Equivalence-Checking on Infinite-State Systems: Techniques and Results

The paper presents a selection of recently developed and/or used techniques for equivalence-checking on infinite-state systems, and an up-to-date overview of existing results (as of September 2004)

Beyond Language Equivalence on Visibly Pushdown Automata

We study (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly one-counter automata. We describe generic methods for proving complexity upper and lower bounds for a number of studied preorders and equivalences like simulation, completed simulation, ready simulation, 2-nested simulation preorders/equivalences and bisimulation equivalence. Our main results are that all the mentioned equivalences and preorders are EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for visibly one-counter automata improves also the previously known DP-hardness results for ordinary one-counter automata and one-counter nets. Finally, we study regularity checking problems for visibly pushdown automata and show that they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC

Branching Bisimilarity of Normed BPA Processes is in NEXPTIME

Branching bisimilarity on normed BPA processes was recently shown to be decidable by Yuxi Fu (ICALP 2013) but his proof has not provided any upper complexity bound. We present a simpler approach based on relative prime decompositions that leads to a nondeterministic exponential-time algorithm; this is close to the known exponential-time lower bound.Comment: This is the same text as in July 2014, but only with some acknowledgment added due to administrative need

Fresh-Register Automata

What is a basic automata-theoretic model of computation with names and fresh-name generation? We introduce Fresh-Register Automata (FRA), a new class of automata which operate on an infinite alphabet of names and use a finite number of registers to store fresh names, and to compare incoming names with previously stored ones. These finite machines extend Kaminski and Francez’s Finite-Memory Automata by being able to recognise globally fresh inputs, that is, names fresh in the whole current run. We exam-ine the expressivity of FRA’s both from the aspect of accepted languages and of bisimulation equivalence. We establish primary properties and connections between automata of this kind, and an-swer key decidability questions. As a demonstrating example, we express the theory of the pi-calculus in FRA’s and characterise bisimulation equivalence by an appropriate, and decidable in the finitary case, notion in these automata

A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPA

Strong bisimilarity on normed BPA is polynomial-time decidable, while weak bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the computational complexity of branching bisimilarity on totally normed BPA lies. This paper confirms that this problem is polynomial-time decidable. To our knowledge, in the presence of silent transitions, this is the first bisimilarity checking algorithm on infinite state systems which runs in polynomial time. This result spots an instance in which branching bisimilarity and weak bisimilarity are both decidable but lie in different complexity classes (unless NP=P), which is not known before. The algorithm takes the partition refinement approach and the final implementation can be thought of as a generalization of the previous algorithm of Czerwi\'{n}ski and Lasota. However, unexpectedly, the correctness of the algorithm cannot be directly generalized from previous works, and the correctness proof turns out to be subtle. The proof depends on the existence of a carefully defined refinement operation fitted for our algorithm and the proposal of elaborately developed techniques, which are quite different from previous works.Comment: 32 page

Bisimilarity of Pushdown Systems is Nonelementary

Given two pushdown systems, the bisimilarity problem asks whether they are bisimilar. While this problem is known to be decidable our main result states that it is nonelementary, improving EXPTIME-hardness, which was the previously best known lower bound for this problem. Our lower bound result holds for normed pushdown systems as well

Resource Bisimilarity in Petri Nets is Decidable

Petri nets are a popular formalism for modeling and analyzing distributed systems. Tokens in Petri net models can represent the control flow state or resources produced/consumed by transition firings. We define a resource as a part (submultiset) of the Petri net marking and call two resources equivalent iff replacing one of them with another in any marking does not change the observable Petri net behavior. We investigate the resource similarity and the resource bisimilarity -- congruent restrictions of the bisimulation equivalence on Petri net markings and prove that the resource bisimilarity is decidable in contrast to the resource similarity.Comment: New version for submission to the journa