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Verification on Infinite Structures
, 2000
"... In this chapter, we present a hierarchy of infinite-state systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonly-studied classes of systems such as context-free and pushdown automata, and Petri net processes. We then examine the ..."
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Cited by 90 (2 self)
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In this chapter, we present a hierarchy of infinite-state systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonly-studied classes of systems such as context-free 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 branching-time temporal logics.
Petri Nets, Commutative Context-Free Grammars, and Basic Parallel Processes
, 1997
"... . The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NP-complete. Further consequences are: the uniform word problem for commutative co ..."
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Cited by 65 (6 self)
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. The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NP-complete. Further consequences are: the uniform word problem for commutative context-free grammars is NP-complete; weak-bisimilarity is semidecidable for Basic Parallel Processes. Keywords: Petri nets, Commutative Context-free Grammars, Basic Parallel Processes, Weak bisimilarity. 1. Introduction The reachability problem plays a central role in Petri net theory, and has been studied in numerous papers (see [5] for a comprehensive list of references). In the first part of this paper we study it for the nets in which every transition needs exactly one token to occur. Following [8], we call them communication-free nets, because no cooperation between places is needed in order to fire a transition; every transition is activated by one single token, and the tokens may flow...
Deciding Bisimulation-Like Equivalences with Finite-State Processes
, 1999
"... We show that characteristic formulae for nite-state systems up to bisimulation-like equivalences (e.g., strong and weak bisimilarity) can be given in the simple branching-time temporal logic EF. Since EF is a very weak fragment of the modal µ-calculus, model checking with EF is decidable for many mo ..."
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Cited by 46 (16 self)
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We show that characteristic formulae for nite-state systems up to bisimulation-like equivalences (e.g., strong and weak bisimilarity) can be given in the simple branching-time temporal logic EF. Since EF is a very weak fragment of the modal µ-calculus, model checking with EF is decidable for many more classes of infinite-state systems. This yields a general method for proving decidability of bisimulation-like equivalences between infinite-state processes and finite-state ones. We apply this method to the class of PAD processes, which strictly subsumes PA and pushdown (PDA) processes, showing that a large class of bisimulation-like equivalences (including, e.g., strong and weak bisimilarity) is decidable between PAD and finite-state processes. On the other hand, we also demonstrate that no `reasonable' bisimulation-like equivalence is decidable between state-extended PA processes and finite-state ones. Furthermore, weak bisimilarity with finite-state processes is shown to be undecidable even for state-...
On the Expressiveness and Decidability of Higher-Order Process Calculi
, 2008
"... In higher-order process calculi the values exchanged in communications may contain processes. A core calculus of higher-order concurrency is studied; it has only the operators necessary to express higher-order communications: input prefix, process output, and parallel composition. By exhibiting a ne ..."
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Cited by 20 (8 self)
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In higher-order process calculi the values exchanged in communications may contain processes. A core calculus of higher-order concurrency is studied; it has only the operators necessary to express higher-order communications: input prefix, process output, and parallel composition. By exhibiting a nearly deterministic encoding of Minsky Machines, the calculus is shown to be Turing Complete and therefore its termination problem is undecidable. Strong bisimilarity, however, is proved to be decidable. Further, the main forms of strong bisimilarity for higher-order processes (higher-order bisimilarity, context bisimilarity, normal bisimilarity, barbed congruence) coincide. They also coincide with their asynchronous versions. A sound and complete axiomatization of bisimilarity is given. Finally, bisimilarity is shown to become undecidable if at least four static (i.e., top-level) restrictions are added to the calculus.
Roadmap of Infinite Results
, 2008
"... This paper provides a comprehensive summary of equivalence checking results for infinite-state 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 web-page ..."
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Cited by 19 (0 self)
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This paper provides a comprehensive summary of equivalence checking results for infinite-state 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 web-page
Weak Bisimulation and Model Checking for Basic Parallel Processes
- IN FOUNDATIONS OF SOFTWARE TECHNOLOGY AND THEORETICAL COMPUTER SCIENCE (FST&TCS'96), VOLUME 1180 OF LNCS
, 1996
"... Basic Parallel Processes (BPP) are a natural subclass of CCS infinite-state processes. They are also equivalent to a special class of Petri nets. We show that unlike for general Petri nets, it is decidable if a BPP and a finite-state system are weakly bisimilar. To the best of our knowledge, this i ..."
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Cited by 17 (9 self)
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Basic Parallel Processes (BPP) are a natural subclass of CCS infinite-state processes. They are also equivalent to a special class of Petri nets. We show that unlike for general Petri nets, it is decidable if a BPP and a finite-state system are weakly bisimilar. To the best of our knowledge, this is the first decidability result for weak bisimulation and a non-trivial class of infinite-state systems. We also show that the model checking problem for BPPs and the branching time logic UB- is PSPACE-complete. This settles a conjecture of [4].
Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets
"... Time dependant models have been intensively studied for many reasons, among others because of their applications in software verification and due to the development of embedded platforms where reliability and safety depend to a large extent on the time features. Many of the time dependant models w ..."
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Cited by 16 (2 self)
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Time dependant models have been intensively studied for many reasons, among others because of their applications in software verification and due to the development of embedded platforms where reliability and safety depend to a large extent on the time features. Many of the time dependant models were suggested as real-time extensions of several well-known untimed models. The most studied formalisms include Networks of Timed Automata which extend the model of communicating finite-state machines with a finite number of real-valued clocks, and timed extensions of Petri nets where the added time constructs include e.g. time intervals that are assigned to the transitions (Time Petri Nets) or to the arcs (Timed-Arc Petri Nets). In this paper, we shall semiformally introduce these models, discuss their strengths and weaknesses, and provide an overview of the known results about the relationships among the models.
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 PSPACE-hard. In particular, we show that (1) Weak bisimilarity of pushdown automata and finite automata is PSPACE-hard, even for a small fixed finite automaton, (2) Strong bisimilarity of pushdown automata and finite automata is PSPACE-har ..."
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Cited by 15 (7 self)
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All bisimulation problems for pushdown automata are at least PSPACE-hard. In particular, we show that (1) Weak bisimilarity of pushdown automata and finite automata is PSPACE-hard, even for a small fixed finite automaton, (2) Strong bisimilarity of pushdown automata and finite automata is PSPACE-hard, but polynomial for every fixed finite automaton, (3) Regularity (finiteness) of pushdown automata w.r.t. weak and strong bisimilarity is PSPACE-hard.
Fresh-register automata
- In Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL ’11
, 2011
"... 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 wi ..."
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Cited by 13 (1 self)
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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.
