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60
PartialOrder Methods for the Verification of Concurrent Systems  An Approach to the StateExplosion Problem
, 1995
"... Statespace exploration techniques are increasingly being used for debugging and proving correct finitestate concurrent reactive systems. The reason for this success is mainly the simplicity of these techniques. Indeed, they are easy to understand, easy to implement and, last but not least, easy to ..."
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Cited by 289 (11 self)
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Statespace exploration techniques are increasingly being used for debugging and proving correct finitestate concurrent reactive systems. The reason for this success is mainly the simplicity of these techniques. Indeed, they are easy to understand, easy to implement and, last but not least, easy to use: they are fully automatic. Moreover, the range of properties that they can verify has been substantially broadened thanks to the development of modelchecking methods for various temporal logics. The main limit of statespace exploration verification techniques is the often excessive size of the state space due, among other causes, to the modeling of concurrency by interleaving. However, exploring all interleavings of concurrent events is not a priori necessary for verification: interleavings corresponding to the same concurrent execution contain related information. One can thus hope to be able to verify properties of a concurrent system without exploring all interleavings of its concu...
An automatatheoretic approach to linear temporal logic
 Logics for Concurrency: Structure versus Automata, volume 1043 of Lecture Notes in Computer Science
, 1996
"... Abstract. The automatatheoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over s ..."
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Cited by 217 (23 self)
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Abstract. The automatatheoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over some alphabet. Thus,programs and specificationscan be viewed as descriptions of languagesover some alphabet. The automatatheoretic perspective considers the relationships between programs and their specifications as relationships between languages.By translating programs and specifications to automata, questions about programs and their specifications can be reduced to questions about automata. More specifically, questions such as satisfiability of specifications and correctness of programs with respect to their specifications can be reduced to questions such as nonemptiness and containment of automata. Unlike classical automata theory, which focused on automata on finite words, the applications to program specification, verification, and synthesis, use automata on infinite words, since the computations in which we are interested are typically infinite. This paper provides an introduction to the theory of automata on infinite words and demonstrates its applications to program specification, verification, and synthesis. 1
Realtime logics: complexity and expressiveness
 INFORMATION AND COMPUTATION
, 1993
"... The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via ..."
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Cited by 202 (16 self)
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The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by! regular sets. Several more expressive variants are proved to be highly undecidable. This framework allows us to classify a wide variety of realtime logics according to their complexity and expressiveness. Indeed, it follows that most formalisms proposed in the literature cannot be decided. We are, however, able to identify two elementary realtime temporal logics as expressively complete fragments of the theory of timed state sequences, and we present tableaubased decision procedures for checking validity. Consequently, these two formalisms are wellsuited for the speci cation and veri cation of realtime systems.
Efficient Büchi Automata from LTL Formulae
 CAV 2000, LNCS 1855:247–263
, 2000
"... We present an algorithm to generate small Büchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure, and simplification of the resulting automaton. We present a translation procedure that is optimal w ..."
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Cited by 103 (12 self)
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We present an algorithm to generate small Büchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure, and simplification of the resulting automaton. We present a translation procedure that is optimal within a certain class of translation procedures. The simplification algorithm can be used for Buchi automata in general. It reduces the number of states and transitions, as well as the number and size of the accepting setspossibly reducing the strength of the resulting automaton. This leads to more efficient model checking of lineartime logic formulae. We compare our method to previous work, and show that it is significantly more efficient for both random formulae, and formulae in common use and from the literature.
EventClock Automata: A Determinizable Class of Timed Automata
 Theoretical Computer Science
, 1999
"... We introduce eventrecording automata. An eventrecording automaton is a timed automaton that contains, for every event a, a clock that records the time of the last occurrence of a. The class of eventrecording automata is, on one hand, expressive enough to model (finite) timed transition systems an ..."
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Cited by 91 (3 self)
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We introduce eventrecording automata. An eventrecording automaton is a timed automaton that contains, for every event a, a clock that records the time of the last occurrence of a. The class of eventrecording automata is, on one hand, expressive enough to model (finite) timed transition systems and, on the other hand, determinizable and closed under all boolean operations. As a result, the language inclusion problem is decidable for eventrecording automata. We present a translation from timed transition systems to eventrecording automata, which leads to an algorithm for checking if two timed transition systems have the same set of timed behaviors. We also consider eventpredicting automata, which contain clocks that predict the time of the next occurrence of an event. The class of eventclock automata, which contain both eventrecording and eventpredicting clocks, is a suitable specification language for realtime properties. We provide an algorithm for checking if a timed automa...
Specifying Timed State Sequences in Powerful Decidable Logics and Timed Automata (Extended Abstract)
 LNCS 863
, 1994
"... ) Thomas Wilke ChristianAlbrechtsUniversitat zu Kiel, Institut fur Informatik und Praktische Mathematik, D24098 Kiel, Germany ? Abstract. A monadic secondorder language, denoted by Ld, is introduced for the specification of sets of timed state sequences. A fragment of Ld, denoted by L $ d, is ..."
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Cited by 52 (0 self)
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) Thomas Wilke ChristianAlbrechtsUniversitat zu Kiel, Institut fur Informatik und Praktische Mathematik, D24098 Kiel, Germany ? Abstract. A monadic secondorder language, denoted by Ld, is introduced for the specification of sets of timed state sequences. A fragment of Ld, denoted by L $ d, is proved to be expressively complete for timed automata (Alur and Dill), i. e., every timed regular language is definable by a L $ dformula and every L $ dformula defines a timed regular language. As a consequence the satisfiability problem for L $ d is decidable. Timed temporal logics are shown to be effectively embeddable into L $ d and hence turn out to have a decidable theory. This applies to TL \Gamma (Manna and Pnueli) and EMITLp , which is obtained by extending the logic MITLp (Alur and Henzinger) by automata operators (Sistla, Vardi, and Wolper). For every positive natural number k the full monadic secondorder logic Ld and L $ d are equally expressive modulo the set of timed...
ModelChecking of Causality Properties
, 1995
"... A temporal logic for causality (Tlc) is introduced. The logic is interpreted over causal structures corresponding to partial order executions of programs. For causal structures describing the behavior of a finite fixed set of processes, a Tlcformula can, equivalently, be interpreted over their line ..."
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Cited by 43 (10 self)
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A temporal logic for causality (Tlc) is introduced. The logic is interpreted over causal structures corresponding to partial order executions of programs. For causal structures describing the behavior of a finite fixed set of processes, a Tlcformula can, equivalently, be interpreted over their linearizations. The main result of the paper is a tableau construction that gives a singlyexponential translation from a Tlc formula ' to a Streett automaton that accepts the set of linearizations satisfying '. This allows both checking the validity of Tlc formulas and modelchecking of program properties. As the logic Tlc does not distinguish among different linearizations of the same partial order execution, partial order reduction techniques can be applied to alleviate the statespace explosion problem of modelchecking. 1 Introduction One of the most successful techniques for automatic verification of finitestate systems has been modelchecking . A modelchecking algorithm decides wheth...
Dynamic Linear Time Temporal Logic
 IN ANNALS OF PURE AND APPLIED LOGIC
, 1997
"... A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S ..."
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Cited by 42 (3 self)
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A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S1S, the monadic secondorder theory of !sequences. In fact a sublogic of DLTL which corresponds to propositional dynamic logic with a linear time semantics is already as expressive as S1S. We pin down in an obvious manner the sublogic of DLTL which correponds to the first order fragment of S1S. We show that DLTL has an exponential time decision procedure. We also obtain an axiomatization of DLTL. Finally, we point to some natural extensions of the approach presented here for bringing together propositional dynamic and temporal logics in a linear time setting.
Complexity of Automata on Infinite Objects
, 1989
"... We investigate in this thesis problems concerning the complexity of translation among, and decision procedure for, different types of finite automata on infinite words (! automata). An !automaton is the same as usual finite automata over finite strings but it accepts or rejects infinite strings. I ..."
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Cited by 38 (0 self)
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We investigate in this thesis problems concerning the complexity of translation among, and decision procedure for, different types of finite automata on infinite words (! automata). An !automaton is the same as usual finite automata over finite strings but it accepts or rejects infinite strings. It may be either deterministic or nondeterministic, and may have different types of acceptance condition. Our main result is a new, simpler, determinization construction that yields a single exponent upper bound for the translation of any Buchi nondeterministic !automaton into a deterministic !auomaton. This construction is optimal. We also look at the complexity of the complementation problem for different types of !automata, and, among other results, obtain an exponential complementation for Streett !automata. These results can be used to improve the complexity of decision procedures for different logics that use automatatheoretic techniques. Acknowledgement First and foremost, I o...
Optimizations for LTL synthesis
 In 6th Conference on Formal Methods in Computer Aided Design (FMCAD’06
, 2006
"... Abstract — We present an approach to automatic synthesis of specifications given in Linear Time Logic. The approach is based on a translation through universal coBüchi tree automata and alternating weak tree automata [1]. By careful optimization of all intermediate automata, we achieve a major impr ..."
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Cited by 36 (9 self)
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Abstract — We present an approach to automatic synthesis of specifications given in Linear Time Logic. The approach is based on a translation through universal coBüchi tree automata and alternating weak tree automata [1]. By careful optimization of all intermediate automata, we achieve a major improvement in performance. We present several optimization techniques for alternating tree automata, including a gamebased approximation to language emptiness and a simulationbased optimization. Furthermore, we use an incremental algorithm to compute the emptiness of nondeterministic Büchi tree automata. All our optimizations are computed in time polynomial in the size of the automaton on which they are computed. We have applied our implementation to several examples and show a significant improvement over the straightforward implementation. Although our examples are still small, this work constitutes the first implementation of a synthesis algorithm for full LTL. We believe that the optimizations discussed here form an important step towards making LTL synthesis practical. I.