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28
Verification on Infinite Structures
, 2000
"... In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the ..."
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Cited by 69 (2 self)
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In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear and branchingtime temporal logics.
Process Rewrite Systems
 INFORMATION AND COMPUTATION
, 1997
"... Many formal models for infinitestate concurrent systems are equivalent to special classes of rewrite systems. We classify these models by their expressiveness and define a hierarchy of classes of rewrite systems. We show that this hierarchy is strict with respect to bisimulation equivalence. The mo ..."
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Cited by 62 (9 self)
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Many formal models for infinitestate concurrent systems are equivalent to special classes of rewrite systems. We classify these models by their expressiveness and define a hierarchy of classes of rewrite systems. We show that this hierarchy is strict with respect to bisimulation equivalence. The most general and most expressive class of systems in this hierarchy is called Process Rewrite Systems (PRS). They subsume Petri nets, PAProcesses and pushdown processes and are strictly more expressive than any of these. Intuitively, PRS can be seen as an extension of Petri nets by subroutines that can return a value to their caller. We show that the reachability problem is decidable for PRS. It is even decidable if there is a reachable state that satisfies certain properties that can be encoded in a simple logic. Thus PRS are more expressive than Petri nets, but not Turingpowerful.
Decidability of Bisimulation Equivalence for Normed Pushdown Processes
 Theoretical Computer Science
, 1996
"... We prove that bisimulation equivalence is decidable for normed pushdown processes. 1 Introduction In the classical theory of automata the expressive power of pushdown automata is matched by contextfree grammars. Both accept the same family of languages, the contextfree languages. Concurrency theo ..."
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Cited by 24 (7 self)
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We prove that bisimulation equivalence is decidable for normed pushdown processes. 1 Introduction In the classical theory of automata the expressive power of pushdown automata is matched by contextfree grammars. Both accept the same family of languages, the contextfree languages. Concurrency theory requires a more intensional exposition of behaviour (as language equivalence need not be preserved in the presence of communicating abstract machines). Many finer equivalences have been proposed. Bisimulation equivalence, due to Park and Milner, has received much attention. Baeten, Bergstra and Klop proved that bisimulation equivalence is decidable for irredundant contextfree grammars (without the empty production) . Within process calculus theory these grammars correspond to normed BPA processes. Their proof relies on isolating a complex periodicity from the transition graphs of these processes. Simpler proofs of the result soon followed which expose algebraic structure. Caucal and Monf...
Regularity is Decidable for Normed PA Processes in Polynomial Time
, 1996
"... A process # is regular if it is bisimilar to a process # # with finitely many states. We prove that regularity of normed PA processes is decidable and we present a practically usable polynomialtime algorithm. Moreover, if the tested normed PA process # is regular then the process # # can be ..."
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Cited by 18 (3 self)
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A process # is regular if it is bisimilar to a process # # with finitely many states. We prove that regularity of normed PA processes is decidable and we present a practically usable polynomialtime algorithm. Moreover, if the tested normed PA process # is regular then the process # # can be e#ectively constructed. It implies decidability of bisimulation equivalence for any pair of processes such that one process of this pair is a normed PA process and the other process has finitely many states.
The Joys of Bisimulation
, 1998
"... this paper we review results about bisimulation, from both the point of view of automata and from a logical point of view. We also consider how bisimulation has a role in finite model theory, and we offer a new undefinability result. ..."
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Cited by 17 (0 self)
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this paper we review results about bisimulation, from both the point of view of automata and from a logical point of view. We also consider how bisimulation has a role in finite model theory, and we offer a new undefinability result.
On the Complexity of Bisimulation Problems for Pushdown Automata
 In Proceedings of IFIP TCS’2000, volume 1872 of LNCS
, 2000
"... All bisimulation problems for pushdown automata are at least PSPACEhard. In particular, we show that (1) Weak bisimilarity of pushdown automata and finite automata is PSPACEhard, even for a small fixed finite automaton, (2) Strong bisimilarity of pushdown automata and finite automata is PSPACEhar ..."
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Cited by 14 (6 self)
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All bisimulation problems for pushdown automata are at least PSPACEhard. In particular, we show that (1) Weak bisimilarity of pushdown automata and finite automata is PSPACEhard, even for a small fixed finite automaton, (2) Strong bisimilarity of pushdown automata and finite automata is PSPACEhard, but polynomial for every fixed finite automaton, (3) Regularity (finiteness) of pushdown automata w.r.t. weak and strong bisimilarity is PSPACEhard.
More Infinite Results
 UNIVERSITY OF PASSAU. UNIVERSITY OF PASSAU
, 1996
"... Recently there has been a spurt of activity in concurrency theory centered on the analysis of infinitestate systems. The following two problems have been intensely investigated: (1) given two infinitestate systems, are they equal with respect to a certain equivalence notion?, and (2) given an i ..."
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Cited by 13 (1 self)
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Recently there has been a spurt of activity in concurrency theory centered on the analysis of infinitestate systems. The following two problems have been intensely investigated: (1) given two infinitestate systems, are they equal with respect to a certain equivalence notion?, and (2) given an infinitestate system and a property expressed in a certain temporal logic, does the system satisfy the property? In his CONCUR '96 paper, Faron Moller surveys some of the key results on the decidability and complexity of (1). The purpose of this paper for CONCUR's satellite INFINITY Workshop is to do the same with (2).
Decidability of Model Checking with the Temporal Logic EF
 Theoretical Computer Science
, 1999
"... The branchingtime temporal logic EF is a simple, but natural fragment of computation tree logic (CTL) and the modal calculus. We study the decidability of the model checking problem for EF and infinitestate systems. We use process rewrite systems (PRS) to describe infinitestate systems and defi ..."
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Cited by 12 (0 self)
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The branchingtime temporal logic EF is a simple, but natural fragment of computation tree logic (CTL) and the modal calculus. We study the decidability of the model checking problem for EF and infinitestate systems. We use process rewrite systems (PRS) to describe infinitestate systems and define a hierarchy of subclasses of PRS that includes Petri nets, pushdown processes, Basic Parallel Processes (BPP), contextfree processes and PAProcesses. Then we establish the exact limits of the decidability of model checking with EF in this hierarchy. Model checking with EF is undecidable for Petri nets and even for parallel pushdown automata (the pushdown extension of Basic Parallel Processes). On the other hand, model checking with EF is decidable for PAD, a process model that subsumes both PAprocesses and pushdown processes. Key words: infinitestate systems, temporal logic, EF, model checking, process algebra, PAprocesses, pushdown processes 1 Introduction The branchingtime tempora...
Roadmap of Infinite Results
, 2008
"... This paper provides a comprehensive summary of equivalence checking results for infinitestate systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the webpage ..."
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Cited by 12 (0 self)
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This paper provides a comprehensive summary of equivalence checking results for infinitestate systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the webpage
Decidability of Bisimilarity for OneCounter Processes
, 1997
"... It is shown that bisimulation equivalence is decidable for the processes generated by (nondeterministic) pushdown automata where the pushdown behaves like a counter. Also finiteness up to bisimilarity is shown to be decidable for the mentioned processes. ..."
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Cited by 11 (1 self)
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It is shown that bisimulation equivalence is decidable for the processes generated by (nondeterministic) pushdown automata where the pushdown behaves like a counter. Also finiteness up to bisimilarity is shown to be decidable for the mentioned processes.