A Fast Bisimulation Algorithm

Abstract

In this paper we propose an efficient algorithmic solution to the problem of determining a Bisimulation Relation on a finite structure. Starting from a set-theoretic point of view we propose an algorithm that optimizes the solution to the Relational coarsest Partition problem given by Paige and Tarjan in 1987 and its use in model-checking packages is briefly discussed and tested. Our algorithm reaches, in particular cases, a linear solution.

An Incremental Bisimulation Algorithm

“…This benchmark is a downward closed tree (Test 2 of [7]) of 65535 nodes obtained by closing downward a binary tree using the rule: if m, n and n, p are edges then add a new edge n, p and two different labels are put to the alternate nodes in each ranked strata of the tree. The initial FBA time is 0.5s.…”

Information flow security in dynamic contexts

“…P BNDC can be also proved by following the method proposed in [24] where the verification of a process equivalence is reduced to the problem of verifying a strong bisimulation between two transformed processes. Given this transformation, the strong bisimulation test can be performed using efficient algorithms for strong bisimulation ( [17,12,4,13,5]). Actually, the compositional security checker described in [7] provides an automatic tool for verifying P BNDC over finite state processes: this is done by checking SBSNNI that requires to verify a bisimulation property over all the possible reachable states.…”

Exploiting shared correlations in probabilistic databases

“…These algorithms are generally referred to as bisimulation [17] or computing the relational coarsest partition [19]). Given the special case of the graph being a DAG, there exist algorithms that run in time linear in the size of the graph [10]. Dovier et al [10] describe one such algorithm that runs on an edge-labeled, vertex-labeled graph and not only partitions the set of vertices but also returns another (smaller) graph where each disjoint set in the partition is represented by a vertex and the edges between vertices p 1 , representing one disjoint set in the partition, and p 2 , representing another disjoint set in the partition, are the result of taking the union of all edges between all vertices from the input graph in p 1 and all vertices from p 2 .…”

“…Given the special case of the graph being a DAG, there exist algorithms that run in time linear in the size of the graph [10]. Dovier et al [10] describe one such algorithm that runs on an edge-labeled, vertex-labeled graph and not only partitions the set of vertices but also returns another (smaller) graph where each disjoint set in the partition is represented by a vertex and the edges between vertices p 1 , representing one disjoint set in the partition, and p 2 , representing another disjoint set in the partition, are the result of taking the union of all edges between all vertices from the input graph in p 1 and all vertices from p 2 . We will refer to each resulting disjoint set of the vertices of the rv-elim graph as an extent and the resulting graph returned as a result of running bisimulation on the rv-elim graph as the compressed rv-elim graph.…”

“…They take all vertices at rank i, choose orders for each vertices' parents (we will discuss how this is done shortly), forms the label and the key based on this ordering and partitions these vertices based on the constructed key. See Dovier et al [10] for proof of correctness when the vertex and edge labels can be statically allocated. Parent ordering heuristic: We now discuss the parent ordering heuristic we developed.…”