Bisimilarity by Paige and Tarjan
This commit is contained in:
elvis
@ -1,10 +1,10 @@
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use std::collections::{BTreeSet, HashMap};
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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::{ EdgeRef,
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use petgraph::visit::{ EdgeRef, GraphBase, IntoEdgeReferences, IntoEdges, IntoNeighborsDirected, IntoNodeReferences, NodeCount };
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GraphBase,
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use petgraph::Direction::{Incoming, Outgoing};
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IntoEdgeReferences,
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IntoEdges,
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IntoNodeReferences };
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// -----------------------------------------------------------------------------
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// -----------------------------------------------------------------------------
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// Helper Functions
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// Helper Functions
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@ -13,20 +13,20 @@ use petgraph::visit::{ EdgeRef,
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#[inline(always)]
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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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fn equal_vectors<T>(a: &Vec<T>, b: &Vec<T>) -> bool
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where
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where
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T: PartialEq
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T: PartialEq
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{
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{
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for el in a {
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for el in a {
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if !b.contains(el) {
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if !b.contains(el) {
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return false;
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return false;
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}
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}
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}
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}
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for el in b {
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for el in b {
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if !a.contains(el) {
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if !a.contains(el) {
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return false;
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return false;
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}
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}
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}
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}
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true
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true
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}
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}
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@ -34,161 +34,707 @@ where
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// Bisimilarity
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// Bisimilarity
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// -----------------------------------------------------------------------------
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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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struct GraphPartition<'a, G>
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where
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where
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G: GraphBase,
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G: GraphBase,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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{
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{
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pub node_to_block: HashMap<(usize, G::NodeId), u32>,
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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 block_to_node: HashMap<u32, Vec<(usize, G::NodeId)>>,
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pub graphs: [&'a G; 2],
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pub graphs: [&'a G; 2],
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last_block: u32,
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last_block: u32,
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blocks: BTreeSet<u32>
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blocks: BTreeSet<u32>
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}
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}
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impl<'a, G> GraphPartition<'a, G>
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impl<'a, G> GraphPartition<'a, G>
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where
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where
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G: GraphBase,
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G: GraphBase,
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G::NodeId: std::cmp::Eq + std::hash::Hash
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G::NodeId: std::cmp::Eq + std::hash::Hash
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{
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{
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pub fn new(graph_a: &'a G, graph_b: &'a G) -> Self {
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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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GraphPartition { node_to_block: HashMap::new(),
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block_to_node: HashMap::new(),
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block_to_node: HashMap::new(),
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graphs: [graph_a, graph_b],
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graphs: [graph_a, graph_b],
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last_block: 0,
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last_block: 0,
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blocks: BTreeSet::new() }
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blocks: BTreeSet::new() }
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}
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}
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#[inline(always)]
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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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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.node_to_block.insert((graph, node), self.last_block);
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self.block_to_node
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self.block_to_node
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.entry(self.last_block)
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.entry(self.last_block)
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.or_default()
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.or_default()
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.push((graph, node));
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.push((graph, node));
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self.blocks.insert(self.last_block);
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self.blocks.insert(self.last_block);
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}
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}
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#[inline(always)]
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#[inline(always)]
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pub fn iterate_blocks(&self) -> Vec<u32> {
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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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self.blocks.iter().cloned().collect::<Vec<_>>()
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}
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}
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pub fn bisimilar(&self) -> bool {
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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 are
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// if there is a block that has only elements from one graph then they
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// not bisimilar
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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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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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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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if node_list.iter().all(|el| el.0 == graph_id) {
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return false;
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return false;
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}
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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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true
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}
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}
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}
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impl<'a, G> GraphPartition<'a, G>
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impl<'a, G> GraphPartition<'a, G>
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where
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where
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G: IntoEdges,
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G: IntoEdges,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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{
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{
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fn reachable_blocks(
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fn reachable_blocks(
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&self,
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&self,
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label: &G::EdgeRef,
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label: &G::EdgeRef,
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s: &(usize, G::NodeId)
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s: &(usize, G::NodeId)
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) -> Vec<u32>
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) -> Vec<u32>
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where <G as IntoEdgeReferences>::EdgeRef: PartialEq
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where <G as IntoEdgeReferences>::EdgeRef: PartialEq
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{
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{
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let mut val = vec![];
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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 == label) {
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for el in self.graphs[s.0].edges(s.1).filter(|x| x == label) {
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let tmp = (s.0, el.target());
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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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val.push(*self.node_to_block.get(&tmp).unwrap());
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}
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}
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val
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val
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}
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pub fn split(&mut self, block: u32, label: &G::EdgeRef) -> bool
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where <G as IntoEdgeReferences>::EdgeRef: 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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}
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if b2.is_empty() {
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pub fn split(&mut self, block: u32, label: &G::EdgeRef) -> bool
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// all elements go to the same block with label label, so no change
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where <G as IntoEdgeReferences>::EdgeRef: PartialEq
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false
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{
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} else {
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let Some(nodes) = self.block_to_node.get(&block)
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// some elements need to be split into a different block
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else {
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self.last_block += 1;
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return true
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let new_block = self.last_block;
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};
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self.blocks.insert(new_block);
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let mut nodes = nodes.iter();
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let s = nodes.next().unwrap();
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for b in b2 {
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let mut b1 = vec![s];
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self.node_to_block.entry(b).and_modify(|e| *e = new_block);
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let mut b2 = vec![];
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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 reachable_blocks_s = self.reachable_blocks(label, s);
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let index = e.iter().position(|x| *x == b).unwrap();
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e.remove(index);
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for t in nodes {
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});
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let reachable_blocks_t = self.reachable_blocks(label, t);
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}
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if equal_vectors(&reachable_blocks_s, &reachable_blocks_t) {
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true
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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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}
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}
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}
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pub fn bisimilarity_kanellakis_smolka<'a, G>(
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pub fn bisimilarity_kanellakis_smolka<'a, G>(
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graph_a: &'a G,
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graph_a: &'a G,
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graph_b: &'a G
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graph_b: &'a G
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) -> bool
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) -> bool
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where
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where
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G: IntoNodeReferences + IntoEdges,
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G: IntoNodeReferences + IntoEdges,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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G::NodeId: std::cmp::Eq + std::hash::Hash,
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G::EdgeRef: PartialEq
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G::EdgeRef: PartialEq
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{
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{
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let graphs = [graph_a, graph_b];
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let graphs = [graph_a, graph_b];
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let mut partition: GraphPartition<G> = GraphPartition::new(graph_a, graph_b);
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let mut partition: GraphPartition<G> =
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for (p, graph) in graphs.iter().enumerate() {
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GraphPartition::new(graph_a, graph_b);
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for node in graph.node_identifiers() {
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for (p, graph) in graphs.iter().enumerate() {
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partition.add_node_last_partition(node, p);
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for node in graph.node_identifiers() {
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}
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partition.add_node_last_partition(node, p);
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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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.collect::<Vec<_>>();
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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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}
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}
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partition.bisimilar()
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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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.collect::<Vec<_>>();
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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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// -----------------------------------------------------------------------------
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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 NodeTrait {
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fn graph(&self) -> GraphIdType;
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}
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impl NodeTrait for NodeType {
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fn graph(&self) -> GraphIdType {
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self.0
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|
}
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}
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|
trait NextId<T> {
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fn next_id_of_graph(&mut self, graph_id: GraphIdType) -> T;
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}
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|
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|
struct Translator<From, To, State>
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|
where
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|
State: NextId<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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|
}
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|
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||||||
|
impl<From, To, State> Translator<From, To, State>
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||||||
|
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,
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|
State: NextId<To>
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|
{
|
||||||
|
pub fn new() -> Self
|
||||||
|
where
|
||||||
|
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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|
|
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|
pub fn encode(&mut self, val: From, graph_id: GraphIdType) -> To
|
||||||
|
{
|
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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(graph_id)
|
||||||
|
));
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|
self.reverse_data.insert(id, val);
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|
id
|
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|
}
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|
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|
pub fn get(&self, val: &From) -> Option<&To>
|
||||||
|
{
|
||||||
|
self.data.get(val)
|
||||||
|
}
|
||||||
|
|
||||||
|
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)]
|
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|
struct NodeState<const N: usize> {
|
||||||
|
last_ids: [u32; N],
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<const N: usize> NodeState<N> {
|
||||||
|
fn new() -> Self {
|
||||||
|
NodeState { last_ids: [0; N] }
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<const N: usize> Default for NodeState<N> {
|
||||||
|
fn default() -> Self {
|
||||||
|
Self::new()
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<const N: usize> NextId<NodeType> for NodeState<N> {
|
||||||
|
fn next_id_of_graph(&mut self, graph_id: u32) -> NodeType {
|
||||||
|
let graph_id_usize = graph_id as usize;
|
||||||
|
if graph_id_usize > self.last_ids.len() {
|
||||||
|
panic!()
|
||||||
|
}
|
||||||
|
self.last_ids[graph_id_usize] += 1;
|
||||||
|
(graph_id, self.last_ids[graph_id_usize])
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
type Block = Vec<NodeType>;
|
||||||
|
type CounterImage = HashMap<NodeType, Vec<NodeType>>;
|
||||||
|
type NodeToBlockVec = HashMap<NodeType, Rc<RefCell<FineBlock>>>;
|
||||||
|
type CoarsePartition = Vec<Rc<CoarseBlock>>;
|
||||||
|
type FineBlockPointer = Rc<RefCell<FineBlock>>;
|
||||||
|
type CoarseBlockPointer = Rc<CoarseBlock>;
|
||||||
|
type CounterimageGrouped = HashMap<Block, CounterImageGroup>;
|
||||||
|
|
||||||
|
struct FineBlock {
|
||||||
|
values: Block,
|
||||||
|
coarse_block_that_supersets_self: Rc<CoarseBlock>
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
struct CoarseBlock {
|
||||||
|
values: Block,
|
||||||
|
fine_blocks_that_are_subsets_of_self: RefCell<Vec<Rc<RefCell<FineBlock>>>>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl CoarseBlock {
|
||||||
|
fn add_fine_block(&self, fine_block: Rc<RefCell<FineBlock>>) {
|
||||||
|
self.fine_blocks_that_are_subsets_of_self
|
||||||
|
.borrow_mut()
|
||||||
|
.push(fine_block);
|
||||||
|
}
|
||||||
|
fn remove_fine_block(&self, fine_block: &Rc<RefCell<FineBlock>>) {
|
||||||
|
self.fine_blocks_that_are_subsets_of_self
|
||||||
|
.borrow_mut()
|
||||||
|
.retain(|x| !Rc::ptr_eq(x, fine_block));
|
||||||
|
}
|
||||||
|
fn fine_block_count(&self) -> usize {
|
||||||
|
self.fine_blocks_that_are_subsets_of_self.borrow().len()
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
struct CounterImageGroup {
|
||||||
|
block: Rc<RefCell<FineBlock>>,
|
||||||
|
subblock: Block,
|
||||||
|
}
|
||||||
|
|
||||||
|
trait HasValues {
|
||||||
|
fn values(&self) -> Block;
|
||||||
|
}
|
||||||
|
|
||||||
|
impl HasValues for FineBlockPointer {
|
||||||
|
fn values(&self) -> Block {
|
||||||
|
(**self).borrow().values.clone()
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl HasValues for CoarseBlock {
|
||||||
|
fn values(&self) -> Block {
|
||||||
|
self.values.clone()
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
fn initialization<const N: usize, G>(
|
||||||
|
graphs: &[&G; N]
|
||||||
|
) -> ( (FineBlockPointer, FineBlockPointer),
|
||||||
|
CoarsePartition,
|
||||||
|
NodeToBlockVec,
|
||||||
|
Translator<G::NodeId, NodeType, NodeState<N>> )
|
||||||
|
where
|
||||||
|
G: IntoNodeReferences + IntoEdges + IntoNeighborsDirected,
|
||||||
|
G::NodeId: std::cmp::Eq + std::hash::Hash,
|
||||||
|
G::EdgeId: std::cmp::Eq + std::hash::Hash,
|
||||||
|
G::EdgeRef: PartialEq,
|
||||||
|
{
|
||||||
|
// we translate into unique ids
|
||||||
|
let mut convert_nodes: Translator<G::NodeId, NodeType, NodeState<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 coarse_initial_block_pointer: Rc<CoarseBlock> = {
|
||||||
|
let coarse_initial_block = CoarseBlock {
|
||||||
|
values: graph_node_indices.clone(),
|
||||||
|
fine_blocks_that_are_subsets_of_self: RefCell::new(vec![]),
|
||||||
|
};
|
||||||
|
|
||||||
|
Rc::new(coarse_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| {
|
||||||
|
graphs[x.graph() as usize]
|
||||||
|
.neighbors_directed(
|
||||||
|
*convert_nodes.decode(x).unwrap(),
|
||||||
|
Outgoing)
|
||||||
|
.count() == 0
|
||||||
|
}
|
||||||
|
);
|
||||||
|
|
||||||
|
let leaf_node_block = FineBlock {
|
||||||
|
values: leaf_node_indices,
|
||||||
|
coarse_block_that_supersets_self: Rc::clone(&coarse_initial_block_pointer),
|
||||||
|
};
|
||||||
|
let non_leaf_node_block = FineBlock {
|
||||||
|
values: non_leaf_node_indices,
|
||||||
|
coarse_block_that_supersets_self: Rc::clone(&coarse_initial_block_pointer),
|
||||||
|
};
|
||||||
|
|
||||||
|
(
|
||||||
|
Rc::new(RefCell::new(leaf_node_block)),
|
||||||
|
Rc::new(RefCell::new(non_leaf_node_block)),
|
||||||
|
)
|
||||||
|
};
|
||||||
|
|
||||||
|
coarse_initial_block_pointer
|
||||||
|
.fine_blocks_that_are_subsets_of_self
|
||||||
|
.borrow_mut()
|
||||||
|
.extend([
|
||||||
|
Rc::clone(&leaf_node_block_pointer),
|
||||||
|
Rc::clone(&non_leaf_node_block_pointer),
|
||||||
|
]);
|
||||||
|
|
||||||
|
let node_to_block_vec = {
|
||||||
|
let mut tmp = HashMap::new();
|
||||||
|
|
||||||
|
(*non_leaf_node_block_pointer)
|
||||||
|
.borrow()
|
||||||
|
.values
|
||||||
|
.iter()
|
||||||
|
.copied()
|
||||||
|
.for_each(
|
||||||
|
|value|
|
||||||
|
{ tmp.insert(value, Rc::clone(&non_leaf_node_block_pointer)); }
|
||||||
|
);
|
||||||
|
|
||||||
|
(*leaf_node_block_pointer)
|
||||||
|
.borrow()
|
||||||
|
.values
|
||||||
|
.iter()
|
||||||
|
.copied()
|
||||||
|
.for_each(
|
||||||
|
|value|
|
||||||
|
{ tmp.insert(value, Rc::clone(&leaf_node_block_pointer)); }
|
||||||
|
);
|
||||||
|
tmp
|
||||||
|
};
|
||||||
|
|
||||||
|
(
|
||||||
|
(leaf_node_block_pointer, non_leaf_node_block_pointer),
|
||||||
|
vec![coarse_initial_block_pointer],
|
||||||
|
node_to_block_vec,
|
||||||
|
convert_nodes
|
||||||
|
)
|
||||||
|
}
|
||||||
|
|
||||||
|
fn build_counterimage<IndexHolder: HasValues, const N:usize, G>(
|
||||||
|
graphs: &[&G; N],
|
||||||
|
fine_block: IndexHolder,
|
||||||
|
convert_nodes: &Translator<G::NodeId, NodeType, NodeState<N>>
|
||||||
|
) -> CounterImage
|
||||||
|
where
|
||||||
|
G: IntoNodeReferences + IntoEdges + IntoNeighborsDirected,
|
||||||
|
G::NodeId: std::cmp::Eq + std::hash::Hash,
|
||||||
|
G::EdgeId: std::cmp::Eq + std::hash::Hash,
|
||||||
|
G::EdgeRef: PartialEq,
|
||||||
|
{
|
||||||
|
let mut counterimage = HashMap::new();
|
||||||
|
|
||||||
|
fine_block.values().iter().for_each(|node_index_pointer| {
|
||||||
|
counterimage.insert(
|
||||||
|
*node_index_pointer,
|
||||||
|
graphs[node_index_pointer.graph() as usize]
|
||||||
|
.neighbors_directed(
|
||||||
|
*convert_nodes.decode(node_index_pointer).unwrap(),
|
||||||
|
Incoming)
|
||||||
|
.collect::<HashSet<_>>()
|
||||||
|
.into_iter()
|
||||||
|
.map(|e| convert_nodes.get(&e).unwrap())
|
||||||
|
.copied()
|
||||||
|
.collect::<Vec<_>>(),
|
||||||
|
);
|
||||||
|
});
|
||||||
|
|
||||||
|
counterimage
|
||||||
|
}
|
||||||
|
|
||||||
|
fn group_by_counterimage(
|
||||||
|
counterimage: CounterImage,
|
||||||
|
node_to_block: &NodeToBlockVec,
|
||||||
|
) -> CounterimageGrouped {
|
||||||
|
let mut counterimage_grouped: CounterimageGrouped = HashMap::new();
|
||||||
|
|
||||||
|
for incoming_neighbor_group in counterimage.values() {
|
||||||
|
for node in incoming_neighbor_group {
|
||||||
|
let block = Rc::clone(node_to_block.get(node).unwrap());
|
||||||
|
let key = (*block).borrow().values.clone();
|
||||||
|
|
||||||
|
match counterimage_grouped.entry(key) {
|
||||||
|
Entry::Occupied(mut entry) => entry.get_mut().subblock.push(*node),
|
||||||
|
Entry::Vacant(entry) => {
|
||||||
|
entry.insert(CounterImageGroup {
|
||||||
|
block: Rc::clone(&block),
|
||||||
|
subblock: Vec::from([*node]),
|
||||||
|
});
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
counterimage_grouped
|
||||||
|
}
|
||||||
|
|
||||||
|
fn split_blocks_with_grouped_counterimage(
|
||||||
|
mut counterimage_grouped: CounterimageGrouped,
|
||||||
|
node_to_block_vec: &mut NodeToBlockVec,
|
||||||
|
) -> (
|
||||||
|
(Vec<FineBlockPointer>, Vec<FineBlockPointer>),
|
||||||
|
Vec<CoarseBlockPointer>,
|
||||||
|
) {
|
||||||
|
let mut all_new_fine_blocks: Vec<Rc<RefCell<FineBlock>>> = vec![];
|
||||||
|
let mut all_removed_fine_blocks: Vec<Rc<RefCell<FineBlock>>> = vec![];
|
||||||
|
let mut new_compound_coarse_blocks: Vec<Rc<CoarseBlock>> = vec![];
|
||||||
|
|
||||||
|
for (block, counter_image_group) in counterimage_grouped.iter_mut() {
|
||||||
|
let borrowed_coarse_block = Rc::clone(
|
||||||
|
&(*counter_image_group.block)
|
||||||
|
.borrow()
|
||||||
|
.coarse_block_that_supersets_self,
|
||||||
|
);
|
||||||
|
|
||||||
|
let proper_subblock = {
|
||||||
|
let fine_block = FineBlock {
|
||||||
|
values: counter_image_group.subblock.clone(),
|
||||||
|
coarse_block_that_supersets_self: Rc::clone(&borrowed_coarse_block),
|
||||||
|
};
|
||||||
|
|
||||||
|
Rc::new(RefCell::new(fine_block))
|
||||||
|
};
|
||||||
|
let prior_count = borrowed_coarse_block.fine_block_count();
|
||||||
|
borrowed_coarse_block.add_fine_block(Rc::clone(&proper_subblock));
|
||||||
|
|
||||||
|
if prior_count == 1 {
|
||||||
|
new_compound_coarse_blocks.push(Rc::clone(&borrowed_coarse_block));
|
||||||
|
}
|
||||||
|
|
||||||
|
for node_index in counter_image_group.subblock.iter() {
|
||||||
|
node_to_block_vec.insert(*node_index, Rc::clone(&proper_subblock));
|
||||||
|
}
|
||||||
|
|
||||||
|
// subtract subblock from block
|
||||||
|
(*counter_image_group.block).borrow_mut().values = block
|
||||||
|
.iter()
|
||||||
|
.filter(|x| !(*proper_subblock).borrow().values.contains(x))
|
||||||
|
.copied()
|
||||||
|
.collect();
|
||||||
|
|
||||||
|
if (*counter_image_group.block).borrow().values.is_empty() {
|
||||||
|
borrowed_coarse_block.remove_fine_block(&counter_image_group.block);
|
||||||
|
all_removed_fine_blocks.push(Rc::clone(&counter_image_group.block));
|
||||||
|
}
|
||||||
|
all_new_fine_blocks.push(Rc::clone(&proper_subblock));
|
||||||
|
}
|
||||||
|
(
|
||||||
|
(all_new_fine_blocks, all_removed_fine_blocks),
|
||||||
|
new_compound_coarse_blocks,
|
||||||
|
)
|
||||||
|
}
|
||||||
|
|
||||||
|
fn maximum_bisimulation<const N: usize, G>(
|
||||||
|
graphs: &[&G; N]
|
||||||
|
) -> Option<Vec<Block>>
|
||||||
|
where
|
||||||
|
G: IntoNodeReferences + IntoEdges + IntoNeighborsDirected,
|
||||||
|
G::NodeId: std::cmp::Eq + std::hash::Hash,
|
||||||
|
G::EdgeId: std::cmp::Eq + std::hash::Hash,
|
||||||
|
G::EdgeRef: PartialEq,
|
||||||
|
{
|
||||||
|
let (fine_block_tuple,
|
||||||
|
initial_coarse_partition,
|
||||||
|
mut node_to_block_vec,
|
||||||
|
converter) = initialization(graphs);
|
||||||
|
|
||||||
|
let mut queue: CoarsePartition = initial_coarse_partition;
|
||||||
|
let mut all_fine_blocks = vec![fine_block_tuple.0, fine_block_tuple.1];
|
||||||
|
|
||||||
|
loop {
|
||||||
|
let (smaller_component, simple_splitter_block) = {
|
||||||
|
let splitter_block = match queue.pop() {
|
||||||
|
Some(coarse_block) => coarse_block,
|
||||||
|
None => break,
|
||||||
|
};
|
||||||
|
let mut fine_blocks_in_splitter_block = splitter_block
|
||||||
|
.fine_blocks_that_are_subsets_of_self
|
||||||
|
.borrow()
|
||||||
|
.clone();
|
||||||
|
|
||||||
|
let smaller_component_index = fine_blocks_in_splitter_block
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.min_by(|(_, x), (_, y)| {
|
||||||
|
(***x)
|
||||||
|
.borrow()
|
||||||
|
.values
|
||||||
|
.len()
|
||||||
|
.cmp(&(***y).borrow().values.len())
|
||||||
|
})
|
||||||
|
.map(|(index, _)| index)?;
|
||||||
|
|
||||||
|
let smaller_component = fine_blocks_in_splitter_block.remove(smaller_component_index);
|
||||||
|
|
||||||
|
let simple_splitter_block_values: Block = splitter_block
|
||||||
|
.values
|
||||||
|
.clone()
|
||||||
|
.iter()
|
||||||
|
.filter(|x| !(*smaller_component).borrow().values.contains(x))
|
||||||
|
.copied()
|
||||||
|
.collect();
|
||||||
|
|
||||||
|
let simple_splitter_block = CoarseBlock {
|
||||||
|
values: simple_splitter_block_values,
|
||||||
|
fine_blocks_that_are_subsets_of_self: RefCell::new(fine_blocks_in_splitter_block),
|
||||||
|
};
|
||||||
|
let simple_splitter_block_pointer = Rc::new(simple_splitter_block);
|
||||||
|
|
||||||
|
if simple_splitter_block_pointer
|
||||||
|
.fine_blocks_that_are_subsets_of_self
|
||||||
|
.borrow()
|
||||||
|
.len()
|
||||||
|
> 1
|
||||||
|
{
|
||||||
|
queue.push(Rc::clone(&simple_splitter_block_pointer));
|
||||||
|
}
|
||||||
|
|
||||||
|
(smaller_component, simple_splitter_block_pointer)
|
||||||
|
};
|
||||||
|
simple_splitter_block
|
||||||
|
.fine_blocks_that_are_subsets_of_self
|
||||||
|
.borrow()
|
||||||
|
.iter()
|
||||||
|
.for_each(|x| {
|
||||||
|
(*x).borrow_mut().coarse_block_that_supersets_self =
|
||||||
|
Rc::clone(&simple_splitter_block);
|
||||||
|
});
|
||||||
|
|
||||||
|
let mut counterimage = build_counterimage(graphs, smaller_component, &converter);
|
||||||
|
|
||||||
|
let counterimage_group = group_by_counterimage(counterimage.clone(), &node_to_block_vec);
|
||||||
|
let ((new_fine_blocks, removeable_fine_blocks), coarse_block_that_are_now_compound) =
|
||||||
|
split_blocks_with_grouped_counterimage(counterimage_group, &mut node_to_block_vec);
|
||||||
|
|
||||||
|
all_fine_blocks.extend(new_fine_blocks);
|
||||||
|
all_fine_blocks.retain(|x| !removeable_fine_blocks.iter().any(|y| Rc::ptr_eq(x, y)));
|
||||||
|
queue.extend(coarse_block_that_are_now_compound);
|
||||||
|
|
||||||
|
// counterimage = E^{-1}(B) - E^{-1}(S-B)
|
||||||
|
{
|
||||||
|
let counterimage_splitter_complement =
|
||||||
|
build_counterimage(graphs, (*simple_splitter_block).clone(), &converter);
|
||||||
|
|
||||||
|
counterimage_splitter_complement.keys().for_each(|node| {
|
||||||
|
counterimage.remove(node);
|
||||||
|
});
|
||||||
|
}
|
||||||
|
|
||||||
|
let counterimage_group = group_by_counterimage(counterimage, &node_to_block_vec);
|
||||||
|
let ((new_fine_blocks, removeable_fine_blocks), coarse_block_that_are_now_compound) =
|
||||||
|
split_blocks_with_grouped_counterimage(counterimage_group, &mut node_to_block_vec);
|
||||||
|
|
||||||
|
all_fine_blocks.extend(new_fine_blocks);
|
||||||
|
all_fine_blocks.retain(|x| !removeable_fine_blocks.iter().any(|y| Rc::ptr_eq(x, y)));
|
||||||
|
queue.extend(coarse_block_that_are_now_compound);
|
||||||
|
}
|
||||||
|
|
||||||
|
Some(
|
||||||
|
all_fine_blocks
|
||||||
|
.iter()
|
||||||
|
.map(|x| (**x).borrow().values.clone())
|
||||||
|
.filter(|x| !x.is_empty()) // remove leaf block when there are no leaves
|
||||||
|
.collect(),
|
||||||
|
)
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
pub fn bisimilarity_paige_tarjan<G>(
|
||||||
|
graph_a: &G,
|
||||||
|
graph_b: &G
|
||||||
|
) -> bool
|
||||||
|
where
|
||||||
|
G: IntoNodeReferences + IntoEdges + IntoNeighborsDirected + NodeCount,
|
||||||
|
G::NodeId: std::cmp::Eq + std::hash::Hash,
|
||||||
|
G::EdgeId: std::cmp::Eq + std::hash::Hash,
|
||||||
|
G::EdgeRef: PartialEq,
|
||||||
|
{
|
||||||
|
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 =
|
||||||
|
match maximum_bisimulation(&[graph_a, graph_b]) {
|
||||||
|
None => {return false},
|
||||||
|
Some(val) => {
|
||||||
|
val.into_iter()
|
||||||
|
.find(
|
||||||
|
|el| {
|
||||||
|
let mut keep_track = [false, false];
|
||||||
|
for e in el {
|
||||||
|
keep_track[e.graph() as usize] = true;
|
||||||
|
}
|
||||||
|
!keep_track[0] || !keep_track[1]
|
||||||
|
}
|
||||||
|
)
|
||||||
|
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
println!("{:?}", result);
|
||||||
|
|
||||||
|
result.is_none()
|
||||||
}
|
}
|
||||||
|
|||||||
@ -547,7 +547,8 @@ pub fn bisimilar(
|
|||||||
let b: &graph::RSgraph = b;
|
let b: &graph::RSgraph = b;
|
||||||
Ok(format!(
|
Ok(format!(
|
||||||
"{}",
|
"{}",
|
||||||
super::bisimilarity::bisimilarity_kanellakis_smolka(&a, &b)
|
// super::bisimilarity::bisimilarity_kanellakis_smolka(&a, &b)
|
||||||
|
super::bisimilarity::bisimilarity_paige_tarjan(&a, &b)
|
||||||
))
|
))
|
||||||
},
|
},
|
||||||
_ => { unreachable!() }
|
_ => { unreachable!() }
|
||||||
|
|||||||
Reference in New Issue
Block a user