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32
A Direct Symbolic Approach to Model Checking Pushdown Systems (Extended Abstract)
, 1997
"... This paper gives a simple and direct algorithm for computing the always regular set of reachable states of a pushdown system. It then exploits this algorithm for obtaining model checking algorithms for lineartime temporal logic as well as for the logic CTL. For the latter, a new technical tool is i ..."
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Cited by 114 (4 self)
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This paper gives a simple and direct algorithm for computing the always regular set of reachable states of a pushdown system. It then exploits this algorithm for obtaining model checking algorithms for lineartime temporal logic as well as for the logic CTL. For the latter, a new technical tool is introduced: pushdown automata with transitions conditioned on regular predicates on the stack content. Finally, this technical tool is also used to establish that CTL model checking remains decidable when the formulas are allowed to include regular predicates on the stack content.
Bisimulation Equivalence is Decidable for all ContextFree Processes
 Information and Computation
, 1995
"... Introduction Over the past decade much attention has been devoted to the study of process calculi such as CCS, ACP and CSP [13]. Of particular interest has been the study of the behavioural semantics of these calculi as given by labelled transition graphs. One important question is when processes c ..."
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Cited by 92 (15 self)
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Introduction Over the past decade much attention has been devoted to the study of process calculi such as CCS, ACP and CSP [13]. Of particular interest has been the study of the behavioural semantics of these calculi as given by labelled transition graphs. One important question is when processes can be said to exhibit the same behaviour, and a plethora of behavioural equivalences exists today. Their main rationale has been to capture behavioural aspects that language or trace equivalences do not take into account. The theory of finitestate systems and their equivalences can now be said to be wellestablished. There are many automatic verification tools for their analysis which incorporate equivalence checking. Sound and complete equational theories exist for the various known equivalences, an elegant example is [18]. One may be led to wonder what the results will look like for infinitestate systems. Although language equivalence is decidable
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 68 (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.
Bisimulation Collapse and the Process Taxonomy
, 1996
"... . We consider the factorization (collapse) of infinite transition graphs wrt. bisimulation equivalence. It turns out that almost none of the more complex classes of the process taxonomy, which has been established in the last years, are preserved by this operation. However, for the class of BPA grap ..."
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Cited by 38 (1 self)
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. We consider the factorization (collapse) of infinite transition graphs wrt. bisimulation equivalence. It turns out that almost none of the more complex classes of the process taxonomy, which has been established in the last years, are preserved by this operation. However, for the class of BPA graphs (i.e. prefix transition graphs of contextfree grammars) we can show that the factorization is effectively a regular graph, i.e. finitely representable by means of a deterministic hypergraph grammar. Since finiteness of regular graphs is decidable, this yields, as a corollary, a decision procedure for the finiteness problem of contextfree processes wrt. bisimulation equivalence. 1 Introduction In concurrency theory, process calculi are widely accepted as algebraic description languages for concurrent systems. Their semantics are usually formulated in terms of labelled transition graphs which model the dynamic behaviour together with some notion of behavioural equivalence. Since there is...
Undecidable Equivalences for Basic Parallel Processes
 13th Conference on Foundations of Software Technology and Theoretical Computer Science
, 1993
"... . Recent results show that strong bisimilarity is decidable for the class of Basic Parallel Processes (BPP), which corresponds to the subset of CCS definable using recursion, action prefixing, nondeterminism and the full merge operator. In this paper we examine all other equivalences in the linear/b ..."
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Cited by 25 (2 self)
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. Recent results show that strong bisimilarity is decidable for the class of Basic Parallel Processes (BPP), which corresponds to the subset of CCS definable using recursion, action prefixing, nondeterminism and the full merge operator. In this paper we examine all other equivalences in the linear/branching time hierarchy [12] and show that none of them are decidable for BPP. 1 Introduction Much attention has been devoted to the study of process calculi and in particular to behavioural semantics for these calculi. In order to capture the behavioural aspects of processes, a variety of equivalences have been proposed. Various criteria exist for comparing the merits and deficiencies of these equivalences. A systematic approach consists of classifying the equivalences according to their coarseness. For this purpose van Glabbeek proposed the linear/branching time spectrum which is illustrated in Figure 1 [12]. The least discriminating equivalences are at the bottom of the diagram. Arrows i...
Decidability of DPDA equivalence
, 1999
"... A proof of decidability of equivalence between deterministic pushdown automata is presented using a mixture of methods developed in concurrency and language theory. The technique appeals to a tableau proof system for equivalence of configurations of strict deterministic grammars. ..."
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Cited by 24 (2 self)
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A proof of decidability of equivalence between deterministic pushdown automata is presented using a mixture of methods developed in concurrency and language theory. The technique appeals to a tableau proof system for equivalence of configurations of strict deterministic grammars.
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.
An Elementary Bisimulation Decision Procedure for Arbitrary ContextFree Processes
, 1994
"... We present an elementary algorithm for deciding bisimulation equivalence between arbitrary contextfree processes. This improves on the state of the art algorithm of Christensen, Huttel and Stirling consisting of two semidecision procedures running in parallel, which prohibits any complexity est ..."
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Cited by 16 (2 self)
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We present an elementary algorithm for deciding bisimulation equivalence between arbitrary contextfree processes. This improves on the state of the art algorithm of Christensen, Huttel and Stirling consisting of two semidecision procedures running in parallel, which prohibits any complexity estimation. The point of our algorithm is the effective construction of a finite relation characterizing all bisimulation equivalence classes, whose mere existence was exploited for the above mentioned decidability result.