Distributed Branching Bisimulation Minimization by Inductive Signatures

Abstract

We present a new distributed algorithm for state space minimization modulo branching bisimulation. Like its predecessor it uses signatures for refinement, but the refinement process and the signatures have been optimized to exploit the fact that the input graph contains no tau-loops. The optimization in the refinement process is meant to reduce both the number of iterations needed and the memory requirements. In the former case we cannot prove that there is an improvement, but our experiments show that in many cases the number of iterations is smaller. In the latter case, we can prove that the worst case memory use of the new algorithm is linear in the size of the state space, whereas the old algorithm has a quadratic upper bound. The paper includes a proof of correctness of the new algorithm and the results of a number of experiments that compare the performance of the old and the new algorithms

An $$O(m\log n)$$ Algorithm for Stuttering Equivalence and Branching Bisimulation

“…

We provide a new algorithm to determine stuttering equivalence with time complexity O(m log n), where n is the number of states and m is the number of transitions of a Kripke structure. This algorithm can also be used to determine branching bisimulation in O(m(log |Act| + log n)) time where Act is the set of actions in a labelled transition system.Theoretically, our algorithm substantially improves upon existing algorithms which all have time complexity O(mn) at best [2,3,9]. Moreover, it has better or equal space complexity.

…”

“…In [3], the space complexity is brought back to O(m+n). A technique to be performed on Graphics Processing Units based on both GV and [2,3] is proposed in [19]. This improves the required runtime considerably by employing parallelism, but it does not imply any improvement to the single-threaded algorithm.…”

Sharp Congruences Adequate with Temporal Logics Combining Weak and Strong Modalities

“…Yet, to be both usable by non-experts and fully efficient, at least two components are still missing: (1) The sets of strong actions, which are a key ingredient in the success of this approach, still have to be computed either using pencil and paper or using tools dedicated to restricted logics; automating their computation in the case of arbitrary L μ formulas is not easy, but likely feasible, opening the way to a new research track; finding a minimal set of strong actions automatically is challenging, and since it is not unique, even more challenging is the quest for the set that will incur the best reductions. (2) Efficient algorithms are needed to minimize LTS for sharp bisimilarity; they could probably be obtained by adapting the known algorithms for strong and divbranching minimizations (at least using some kind of signaturebased partition refinement algorithm in the style of Blom et al [3][4][5] in a first step), but this remains to be done.…”

Recent advances in interactive and automated analysis

“…This verification approach is based on bisimulation relations [12] between LTSs, and consists essentially in computing the equivalence classes on states by using partition refinement algorithms. After the early parallelization of the classical partition refinement algorithms [34], equivalence checking has been primarily subject to distributed algorithms based on the computation of signatures over states and transitions in order to accelerate the convergence of partition refinement [7,8].…”