std::cmp::Eq + std::hash::Hash
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{
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pub fn new(graph_a: &'a G, graph_b: &'a G) -> Self {
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GraphPartition { node_to_block: HashMap::new(),
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block_to_node: HashMap::new(),
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graphs: [graph_a, graph_b],
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last_block: 0,
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blocks: BTreeSet::new() }
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}
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#[inline(always)]
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pub fn add_node_last_partition(&mut self, node: G::NodeId, graph: usize) {
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self.node_to_block.insert((graph, node), self.last_block);
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self.block_to_node
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.entry(self.last_block)
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.or_default()
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.push((graph, node));
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self.blocks.insert(self.last_block);
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}
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#[inline(always)]
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pub fn iterate_blocks(&self) -> Vec<u32> {
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self.blocks.iter().cloned().collect::<Vec<_>>()
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}
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pub fn bisimilar(&self) -> bool {
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// if there is a block that has only elements from one graph then they
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// are not bisimilar
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for (_block, node_list) in self.block_to_node.iter() {
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let graph_id = node_list.first().unwrap().0;
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if node_list.iter().all(|el| el.0 == graph_id) {
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return false;
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}
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}
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true
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}
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}
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impl<'a, G> GraphPartition<'a, G>
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where
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G: IntoEdges,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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{
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fn reachable_blocks(
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&self,
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label: &G::EdgeWeight,
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s: &(usize, G::NodeId)
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) -> Vec<u32>
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where G::EdgeWeight: PartialEq
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{
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let mut val = vec![];
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for el in self.graphs[s.0].edges(s.1).filter(|x| x.weight() == label) {
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let tmp = (s.0, el.target());
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val.push(*self.node_to_block.get(&tmp).unwrap());
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}
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val
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}
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pub fn split(&mut self, block: u32, label: &G::EdgeWeight) -> bool
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where G::EdgeWeight: PartialEq
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{
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let Some(nodes) = self.block_to_node.get(&block)
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else {
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return true
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};
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let mut nodes = nodes.iter();
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let s = nodes.next().unwrap();
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let mut b1 = vec![s];
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let mut b2 = vec![];
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let reachable_blocks_s = self.reachable_blocks(label, s);
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for t in nodes {
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let reachable_blocks_t = self.reachable_blocks(label, t);
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if equal_vectors(&reachable_blocks_s, &reachable_blocks_t) {
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b1.push(t);
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} else {
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b2.push(*t);
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}
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}
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if b2.is_empty() {
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// all elements go to the same block with label label, so no change
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false
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} else {
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// some elements need to be split into a different block
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self.last_block += 1;
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let new_block = self.last_block;
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self.blocks.insert(new_block);
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for b in b2 {
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self.node_to_block.entry(b).and_modify(|e| *e = new_block);
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self.block_to_node.entry(new_block).or_default().push(b);
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self.block_to_node.entry(block).and_modify(|e| {
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let index = e.iter().position(|x| *x == b).unwrap();
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e.remove(index);
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});
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}
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true
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}
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}
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}
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pub fn bisimilarity_kanellakis_smolka<'a, G>(
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graph_a: &'a G,
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graph_b: &'a G
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) -> bool
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where
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G: IntoNodeReferences + IntoEdges,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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G::EdgeWeight: std::cmp::Eq + std::hash::Hash + Clone
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{
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let graphs = [graph_a, graph_b];
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let mut partition: GraphPartition<G> =
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GraphPartition::new(graph_a, graph_b);
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for (p, graph) in graphs.iter().enumerate() {
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for node in graph.node_identifiers() {
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partition.add_node_last_partition(node, p);
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}
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}
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let labels =
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graph_a.edge_references()
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.chain(graph_b.edge_references())
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.map(|e| e.weight().clone())
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.collect::<HashSet<_>>();
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let mut changed = true;
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while changed {
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changed = false;
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for block in partition.iterate_blocks() {
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for label in labels.iter() {
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if partition.split(block, label) {
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changed = true;
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}
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}
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}
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}
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partition.bisimilar()
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}
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#[test]
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fn identity_kanellakis_smolka() {
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use petgraph::Graph;
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let mut graph_a = Graph::new();
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let node_a_1 = graph_a.add_node(1);
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let node_a_2 = graph_a.add_node(2);
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graph_a.add_edge(node_a_1, node_a_2, 1);
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assert!(bisimilarity_kanellakis_smolka(&&graph_a, &&graph_a))
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}
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#[test]
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fn identity_kanellakis_smolka_2() {
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use petgraph::Graph;
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let mut graph_a = Graph::new();
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let node_a_1 = graph_a.add_node(1);
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let node_a_2 = graph_a.add_node(2);
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graph_a.add_edge(node_a_1, node_a_2, 1);
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let node_a_3 = graph_a.add_node(3);
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graph_a.add_edge(node_a_1, node_a_3, 1);
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let node_a_6 = graph_a.add_node(6);
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graph_a.add_edge(node_a_2, node_a_6, 2);
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let node_a_4 = graph_a.add_node(4);
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graph_a.add_edge(node_a_3, node_a_4, 2);
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let node_a_7 = graph_a.add_node(7);
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graph_a.add_edge(node_a_6, node_a_7, 2);
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let node_a_5 = graph_a.add_node(5);
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graph_a.add_edge(node_a_4, node_a_5, 2);
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let node_a_8 = graph_a.add_node(8);
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graph_a.add_edge(node_a_7, node_a_8, 3);
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graph_a.add_edge(node_a_8, node_a_7, 3);
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graph_a.add_edge(node_a_8, node_a_8, 3);
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assert!(bisimilarity_kanellakis_smolka(&&graph_a, &&graph_a))
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}
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#[test]
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fn identity_different_weights_kanellakis_smolka() {
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use petgraph::Graph;
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let mut graph_a = Graph::new();
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let node_a_1 = graph_a.add_node(1);
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let node_a_2 = graph_a.add_node(2);
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graph_a.add_edge(node_a_1, node_a_2, 1);
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let mut graph_b = Graph::new();
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let node_b_1 = graph_b.add_node(1);
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let node_b_2 = graph_b.add_node(2);
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graph_b.add_edge(node_b_1, node_b_2, 2);
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assert!(!bisimilarity_kanellakis_smolka(&&graph_a, &&graph_b))
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}
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#[test]
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fn not_bisimilar_kanellakis_smolka() {
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use petgraph::Graph;
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let mut graph_a = Graph::new();
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let node_a_1 = graph_a.add_node(1);
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let node_a_2 = graph_a.add_node(2);
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graph_a.add_edge(node_a_1, node_a_2, 1);
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let mut graph_b = Graph::new();
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let node_b_1 = graph_b.add_node(1);
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let node_b_2 = graph_b.add_node(2);
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graph_b.add_edge(node_b_1, node_b_2, 1);
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let node_b_3 = graph_b.add_node(3);
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graph_b.add_edge(node_b_1, node_b_3, 2);
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assert!(!bisimilarity_kanellakis_smolka(&&graph_a, &&graph_b))
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}
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#[test]
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fn not_bisimilar_kanellakis_smolka_2() {
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use petgraph::Graph;
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let mut graph_a = Graph::new();
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let node_a_1 = graph_a.add_node(1);
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let node_a_2 = graph_a.add_node(2);
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graph_a.add_edge(node_a_1, node_a_2, 1);
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let node_a_3 = graph_a.add_node(3);
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graph_a.add_edge(node_a_1, node_a_3, 1);
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let node_a_6 = graph_a.add_node(6);
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graph_a.add_edge(node_a_2, node_a_6, 2);
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let node_a_4 = graph_a.add_node(4);
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graph_a.add_edge(node_a_3, node_a_4, 2);
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let node_a_7 = graph_a.add_node(7);
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graph_a.add_edge(node_a_6, node_a_7, 2);
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let node_a_5 = graph_a.add_node(5);
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graph_a.add_edge(node_a_4, node_a_5, 2);
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let node_a_8 = graph_a.add_node(8);
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graph_a.add_edge(node_a_7, node_a_8, 3);
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graph_a.add_edge(node_a_8, node_a_7, 3);
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graph_a.add_edge(node_a_8, node_a_8, 3);
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let mut graph_b = Graph::new();
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let node_b_1 = graph_b.add_node(1);
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let node_b_2 = graph_b.add_node(2);
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graph_b.add_edge(node_b_1, node_b_2, 1);
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let node_b_3 = graph_b.add_node(3);
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graph_b.add_edge(node_b_2, node_b_3, 2);
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let node_b_4 = graph_b.add_node(4);
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graph_b.add_edge(node_b_3, node_b_4, 2);
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assert!(!bisimilarity_kanellakis_smolka(&&graph_a, &&graph_b))
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}
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#[test]
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fn not_bisimilar_kanellakis_smolka_3() {
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use petgraph::Graph;
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let mut graph_b = Graph::new();
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let node_b_1 = graph_b.add_node(1);
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let node_b_2 = graph_b.add_node(2);
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graph_b.add_edge(node_b_1, node_b_2, 1);
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let node_b_3 = graph_b.add_node(3);
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graph_b.add_edge(node_b_2, node_b_3, 2);
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let node_b_4 = graph_b.add_node(4);
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graph_b.add_edge(node_b_3, node_b_4, 2);
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let mut graph_c = Graph::new();
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let node_c_1 = graph_c.add_node(1);
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let node_c_2 = graph_c.add_node(2);
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graph_c.add_edge(node_c_1, node_c_2, 1);
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let node_c_3 = graph_c.add_node(3);
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graph_c.add_edge(node_c_1, node_c_3, 2);
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graph_c.add_edge(node_c_2, node_c_3, 2);
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assert!(!bisimilarity_kanellakis_smolka(&&graph_b, &&graph_c))
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}
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#[test]
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fn bisimilar_kanellakis_smolka() {
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use petgraph::Graph;
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let mut graph_b = Graph::new();
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let node_b_1 = graph_b.add_node(1);
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let node_b_2 = graph_b.add_node(2);
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graph_b.add_edge(node_b_1, node_b_2, 1);
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let node_b_3 = graph_b.add_node(3);
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graph_b.add_edge(node_b_2, node_b_3, 2);
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let node_b_4 = graph_b.add_node(4);
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graph_b.add_edge(node_b_3, node_b_4, 2);
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let mut graph_c = Graph::new();
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let node_c_1 = graph_c.add_node(1);
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let node_c_2 = graph_c.add_node(2);
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graph_c.add_edge(node_c_1, node_c_2, 1);
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let node_c_3 = graph_c.add_node(3);
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graph_c.add_edge(node_c_2, node_c_3, 2);
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let node_c_4 = graph_c.add_node(4);
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graph_c.add_edge(node_c_3, node_c_4, 2);
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let node_c_5 = graph_c.add_node(5);
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graph_c.add_edge(node_c_1, node_c_5, 1);
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let node_c_6 = graph_c.add_node(6);
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graph_c.add_edge(node_c_5, node_c_6, 2);
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let node_c_7 = graph_c.add_node(7);
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graph_c.add_edge(node_c_6, node_c_7, 2);
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assert!(bisimilarity_kanellakis_smolka(&&graph_b, &&graph_c))
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}
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#[test]
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fn bisimilar_kanellakis_smolka_2() {
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use petgraph::Graph;
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let mut graph_a = Graph::new();
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let node_a_1 = graph_a.add_node(1);
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let node_a_2 = graph_a.add_node(2);
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graph_a.add_edge(node_a_1, node_a_2, 1);
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let node_a_3 = graph_a.add_node(3);
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graph_a.add_edge(node_a_1, node_a_3, 1);
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graph_a.add_edge(node_a_2, node_a_3, 2);
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graph_a.add_edge(node_a_3, node_a_3, 2);
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let mut graph_b = Graph::new();
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let node_b_1 = graph_b.add_node(1);
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let node_b_2 = graph_b.add_node(2);
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graph_b.add_edge(node_b_1, node_b_2, 1);
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graph_b.add_edge(node_b_2, node_b_2, 2);
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assert!(bisimilarity_kanellakis_smolka(&&graph_a, &&graph_b))
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}
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// -----------------------------------------------------------------------------
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// Bisimilarity by Paige and Tarjan from Three Partition Refinement Algorithms
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|
// by Robert Paige L., Robert Endre Tarjan; pages 977 to 983
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// https://doi.org/10.1137/0216062
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// -----------------------------------------------------------------------------
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|
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type NodeIdType = u32;
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type GraphIdType = u32;
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type NodeType = (GraphIdType, NodeIdType);
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trait NextId<From, T> {
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fn next_id_of_graph(&mut self, val: From) -> T;
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}
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|
|
struct Translator<From, To, State>
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where
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State: NextId<From, To>
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{
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data: HashMap<From, To>,
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reverse_data: HashMap<To, From>,
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last_id: State,
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}
|
|
|
|
impl<From, To, State> Translator<From, To, State>
|
|
where
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To: std::hash::Hash + std::cmp::Eq + Copy,
|
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From: std::hash::Hash + std::cmp::Eq + Clone,
|
|
State: NextId<From, To>
|
|
{
|
|
pub fn new() -> Self
|
|
where
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State: Default
|
|
{
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Translator { data: HashMap::new(),
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reverse_data: HashMap::new(),
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last_id: State::default() }
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}
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|
|
|
pub fn encode(&mut self, val: From) -> To
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{
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let id = *(self.data.entry(val.clone())
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.or_insert(
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self.last_id.next_id_of_graph(val.clone())
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));
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self.reverse_data.insert(id, val);
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id
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}
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|
|
|
pub fn get(&self, val: &From) -> Option<&To>
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{
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self.data.get(val)
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}
|
|
|
|
pub fn decode(&self, val: &To) -> Option<&From> {
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self.reverse_data.get(val)
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}
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}
|
|
|
|
#[derive(Clone, Copy, Hash, PartialEq, Eq, PartialOrd, Ord)]
|
|
struct NodeState<const N: usize> {
|
|
last_ids: [u32; N],
|
|
}
|
|
|
|
impl<const N: usize> NodeState<N> {
|
|
fn new() -> Self {
|
|
NodeState { last_ids: [0; N] }
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|
}
|
|
}
|
|
|
|
impl<const N: usize> Default for NodeState<N> {
|
|
fn default() -> Self {
|
|
Self::new()
|
|
}
|
|
}
|
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|
|
impl<const N: usize, T> NextId<(T, GraphIdType), NodeType> for NodeState<N> {
|
|
fn next_id_of_graph(&mut self, val: (T, GraphIdType)) -> NodeType {
|
|
let graph_id_usize = val.1 as usize;
|
|
assert!(graph_id_usize < N);
|
|
self.last_ids[graph_id_usize] += 1;
|
|
(val.1, self.last_ids[graph_id_usize])
|
|
}
|
|
}
|
|
|
|
type MyNodeTranslator<From, const N: usize> =
|
|
Translator<(From, GraphIdType), NodeType, NodeState<N>>;
|
|
|
|
|
|
type EdgeIdType = u32;
|
|
type EdgeType = EdgeIdType;
|
|
|
|
#[derive(Clone, Copy, Hash, PartialEq, Eq, PartialOrd, Ord)]
|
|
struct EdgeState {
|
|
last_ids: u32,
|
|
}
|
|
|
|
impl EdgeState {
|
|
fn new() -> Self {
|
|
EdgeState { last_ids: 0 }
|
|
}
|
|
}
|
|
|
|
impl Default for EdgeState {
|
|
fn default() -> Self {
|
|
Self::new()
|
|
}
|
|
}
|
|
|
|
impl<T> NextId<T, EdgeType> for EdgeState {
|
|
fn next_id_of_graph(&mut self, _val: T) -> EdgeType {
|
|
self.last_ids += 1;
|
|
self.last_ids
|
|
}
|
|
}
|
|
|
|
type MyEdgeTranslator<From> = Translator<From, EdgeType, EdgeState>;
|
|
|
|
|
|
type Block = Vec<NodeType>;
|
|
type BackEdges = HashMap<NodeType, Vec<NodeType>>;
|
|
type NodeToBlock = HashMap<NodeType, Rc<RefCell<SimpleBlock>>>;
|
|
type CompoundPartition = Vec<Rc<CompoundBlock>>;
|
|
type SimpleBlockPointer = Rc<RefCell<SimpleBlock>>;
|
|
type CompoundBlockPointer = Rc<CompoundBlock>;
|
|
type BackEdgesGrouped = HashMap<Block, BackEdgesGroup>;
|
|
|
|
struct SimpleBlock {
|
|
block: Block,
|
|
coarse_block_that_supersets_self: Rc<CompoundBlock>
|
|
}
|
|
|
|
#[derive(Clone)]
|
|
struct CompoundBlock {
|
|
block: Block,
|
|
simple_blocks_subsets_of_self: RefCell<Vec<Rc<RefCell<SimpleBlock>>>>,
|
|
}
|
|
|
|
impl CompoundBlock {
|
|
fn add_simple_block(&self, fine_block: Rc<RefCell<SimpleBlock>>) {
|
|
self.simple_blocks_subsets_of_self
|
|
.borrow_mut()
|
|
.push(fine_block);
|
|
}
|
|
fn remove_simple_block(&self, fine_block: &Rc<RefCell<SimpleBlock>>) {
|
|
self.simple_blocks_subsets_of_self
|
|
.borrow_mut()
|
|
.retain(|x| !Rc::ptr_eq(x, fine_block));
|
|
}
|
|
fn simple_block_count(&self) -> usize {
|
|
self.simple_blocks_subsets_of_self.borrow().len()
|
|
}
|
|
}
|
|
|
|
struct BackEdgesGroup {
|
|
block: Rc<RefCell<SimpleBlock>>,
|
|
subblock: Block,
|
|
}
|
|
|
|
trait HasBlock {
|
|
fn block(&self) -> Block;
|
|
}
|
|
|
|
impl HasBlock for SimpleBlockPointer {
|
|
fn block(&self) -> Block {
|
|
(**self).borrow().block.clone()
|
|
}
|
|
}
|
|
|
|
impl HasBlock for CompoundBlock {
|
|
fn block(&self) -> Block {
|
|
self.block.clone()
|
|
}
|
|
}
|
|
|
|
#[allow(clippy::type_complexity)]
|
|
fn initialization<const N: usize, G>(
|
|
graphs: &[&G; N]
|
|
) -> ( (SimpleBlockPointer, SimpleBlockPointer),
|
|
CompoundPartition,
|
|
NodeToBlock,
|
|
MyNodeTranslator<G::NodeId, N> )
|
|
where
|
|
G: IntoNodeReferences + IntoNeighborsDirected,
|
|
G::NodeId: std::cmp::Eq + std::hash::Hash
|
|
{
|
|
// translate into unique ids
|
|
let mut convert_nodes: MyNodeTranslator<G::NodeId, N>
|
|
= Translator::new();
|
|
|
|
let graph_node_indices = {
|
|
let mut tmp: Block = vec![];
|
|
|
|
for (pos, graph) in graphs.iter().enumerate() {
|
|
tmp.extend(
|
|
graph.node_identifiers()
|
|
.map(|val| convert_nodes.encode((val, pos as u32)))
|
|
.collect::<Vec<_>>()
|
|
);
|
|
}
|
|
|
|
tmp
|
|
};
|
|
let compound_initial_block_pointer: Rc<CompoundBlock> = {
|
|
let compound_initial_block = CompoundBlock {
|
|
block: graph_node_indices.clone(),
|
|
simple_blocks_subsets_of_self: RefCell::new(vec![]),
|
|
};
|
|
|
|
Rc::new(compound_initial_block)
|
|
};
|
|
|
|
// minor optimization: split nodes between those that have outgoing edges
|
|
// and those that dont
|
|
let (leaf_node_block_pointer, non_leaf_node_block_pointer) = {
|
|
let (leaf_node_indices, non_leaf_node_indices): (Block, Block) =
|
|
graph_node_indices
|
|
.clone()
|
|
.into_iter()
|
|
.partition(
|
|
|x| {
|
|
let (node_id, graph_id) = convert_nodes.decode(x).unwrap();
|
|
graphs[*graph_id as usize]
|
|
.neighbors_directed(
|
|
*node_id,
|
|
Outgoing)
|
|
.count() == 0
|
|
}
|
|
);
|
|
|
|
let leaf_node_block = SimpleBlock {
|
|
block: leaf_node_indices,
|
|
|
|
coarse_block_that_supersets_self:
|
|
Rc::clone(&compound_initial_block_pointer),
|
|
};
|
|
let non_leaf_node_block = SimpleBlock {
|
|
block: non_leaf_node_indices,
|
|
|
|
coarse_block_that_supersets_self:
|
|
Rc::clone(&compound_initial_block_pointer),
|
|
};
|
|
|
|
(
|
|
Rc::new(RefCell::new(leaf_node_block)),
|
|
Rc::new(RefCell::new(non_leaf_node_block)),
|
|
)
|
|
};
|
|
|
|
compound_initial_block_pointer
|
|
.simple_blocks_subsets_of_self
|
|
.borrow_mut()
|
|
.extend([
|
|
Rc::clone(&leaf_node_block_pointer),
|
|
Rc::clone(&non_leaf_node_block_pointer),
|
|
]);
|
|
|
|
let node_to_block = {
|
|
let mut node_to_block = HashMap::new();
|
|
|
|
(*non_leaf_node_block_pointer)
|
|
.borrow()
|
|
.block
|
|
.iter()
|
|
.copied()
|
|
.for_each(
|
|
|value|
|
|
{ node_to_block.insert(value,
|
|
Rc::clone(&non_leaf_node_block_pointer));
|
|
}
|
|
);
|
|
|
|
(*leaf_node_block_pointer)
|
|
.borrow()
|
|
.block
|
|
.iter()
|
|
.copied()
|
|
.for_each(
|
|
|value|
|
|
{ node_to_block.insert(value,
|
|
Rc::clone(&leaf_node_block_pointer));
|
|
}
|
|
);
|
|
node_to_block
|
|
};
|
|
|
|
(
|
|
(leaf_node_block_pointer, non_leaf_node_block_pointer),
|
|
vec![compound_initial_block_pointer],
|
|
node_to_block,
|
|
convert_nodes
|
|
)
|
|
}
|
|
|
|
fn build_backedges<IndexHolder: HasBlock, const N:usize, G>(
|
|
graphs: &[&G; N],
|
|
block: IndexHolder,
|
|
convert_nodes: &MyNodeTranslator<G::NodeId, N>
|
|
) -> BackEdges
|
|
where
|
|
G: IntoNeighborsDirected,
|
|
G::NodeId: std::cmp::Eq + std::hash::Hash
|
|
{
|
|
let mut backedges = HashMap::new();
|
|
|
|
block.block().iter().for_each(|node_index_pointer| {
|
|
backedges.insert(
|
|
*node_index_pointer,
|
|
{
|
|
let (node_id, graph_id) =
|
|
convert_nodes.decode(node_index_pointer).unwrap();
|
|
graphs[*graph_id as usize]
|
|
.neighbors_directed(
|
|
*node_id,
|
|
Incoming)
|
|
.collect::<HashSet<_>>()
|
|
.into_iter()
|
|
// the back edges should be all in the same graph
|
|
.map(|e| convert_nodes.get(&(e, *graph_id)).unwrap())
|
|
.copied()
|
|
.collect::<Vec<_>>()
|
|
}
|
|
);
|
|
});
|
|
|
|
backedges
|
|
}
|
|
|
|
fn group_by_backedges(
|
|
backedges: BackEdges,
|
|
node_to_block: &NodeToBlock,
|
|
) -> BackEdgesGrouped {
|
|
let mut backedges_grouped: BackEdgesGrouped = HashMap::new();
|
|
|
|
for incoming_neighbor_group in backedges.values() {
|
|
for node in incoming_neighbor_group {
|
|
let block = Rc::clone(node_to_block.get(node).unwrap());
|
|
let key = (*block).borrow().block.clone();
|
|
|
|
match backedges_grouped.entry(key) {
|
|
Entry::Occupied(mut entry) =>
|
|
entry.get_mut().subblock.push(*node),
|
|
Entry::Vacant(entry) => {
|
|
entry.insert(BackEdgesGroup {
|
|
block: Rc::clone(&block),
|
|
subblock: Vec::from([*node]),
|
|
});
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
backedges_grouped
|
|
}
|
|
|
|
fn split_blocks_with_grouped_backedges(
|
|
mut backedges_grouped: BackEdgesGrouped,
|
|
node_to_block: &mut NodeToBlock,
|
|
) -> (
|
|
(Vec<SimpleBlockPointer>, Vec<SimpleBlockPointer>),
|
|
Vec<CompoundBlockPointer>,
|
|
) {
|
|
let mut all_new_simple_blocks: Vec<Rc<RefCell<SimpleBlock>>> = vec![];
|
|
let mut all_removed_simple_blocks: Vec<Rc<RefCell<SimpleBlock>>> = vec![];
|
|
let mut new_compound_blocks: Vec<Rc<CompoundBlock>> = vec![];
|
|
|
|
for (block, back_edges_group) in backedges_grouped.iter_mut() {
|
|
let borrowed_compound_block = Rc::clone(
|
|
&(*back_edges_group.block)
|
|
.borrow()
|
|
.coarse_block_that_supersets_self,
|
|
);
|
|
|
|
let proper_subblock = {
|
|
let simple_block = SimpleBlock {
|
|
block: back_edges_group.subblock.clone(),
|
|
|
|
coarse_block_that_supersets_self:
|
|
Rc::clone(&borrowed_compound_block),
|
|
};
|
|
|
|
Rc::new(RefCell::new(simple_block))
|
|
};
|
|
let prior_count = borrowed_compound_block.simple_block_count();
|
|
borrowed_compound_block.add_simple_block(Rc::clone(&proper_subblock));
|
|
|
|
if prior_count == 1 {
|
|
new_compound_blocks.push(Rc::clone(&borrowed_compound_block));
|
|
}
|
|
|
|
for node in back_edges_group.subblock.iter() {
|
|
node_to_block.insert(*node, Rc::clone(&proper_subblock));
|
|
}
|
|
|
|
// subtract subblock from block
|
|
(*back_edges_group.block).borrow_mut().block =
|
|
block
|
|
.iter()
|
|
.filter(|x| !(*proper_subblock).borrow().block.contains(x))
|
|
.copied()
|
|
.collect();
|
|
|
|
if (*back_edges_group.block).borrow().block.is_empty() {
|
|
borrowed_compound_block
|
|
.remove_simple_block(&back_edges_group.block);
|
|
all_removed_simple_blocks.push(Rc::clone(&back_edges_group.block));
|
|
}
|
|
all_new_simple_blocks.push(Rc::clone(&proper_subblock));
|
|
}
|
|
(
|
|
(all_new_simple_blocks, all_removed_simple_blocks),
|
|
new_compound_blocks,
|
|
)
|
|
}
|
|
|
|
fn maximum_bisimulation<const N: usize, G>(
|
|
graphs: &[&G; N]
|
|
) -> (Option<Vec<Block>>, MyNodeTranslator<G::NodeId, N>)
|
|
where
|
|
G: IntoNodeReferences + IntoNeighborsDirected,
|
|
G::NodeId: std::cmp::Eq + std::hash::Hash
|
|
{
|
|
let ((simple_block_0, simple_block_1),
|
|
initial_compound_partition,
|
|
mut node_to_block,
|
|
converter) = initialization(graphs);
|
|
|
|
let mut queue: CompoundPartition = initial_compound_partition;
|
|
let mut all_simple_blocks = vec![simple_block_0, simple_block_1];
|
|
|
|
loop {
|
|
let (smaller_component, simple_splitter_block) = {
|
|
let splitter_block = match queue.pop() {
|
|
Some(coarse_block) => coarse_block,
|
|
None => break,
|
|
};
|
|
let mut simple_blocks_in_splitter_block = splitter_block
|
|
.simple_blocks_subsets_of_self
|
|
.borrow()
|
|
.clone();
|
|
|
|
let smaller_component_index = {
|
|
match simple_blocks_in_splitter_block
|
|
.iter()
|
|
.enumerate()
|
|
.min_by(|(_, x), (_, y)| {
|
|
(***x)
|
|
.borrow()
|
|
.block
|
|
.len()
|
|
.cmp(&(***y).borrow().block.len())
|
|
})
|
|
.map(|(index, _)| index) {
|
|
Some(v) => v,
|
|
None => {return (None, converter)}
|
|
}
|
|
};
|
|
|
|
let smaller_component =
|
|
simple_blocks_in_splitter_block.remove(smaller_component_index);
|
|
|
|
let simple_splitter_block_values: Block = splitter_block
|
|
.block
|
|
.clone()
|
|
.iter()
|
|
.filter(|x| !(*smaller_component).borrow().block.contains(x))
|
|
.copied()
|
|
.collect();
|
|
|
|
let simple_splitter_block = CompoundBlock {
|
|
block: simple_splitter_block_values,
|
|
|
|
simple_blocks_subsets_of_self:
|
|
RefCell::new(simple_blocks_in_splitter_block),
|
|
};
|
|
let simple_splitter_block_pointer = Rc::new(simple_splitter_block);
|
|
|
|
if simple_splitter_block_pointer
|
|
.simple_blocks_subsets_of_self
|
|
.borrow()
|
|
.len()
|
|
> 1
|
|
{
|
|
queue.push(Rc::clone(&simple_splitter_block_pointer));
|
|
}
|
|
|
|
(smaller_component, simple_splitter_block_pointer)
|
|
};
|
|
simple_splitter_block
|
|
.simple_blocks_subsets_of_self
|
|
.borrow()
|
|
.iter()
|
|
.for_each(|x| {
|
|
(*x).borrow_mut().coarse_block_that_supersets_self =
|
|
Rc::clone(&simple_splitter_block);
|
|
});
|
|
|
|
let mut back_edges =
|
|
build_backedges(graphs, smaller_component, &converter);
|
|
|
|
let back_edges_group =
|
|
group_by_backedges(back_edges.clone(), &node_to_block);
|
|
let ((new_simple_blocks, removeable_simple_blocks),
|
|
compound_block_that_are_now_compound) =
|
|
split_blocks_with_grouped_backedges(back_edges_group,
|
|
&mut node_to_block);
|
|
|
|
all_simple_blocks.extend(new_simple_blocks);
|
|
all_simple_blocks.retain(
|
|
|x| !removeable_simple_blocks.iter().any(|y| Rc::ptr_eq(x, y)) );
|
|
queue.extend(compound_block_that_are_now_compound);
|
|
|
|
// back edges = E^{-1}(B) - E^{-1}(S-B)
|
|
{
|
|
let back_edges_splitter_complement =
|
|
build_backedges(graphs,
|
|
(*simple_splitter_block).clone(),
|
|
&converter);
|
|
|
|
back_edges_splitter_complement.keys().for_each(|node| {
|
|
back_edges.remove(node);
|
|
});
|
|
}
|
|
|
|
let back_edges_group = group_by_backedges(back_edges, &node_to_block);
|
|
let ((new_fine_blocks, removeable_fine_blocks),
|
|
coarse_block_that_are_now_compound) =
|
|
split_blocks_with_grouped_backedges(back_edges_group,
|
|
&mut node_to_block);
|
|
|
|
all_simple_blocks.extend(new_fine_blocks);
|
|
all_simple_blocks.retain(
|
|
|x| !removeable_fine_blocks.iter().any(|y| Rc::ptr_eq(x, y)) );
|
|
queue.extend(coarse_block_that_are_now_compound);
|
|
}
|
|
|
|
(Some(
|
|
all_simple_blocks
|
|
.iter()
|
|
.map(|x| (**x).borrow().block.clone())
|
|
// remove leaf block when there are no leaves
|
|
.filter(|x| !x.is_empty())
|
|
.collect(),
|
|
), converter)
|
|
}
|
|
|
|
/// Creates a new graph with nodes as signifiers instead of different weights on
|
|
/// the edges.
|
|
fn create_modified_graph<G>(
|
|
graph: &G,
|
|
converter_edges: &MyEdgeTranslator<G::EdgeWeight>
|
|
) -> (petgraph::Graph<u32, u32>, HashSet<u32>)
|
|
where
|
|
G: NodeCount + EdgeCount + IntoEdgeReferences + IntoNodeIdentifiers,
|
|
G::NodeId: std::cmp::Eq + std::hash::Hash,
|
|
G::EdgeWeight: std::cmp::Eq + std::hash::Hash + Clone
|
|
{
|
|
let mut new_graph_a: petgraph::Graph<_, u32> =
|
|
petgraph::Graph::with_capacity(graph.node_count()*4,
|
|
graph.edge_count()*4);
|
|
let mut association_weight_id = HashMap::new();
|
|
let mut original_nodes = HashSet::new();
|
|
let mut last_id = 0;
|
|
|
|
for edge in graph.edge_references() {
|
|
let source_id =
|
|
match association_weight_id.get(&edge.source()) {
|
|
Some(id) => *id,
|
|
None => {
|
|
let id = new_graph_a.add_node(last_id);
|
|
original_nodes.insert(last_id);
|
|
last_id += 1;
|
|
association_weight_id.insert(edge.source(), id);
|
|
id
|
|
}
|
|
};
|
|
let target_id =
|
|
match association_weight_id.get(&edge.target()) {
|
|
Some(id) => *id,
|
|
None => {
|
|
let id = new_graph_a.add_node(last_id);
|
|
original_nodes.insert(last_id);
|
|
last_id += 1;
|
|
association_weight_id.insert(edge.target(), id);
|
|
id
|
|
}
|
|
};
|
|
let weight = *converter_edges.get(edge.weight()).unwrap();
|
|
|
|
let middle_node_id = new_graph_a.add_node(0);
|
|
|
|
new_graph_a.add_edge(source_id, middle_node_id, weight);
|
|
new_graph_a.add_edge(middle_node_id, target_id, weight);
|
|
|
|
|
|
let mut previous = middle_node_id;
|
|
for _ in 0..weight {
|
|
let path = new_graph_a.add_node(0);
|
|
new_graph_a.add_edge(previous, path, weight);
|
|
previous = path;
|
|
}
|
|
}
|
|
|
|
for node in graph.node_identifiers() {
|
|
let mut previous = *association_weight_id.get(&node).unwrap();
|
|
for _ in 0..converter_edges.last_id.last_ids+2 {
|
|
let path = new_graph_a.add_node(0);
|
|
new_graph_a.add_edge(previous, path, 0);
|
|
previous = path;
|
|
}
|
|
}
|
|
|
|
(new_graph_a, original_nodes)
|
|
}
|
|
|
|
#[allow(clippy::type_complexity)]
|
|
fn modify_graph<G>(
|
|
graph_a: &G,
|
|
graph_b: &G
|
|
) -> ( (petgraph::Graph<u32, u32>, HashSet<u32>),
|
|
(petgraph::Graph<u32, u32>, HashSet<u32>), )
|
|
where
|
|
G: IntoNodeReferences + IntoNeighborsDirected + NodeCount + EdgeCount,
|
|
G: IntoEdgeReferences,
|
|
G::NodeId: std::cmp::Eq + std::hash::Hash,
|
|
G::EdgeWeight: std::cmp::Eq + std::hash::Hash + Clone,
|
|
{
|
|
let converter_edges: MyEdgeTranslator<G::EdgeWeight> = {
|
|
let mut converter_edges = Translator::new();
|
|
let mut labels: HashMap<G::EdgeWeight, u32> = HashMap::new();
|
|
|
|
for edge in graph_a.edge_references() {
|
|
*labels.entry(edge.weight().clone()).or_default() += 1;
|
|
}
|
|
for edge in graph_b.edge_references() {
|
|
*labels.entry(edge.weight().clone()).or_default() += 1;
|
|
}
|
|
// slight optimization: we reorder the edges such that edges with the
|
|
// most occurrences have smaller index
|
|
let mut labels: Vec<(G::EdgeWeight, u32)> =
|
|
labels.into_iter().collect();
|
|
labels.sort_by(|a, b| b.1.cmp(&a.1));
|
|
|
|
for (label, _) in labels.into_iter() {
|
|
let _ = converter_edges.encode(label);
|
|
}
|
|
converter_edges
|
|
};
|
|
|
|
let new_graph_a = create_modified_graph(graph_a, &converter_edges);
|
|
let new_graph_b = create_modified_graph(graph_b, &converter_edges);
|
|
|
|
(new_graph_a, new_graph_b)
|
|
}
|
|
|
|
|
|
/// check if every block contains either no original nodes or nodes from both
|
|
/// graphs
|
|
fn check_bisimilarity<G>(
|
|
val: Vec<Vec<NodeType>>,
|
|
converter_bisimulated_graph:
|
|
&MyNodeTranslator<<petgraph::Graph<u32, u32> as GraphBase>::NodeId, 2>,
|
|
original_nodes: [HashSet<u32>; 2]
|
|
) -> bool
|
|
where
|
|
G: IntoEdgeReferences,
|
|
G::EdgeWeight: std::cmp::Eq + std::hash::Hash + Clone,
|
|
{
|
|
val.into_iter()
|
|
.all(
|
|
|el| {
|
|
let mut keep_track = [false, false];
|
|
for e in el {
|
|
let (_node_id, graph_id) =
|
|
converter_bisimulated_graph.decode(&e).unwrap();
|
|
if original_nodes[*graph_id as usize].contains(&e.0) {
|
|
keep_track[*graph_id as usize] = true;
|
|
}
|
|
}
|
|
!(keep_track[0] ^ keep_track[1])
|
|
}
|
|
)
|
|
}
|
|
|
|
// -----------------------------------------------------------------------------
|
|
|
|
pub fn bisimilarity_paige_tarjan<G>(
|
|
graph_a: &G,
|
|
graph_b: &G
|
|
) -> bool
|
|
where
|
|
G: IntoNodeReferences + IntoNeighborsDirected + NodeCount + EdgeCount,
|
|
G: IntoEdgeReferences,
|
|
G::NodeId: std::cmp::Eq + std::hash::Hash,
|
|
G::EdgeWeight: std::cmp::Eq + std::hash::Hash + Clone,
|
|
{
|
|
if graph_a.node_count() == 0 && graph_b.node_count() == 0 {
|
|
return true
|
|
}
|
|
if graph_a.node_count() == 0 || graph_b.node_count() == 0 {
|
|
return false
|
|
}
|
|
|
|
let ((new_graph_a, original_nodes_a), (new_graph_b, original_nodes_b)) =
|
|
modify_graph(graph_a, graph_b);
|
|
|
|
let (result, _converter) =
|
|
match maximum_bisimulation(&[&&new_graph_a, &&new_graph_b]) {
|
|
(None, _) => { return false },
|
|
(Some(val), converter) => {
|
|
(check_bisimilarity::<G>(val,
|
|
&converter,
|
|
[original_nodes_a, original_nodes_b]),
|
|
converter)
|
|
|
|
}
|
|
};
|
|
|
|
result
|
|
}
|
|
|
|
pub fn bisimilarity_paige_tarjan_ignore_labels<G>(
|
|
graph_a: &G,
|
|
graph_b: &G
|
|
) -> bool
|
|
where
|
|
G: IntoNodeReferences + IntoNeighborsDirected + NodeCount,
|
|
G::NodeId: std::cmp::Eq + std::hash::Hash
|
|
{
|
|
if graph_a.node_count() == 0 && graph_b.node_count() == 0 {
|
|
return true
|
|
}
|
|
if graph_a.node_count() == 0 || graph_b.node_count() == 0 {
|
|
return false
|
|
}
|
|
|
|
let (result, _converter) =
|
|
match maximum_bisimulation(&[graph_a, graph_b]) {
|
|
(None, _) => { return false },
|
|
(Some(val), converter) => {
|
|
(val.into_iter()
|
|
.find(
|
|
|el| {
|
|
let mut keep_track = [false, false];
|
|
for e in el {
|
|
let (_node_id, graph_id) =
|
|
converter.decode(e).unwrap();
|
|
keep_track[*graph_id as usize] = true;
|
|
}
|
|
!keep_track[0] || !keep_track[1]
|
|
}
|
|
), converter)
|
|
|
|
}
|
|
};
|
|
|
|
result.is_none()
|
|
}
|
|
|
|
|
|
#[test]
|
|
fn identity_paige_tarjan() {
|
|
use petgraph::Graph;
|
|
let mut graph_a = Graph::new();
|
|
|
|
let node_a_1 = graph_a.add_node(1);
|
|
let node_a_2 = graph_a.add_node(2);
|
|
graph_a.add_edge(node_a_1, node_a_2, 1);
|
|
|
|
assert!(bisimilarity_paige_tarjan(&&graph_a, &&graph_a));
|
|
assert!(bisimilarity_paige_tarjan_ignore_labels(&&graph_a, &&graph_a))
|
|
}
|
|
|
|
#[test]
|
|
fn identity_paige_tarjan_2() {
|
|
use petgraph::Graph;
|
|
let mut graph_a = Graph::new();
|
|
|
|
let node_a_1 = graph_a.add_node(1);
|
|
let node_a_2 = graph_a.add_node(2);
|
|
graph_a.add_edge(node_a_1, node_a_2, 1);
|
|
let node_a_3 = graph_a.add_node(3);
|
|
graph_a.add_edge(node_a_1, node_a_3, 1);
|
|
let node_a_6 = graph_a.add_node(6);
|
|
graph_a.add_edge(node_a_2, node_a_6, 2);
|
|
let node_a_4 = graph_a.add_node(4);
|
|
graph_a.add_edge(node_a_3, node_a_4, 2);
|
|
let node_a_7 = graph_a.add_node(7);
|
|
graph_a.add_edge(node_a_6, node_a_7, 2);
|
|
let node_a_5 = graph_a.add_node(5);
|
|
graph_a.add_edge(node_a_4, node_a_5, 2);
|
|
let node_a_8 = graph_a.add_node(8);
|
|
graph_a.add_edge(node_a_7, node_a_8, 3);
|
|
graph_a.add_edge(node_a_8, node_a_7, 3);
|
|
graph_a.add_edge(node_a_8, node_a_8, 3);
|
|
|
|
assert!(bisimilarity_paige_tarjan(&&graph_a, &&graph_a));
|
|
assert!(bisimilarity_paige_tarjan_ignore_labels(&&graph_a, &&graph_a))
|
|
}
|
|
|
|
#[test]
|
|
fn identity_different_weights_paige_tarjan() {
|
|
use petgraph::Graph;
|
|
let mut graph_a = Graph::new();
|
|
|
|
let node_a_1 = graph_a.add_node(1);
|
|
let node_a_2 = graph_a.add_node(2);
|
|
graph_a.add_edge(node_a_1, node_a_2, 1);
|
|
|
|
let mut graph_b = Graph::new();
|
|
|
|
let node_b_1 = graph_b.add_node(1);
|
|
let node_b_2 = graph_b.add_node(2);
|
|
graph_b.add_edge(node_b_1, node_b_2, 2);
|
|
|
|
assert!(!bisimilarity_paige_tarjan(&&graph_a, &&graph_b));
|
|
assert!(bisimilarity_paige_tarjan_ignore_labels(&&graph_a, &&graph_b))
|
|
}
|
|
|
|
#[test]
|
|
fn not_bisimilar_paige_tarjan() {
|
|
use petgraph::Graph;
|
|
let mut graph_a = Graph::new();
|
|
|
|
let node_a_1 = graph_a.add_node(1);
|
|
let node_a_2 = graph_a.add_node(2);
|
|
graph_a.add_edge(node_a_1, node_a_2, 1);
|
|
|
|
let mut graph_b = Graph::new();
|
|
|
|
let node_b_1 = graph_b.add_node(1);
|
|
let node_b_2 = graph_b.add_node(2);
|
|
graph_b.add_edge(node_b_1, node_b_2, 1);
|
|
let node_b_3 = graph_b.add_node(3);
|
|
graph_b.add_edge(node_b_1, node_b_3, 2);
|
|
|
|
assert!(!bisimilarity_paige_tarjan(&&graph_a, &&graph_b));
|
|
assert!(bisimilarity_paige_tarjan_ignore_labels(&&graph_a, &&graph_b))
|
|
}
|
|
|
|
#[test]
|
|
fn not_bisimilar_paige_tarjan_2() {
|
|
use petgraph::Graph;
|
|
let mut graph_a = Graph::new();
|
|
|
|
let node_a_1 = graph_a.add_node(1);
|
|
let node_a_2 = graph_a.add_node(2);
|
|
graph_a.add_edge(node_a_1, node_a_2, 1);
|
|
let node_a_3 = graph_a.add_node(3);
|
|
graph_a.add_edge(node_a_1, node_a_3, 1);
|
|
let node_a_6 = graph_a.add_node(6);
|
|
graph_a.add_edge(node_a_2, node_a_6, 2);
|
|
let node_a_4 = graph_a.add_node(4);
|
|
graph_a.add_edge(node_a_3, node_a_4, 2);
|
|
let node_a_7 = graph_a.add_node(7);
|
|
graph_a.add_edge(node_a_6, node_a_7, 2);
|
|
let node_a_5 = graph_a.add_node(5);
|
|
graph_a.add_edge(node_a_4, node_a_5, 2);
|
|
let node_a_8 = graph_a.add_node(8);
|
|
graph_a.add_edge(node_a_7, node_a_8, 3);
|
|
graph_a.add_edge(node_a_8, node_a_7, 3);
|
|
graph_a.add_edge(node_a_8, node_a_8, 3);
|
|
|
|
let mut graph_b = Graph::new();
|
|
|
|
let node_b_1 = graph_b.add_node(1);
|
|
let node_b_2 = graph_b.add_node(2);
|
|
graph_b.add_edge(node_b_1, node_b_2, 1);
|
|
let node_b_3 = graph_b.add_node(3);
|
|
graph_b.add_edge(node_b_2, node_b_3, 2);
|
|
let node_b_4 = graph_b.add_node(4);
|
|
graph_b.add_edge(node_b_3, node_b_4, 2);
|
|
|
|
assert!(!bisimilarity_paige_tarjan(&&graph_a, &&graph_b));
|
|
assert!(!bisimilarity_paige_tarjan_ignore_labels(&&graph_a, &&graph_b))
|
|
}
|
|
|
|
#[test]
|
|
fn not_bisimilar_paige_tarjan_3() {
|
|
use petgraph::Graph;
|
|
let mut graph_b = Graph::new();
|
|
|
|
let node_b_1 = graph_b.add_node(1);
|
|
let node_b_2 = graph_b.add_node(2);
|
|
graph_b.add_edge(node_b_1, node_b_2, 1);
|
|
let node_b_3 = graph_b.add_node(3);
|
|
graph_b.add_edge(node_b_2, node_b_3, 2);
|
|
let node_b_4 = graph_b.add_node(4);
|
|
graph_b.add_edge(node_b_3, node_b_4, 2);
|
|
|
|
let mut graph_c = Graph::new();
|
|
|
|
let node_c_1 = graph_c.add_node(1);
|
|
let node_c_2 = graph_c.add_node(2);
|
|
graph_c.add_edge(node_c_1, node_c_2, 1);
|
|
let node_c_3 = graph_c.add_node(3);
|
|
graph_c.add_edge(node_c_1, node_c_3, 2);
|
|
graph_c.add_edge(node_c_2, node_c_3, 2);
|
|
|
|
assert!(!bisimilarity_paige_tarjan(&&graph_b, &&graph_c));
|
|
assert!(!bisimilarity_paige_tarjan_ignore_labels(&&graph_b, &&graph_c))
|
|
}
|
|
|
|
#[test]
|
|
fn bisimilar_paige_tarjan() {
|
|
use petgraph::Graph;
|
|
let mut graph_b = Graph::new();
|
|
|
|
let node_b_1 = graph_b.add_node(1);
|
|
let node_b_2 = graph_b.add_node(2);
|
|
graph_b.add_edge(node_b_1, node_b_2, 1);
|
|
let node_b_3 = graph_b.add_node(3);
|
|
graph_b.add_edge(node_b_2, node_b_3, 2);
|
|
let node_b_4 = graph_b.add_node(4);
|
|
graph_b.add_edge(node_b_3, node_b_4, 2);
|
|
|
|
let mut graph_c = Graph::new();
|
|
|
|
let node_c_1 = graph_c.add_node(1);
|
|
let node_c_2 = graph_c.add_node(2);
|
|
graph_c.add_edge(node_c_1, node_c_2, 1);
|
|
let node_c_3 = graph_c.add_node(3);
|
|
graph_c.add_edge(node_c_2, node_c_3, 2);
|
|
let node_c_4 = graph_c.add_node(4);
|
|
graph_c.add_edge(node_c_3, node_c_4, 2);
|
|
let node_c_5 = graph_c.add_node(5);
|
|
graph_c.add_edge(node_c_1, node_c_5, 1);
|
|
let node_c_6 = graph_c.add_node(6);
|
|
graph_c.add_edge(node_c_5, node_c_6, 2);
|
|
let node_c_7 = graph_c.add_node(7);
|
|
graph_c.add_edge(node_c_6, node_c_7, 2);
|
|
|
|
assert!(bisimilarity_paige_tarjan(&&graph_b, &&graph_c));
|
|
assert!(bisimilarity_paige_tarjan_ignore_labels(&&graph_b, &&graph_c))
|
|
}
|
|
|
|
#[test]
|
|
fn bisimilar_paige_tarjan_2() {
|
|
use petgraph::Graph;
|
|
let mut graph_a = Graph::new();
|
|
|
|
let node_a_1 = graph_a.add_node(1);
|
|
let node_a_2 = graph_a.add_node(2);
|
|
graph_a.add_edge(node_a_1, node_a_2, 1);
|
|
let node_a_3 = graph_a.add_node(3);
|
|
graph_a.add_edge(node_a_1, node_a_3, 1);
|
|
graph_a.add_edge(node_a_2, node_a_3, 2);
|
|
graph_a.add_edge(node_a_3, node_a_3, 2);
|
|
|
|
let mut graph_b = Graph::new();
|
|
|
|
let node_b_1 = graph_b.add_node(1);
|
|
let node_b_2 = graph_b.add_node(2);
|
|
graph_b.add_edge(node_b_1, node_b_2, 1);
|
|
graph_b.add_edge(node_b_2, node_b_2, 2);
|
|
|
|
assert!(bisimilarity_paige_tarjan(&&graph_a, &&graph_b));
|
|
assert!(bisimilarity_paige_tarjan_ignore_labels(&&graph_a, &&graph_b))
|
|
}
|