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86
Languages, Automata, and Logic
 Handbook of Formal Languages
, 1996
"... This paper is a survey on logical aspects of finite automata. Central points are the connection between finite automata and monadic secondorder logic, the EhrenfeuchtFraiss'e technique in the context of formal language theory, finite automata on !words and their determinization, and a selfcontai ..."
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Cited by 182 (4 self)
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This paper is a survey on logical aspects of finite automata. Central points are the connection between finite automata and monadic secondorder logic, the EhrenfeuchtFraiss'e technique in the context of formal language theory, finite automata on !words and their determinization, and a selfcontained proof of the "Rabin Tree Theorem". Sections 5 and 6 contain material presented in a lecture series to the "Final Winter School of AMICS" (Palermo, February 1996). A modified version of the paper will be a chapter of the "Handbook of Formal Language Theory", edited by G. Rozenberg and A. Salomaa, to appear in SpringerVerlag. Keywords: Finite automata, monadic secondorder logic, firstorder logic, regular languages, starfree languages, tree automata, EhrenfeuchtFraiss'e game, !automata, temporal logic, Buchi automata, Rabin tree automata, determinacy, decidable theories. Contents 1 Introduction 1 2 Models and Formulas 2 2.1 Words, Trees, and Graphs as Models . . . . . . . . . . ....
On the Expressive Completeness of the Propositional MuCalculus With Respect to Monadic Second Order Logic
, 1996
"... . Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over tran ..."
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Cited by 65 (3 self)
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. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...
Deriving Petri Nets from Finite Transition Systems
 IEEE Transactions on Computers
, 1998
"... This paper presents a novel method to derive a Petri net from any specification model that can be mapped into a statebased representation with arcs labeled with symbols from an alphabet of events (a Transition System, TS). The method is based on the theory of regions for Elementary Transition Syst ..."
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Cited by 61 (7 self)
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This paper presents a novel method to derive a Petri net from any specification model that can be mapped into a statebased representation with arcs labeled with symbols from an alphabet of events (a Transition System, TS). The method is based on the theory of regions for Elementary Transition Systems (ETS). Previous work has shown that for any ETS there exists a Petri net with minimum transition count (one transition for each label) with a reachability graph isomorphic to the original Transition System. The method makes use of the following three mechanisms, providing a framework for synthesis of safe Petri nets from arbitrary TSs. Firstly, the requirement of isomorphism is relaxed to a "more behavioural" form of equivalence, bisimulation of TSs, thus extending the class of synthesizable TSs to a new class called ExcitationClosed Transition Systems(ECTS). Secondly, previous work required an oracle (usually the designer) to identify sets of events labeling the TS that were mapped to...
An Unfolding Algorithm for Synchronous Products of Transition Systems
 In Proceedings of the 10th International Conference on Concurrency Theory (Concur'99
, 1999
"... The unfolding method, initially introduced for systems modelled by Petri nets, is applied to synchronous products of transition systems, a model introduced by Arnold [2]. An unfolding procedure is provided which exploits the product structure of the model. Its performance is evaluated on a set of be ..."
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Cited by 39 (2 self)
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The unfolding method, initially introduced for systems modelled by Petri nets, is applied to synchronous products of transition systems, a model introduced by Arnold [2]. An unfolding procedure is provided which exploits the product structure of the model. Its performance is evaluated on a set of benchmarks. 1 Introduction The unfolding method is a partial order approach to the verification of concurrent systems introduced by McMillan in his Ph. D. Thesis [6]. A finite state system, modelled as a Petri net, is unfolded to yield an equivalent acyclic net with a simpler structure. This net is usually infinite, and so in general it cannot be used for automatic verification. However, it is possible to construct a complete finite prefix of it containing as much information as the infinite net itself: Loosely speaking, this prefix already contains all the reachable states of the system. The prefix is usually far smaller than the state space, and often smaller than a BDD representation of ...
Weighted automata and weighted logics
 In Automata, Languages and Programming – 32nd International Colloquium, ICALP 2005
, 2005
"... Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speechtotext processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We g ..."
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Cited by 39 (7 self)
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Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speechtotext processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We generalize Büchi’s and Elgot’s fundamental theorems to this quantitative setting. We introduce a weighted version of MSO logic and prove that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with our weighted logic. We also consider weighted firstorder logic and show that aperiodic series coincide with the firstorder definable ones, if the semiring is locally finite, commutative and has some aperiodicity property. 1
Products of Modal Logics, Part 1
 LOGIC JOURNAL OF THE IGPL
, 1998
"... The paper studies manydimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: pmorphisms, the finite depth method, normal forms, ..."
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Cited by 36 (1 self)
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The paper studies manydimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: pmorphisms, the finite depth method, normal forms, filtrations. Applications to first order predicate logics are considered too. The introduction and the conclusion contain a discussion of many related results and open problems in the area.
A Logical Characterization of Bisimulation for Labeled Markov Processes
, 1998
"... This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In ..."
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Cited by 34 (11 self)
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This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In the present paper we study the logical characterization of probabilistic bisimulation for such general systems. This study revealed some unexpected results even for discrete probabilistic systems. ffl Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be characterized by several inequivalent logics; we report five in this paper. ffl We do not need any finite branching assumption yet there is no need of infinitary conjunction. ffl The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts abou...
Hierarchical Interfacebased Supervisory Control: AIP Example for Parallel Case
, 2001
"... In this report we present a large manufacturing example (7:01 10 states) that uses the Hierarchical Interfacebased Supervisory Control method that we presented in [14]. We discuss the application of our method to the Atelier Interetablissement de Productique (AIP), a highly automated manufactu ..."
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Cited by 30 (7 self)
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In this report we present a large manufacturing example (7:01 10 states) that uses the Hierarchical Interfacebased Supervisory Control method that we presented in [14]. We discuss the application of our method to the Atelier Interetablissement de Productique (AIP), a highly automated manufacturing system. We describe the system, and our supervisor design, closing by discussing the results of successfully applying our method to show that the system is nonblocking and that our supervisors are controllable. This example demonstrates that our method can be applied to interesting systems of realistic complexity that were previously far beyond our means.
Foundations of the Trace Assertion Method of Module Interface Specification
, 2000
"... The trace assertion method is a formal state machine based method for specifying module interfaces. A module interface specification treats the module as a blackbox, identifying all module's ..."
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Cited by 17 (1 self)
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The trace assertion method is a formal state machine based method for specifying module interfaces. A module interface specification treats the module as a blackbox, identifying all module's
Formal Verification of Safety Properties in Timed Circuits
, 2000
"... The incorporation of timing makes circuit verification computationally expensive. This paper proposes a new approach for the verification of timed circuits. Rather than calculating the exact timed state space, a conservative overestimation that fulfills the property under verification is derived. Ti ..."
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Cited by 17 (6 self)
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The incorporation of timing makes circuit verification computationally expensive. This paper proposes a new approach for the verification of timed circuits. Rather than calculating the exact timed state space, a conservative overestimation that fulfills the property under verification is derived. Timing analysis with absolute delays is efficiently performed at the level of event structures and transformed into a set of relative timing constraints. With this approach, conventional symbolic techniques for reachability analysis can be efficiently combined with timing analysis. Moreover, the set of timing constraints used to prove the correctness of the circuit can also be reported for backannotation purposes. Some preliminary results obtained by a naive implementation of the approach show that systems with more than 10^6 untimed states can be verified.