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

Two Lower Bounds for BPA

Branching bisimilarity of normed Basic Process Algebra (nBPA) was claimed to be EXPTIME-hard in previous papers without any explicit proof. Recently it has been pointed out by Petr Jancar that the claim lacked proper justification. In this paper, we develop a new complete proof for the EXPTIME-hardness of branching bisimilarity of nBPA. We also prove that the associated regularity problem of nBPA is PSPACE-hard. This improves previous P-hard result

Bisimulation equivalence of a BPP and a finite-state system can be decided in polynomial time

AbstractIn this paper we consider the problem of deciding bisimulation equivalence of a BPP and a finite-state system. We show that the problem can be solved in polynomial time and we present an algorithm deciding the problem in time O(n4). The algorithm also constructs for each state of the finite-state system a ‘symbolic’ semilinear representation of the set of all states of the BPP system which are bisimilar with this state

Bisimulation equivalence and regularity for real-time one-counter automata

A one-counter automaton is a pushdown automaton with a singleton stack alphabet, where stack emptiness can be tested; it is a real-time automaton if it contains no ε -transitions. We study the computational complexity of the problems of equivalence and regularity (i.e. semantic finiteness) on real-time one-counter automata. The first main result shows PSPACEPSPACE-completeness of bisimulation equivalence; this closes the complexity gap between decidability [23] and PSPACEPSPACE-hardness [25]. The second main result shows NLNL-completeness of language equivalence of deterministic real-time one-counter automata; this improves the known PSPACEPSPACE upper bound (indirectly shown by Valiant and Paterson [27]). Finally we prove PP-completeness of the problem if a given one-counter automaton is bisimulation equivalent to a finite system, and NLNL-completeness of the problem if the language accepted by a given deterministic real-time one-counter automaton is regular.Web of Science80474372

Decidability Issues for Petri Nets

This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics

Weak Bisimulation Approximants

Bisimilarity ∼ and weak bisimilarity ≈ are canonical notions of equivalence between processes, which are defined co-inductively, but may be approached – and even reached – by their (transfinite) inductively-defined approximants ∼α and ≈α. For arbitrary processes this approximation may need to climb arbitrarily high through the infinite ordinals before stabilising. In this paper we consider a simple yet well-studied process algebra, the Basic Parallel Processes (BPP), and investigate for this class of processes the minimal ordinal α such that ≈ = ≈α. The main tool in our investigation is a novel proof of Dickson’s Lemma. Unlike classical proofs, the proof we provide gives rise to a tight ordinal bound, of ω n, on the order type of non-increasing sequences of n-tuples of natural numbers. With this we are able to reduce a long-standing bound on the approximation hierarchy for weak bisimilarity ≈ over BPP, and show that ≈ = ≈ω ω