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12
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.
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 39 (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...
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.
Decidability of bisimulation equivalence for pushdown processes
, 2000
"... We show that bisimulation equivalence is decidable for pushdown automata without ǫtransitions. 1 ..."
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Cited by 9 (0 self)
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We show that bisimulation equivalence is decidable for pushdown automata without ǫtransitions. 1
On the Complexity of Deciding Behavioural Equivalences and Preorders  A Survey
, 1996
"... This paper gives an overview of the computational complexity of all the equivalences in the linear/branching time hierarchy [vG90a] and the preorders in the corresponding hierarchy of preorders. We consider finite state or regular processes as well as infinitestate BPA [BK84b] processes. A disti ..."
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Cited by 7 (0 self)
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This paper gives an overview of the computational complexity of all the equivalences in the linear/branching time hierarchy [vG90a] and the preorders in the corresponding hierarchy of preorders. We consider finite state or regular processes as well as infinitestate BPA [BK84b] processes. A distinction
On the Complexity of Bisimulation Problems for Basic Parallel Processes
 In Proc. of ICALP'2000, volume ? of LNCS
, 2000
"... Strong bisimilarity of Basic Parallel Processes (BPP) is decidable, but the best known algorithm has nonelementary complexity [7]. On the other hand, no lower bound for the problem was known. We show that strong bisimilarity of BPP is coNPhard. Weak bisimilarity of BPP is not known to be decidabl ..."
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Cited by 5 (1 self)
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Strong bisimilarity of Basic Parallel Processes (BPP) is decidable, but the best known algorithm has nonelementary complexity [7]. On the other hand, no lower bound for the problem was known. We show that strong bisimilarity of BPP is coNPhard. Weak bisimilarity of BPP is not known to be decidable, but an NP lower bound has been shown in [31]. We improve this result by showing that weak bisimilarity of BPP is \Pi p 2 hard. Finally, we show that the problems if a BPP is regular (i.e., finite) w.r.t. strong and weak bisimilarity are coNPhard and \Pi p 2 hard, respectively.
Weak Bisimilarity and Regularity of BPA is EXPTIMEhard
 In Proccedings of the 10th International Workshop on Expressiveness in Concurrency (EXPRESS’03
, 2002
"... We show that checking weak bisimulation equivalence of two contextfree processes (also called BPAprocesses) is EXPTIMEhard, even under the condition that the processes are normed. Furthermore, checking weak regularity (finiteness up to weak bisimilarity) for contextfree processes is EXPTIMEhard a ..."
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Cited by 3 (0 self)
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We show that checking weak bisimulation equivalence of two contextfree processes (also called BPAprocesses) is EXPTIMEhard, even under the condition that the processes are normed. Furthermore, checking weak regularity (finiteness up to weak bisimilarity) for contextfree processes is EXPTIMEhard as well.
Semantic Reachability
 Electronic Notes in Theoretical Computer Science (ENTCS
, 1997
"... This paper is an approach to combine the reachability problem with semantic notions like bisimulation equivalence. It deals with questions of the following form: Is there a reachable state that is bisimulation equivalent to a given state ? Here we show some decidability results for process algebras ..."
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Cited by 1 (1 self)
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This paper is an approach to combine the reachability problem with semantic notions like bisimulation equivalence. It deals with questions of the following form: Is there a reachable state that is bisimulation equivalent to a given state ? Here we show some decidability results for process algebras and Petri nets. 1 Introduction The reachability problem plays an important role in the theory of concurrent systems. The question is if a given state is reachable from the initial state by a sequence of actions. The complexity of this problem has been extensively studied (for example it is decidable and EXPSPACEhard for general Petri nets and NPcomplete for Basic Parallel Processes (BPP) [4]). Here we generalize the reachability problem by regarding classes of semantically equivalent states instead of single states. The question is now if a state is reachable (from the initial state) that is a member of a given class. In other words: Is it possible to reach a state that is at least semant...
Language Theory and Infinite Graphs
, 2003
"... Automata and language theory study finitely presented mechanisms for generating languages. A language is a family of words. A slight shift in focus is very revealing. Instead of grammars and automata as language generators, one views them as propagators of possibly infinite labelled transition graph ..."
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Automata and language theory study finitely presented mechanisms for generating languages. A language is a family of words. A slight shift in focus is very revealing. Instead of grammars and automata as language generators, one views them as propagators of possibly infinite labelled transition graphs. This is our starting point for pushdown automata. The main goal is to report on a proof of decidability of language equivalence for deterministic pushdown automata that uses both graph theoretic and combinatorial arguments. The main