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19
Safraless Decision Procedures
, 2005
"... The automatatheoretic approach is one of the most fundamental approaches to developing decision procedures in mathematical logics. To decide whether a formula in a logic with the treemodel property is satisfiable, one constructs an automaton that accepts all (or enough) tree models of the formu ..."
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Cited by 50 (19 self)
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The automatatheoretic approach is one of the most fundamental approaches to developing decision procedures in mathematical logics. To decide whether a formula in a logic with the treemodel property is satisfiable, one constructs an automaton that accepts all (or enough) tree models of the formula and then checks that the language of this automaton is nonempty. The standard approach translates formulas into alternating parity tree automata, which are then translated, via Safra's determinization construction, into nondeterministic parity automata. This approach is not amenable to implementation because of the difficulty of implementing Safra's construction and the nonemptiness test for nondeterministic parity tree automata. In this
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.
Safraless compositional synthesis
 In CAV
, 2006
"... Abstract. In automated synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. In spite of the rich theory developed for system synthesis, little of this theory has been reduced to practice. This is in contrast with of modelchecking theory, which has l ..."
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Cited by 17 (6 self)
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Abstract. In automated synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. In spite of the rich theory developed for system synthesis, little of this theory has been reduced to practice. This is in contrast with of modelchecking theory, which has led to industrial development and use of formal verification tools. We see two main reasons for the lack of practical impact of synthesis. The first is algorithmic: synthesis involves Safra’s determinization of automata on infinite words, and a solution of parity games with highly complex state spaces; both problems have been notoriously resistant to efficient implementation. The second is methodological: current theory of synthesis assumes a single comprehensive specification. In practice, however, the specification is composed of a set of properties, which is typically evolving – properties may be added, deleted, or modified. In this work we address both issues. We extend the Safraless synthesis algorithm of Kupferman and Vardi so that it handles LTL formulas by translating them to nondeterministic generalized Büchi automata. This leads to an exponential improvement in the complexity of the algorithm. Technically, our algorithm reduces the synthesis problem to the emptiness problem of a nondeterministic Büchi tree automaton A. The generation of A avoids determinization, avoids the parity acceptance condition, and is based on an analysis of runs of universal generalized coBüchi tree automata. The clean and simple structure of A enables optimizations and a symbolic implementation. In addition, it makes it possible to use information gathered during the synthesis process of properties in the process of synthesizing their conjunction. 1
From Complementation to Certification
, 2004
"... In the automatatheoretic approach to model checking we check the emptiness of the product of a system S with an automaton A: for the complemented specification. This gives rise to two automatatheoretic problems: complementation of word automata, which is used in order to generate A: , and the ..."
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Cited by 14 (3 self)
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In the automatatheoretic approach to model checking we check the emptiness of the product of a system S with an automaton A: for the complemented specification. This gives rise to two automatatheoretic problems: complementation of word automata, which is used in order to generate A: , and the emptiness problem, to which model checking is reduced. Both problems have numerous other applications, and have been extensively studied for nondeterministic Buchi word automata (NBW). Nondeterministic generalized Buchi word automata (NGBW) have become popular in specification and verification and are now used in applications traditionally assigned to NBW. This is due to their richer acceptance condition, which leads to automata with fewer states and a simpler underlying structure.
BÜCHI COMPLEMENTATION MADE TIGHT
, 2009
"... The precise complexity of complementing Büchi automata is an intriguing and long standing problem. While optimal complementation techniques for finite automata are simple – it suffices to determinize them using a simple subset construction and to dualize the acceptance condition of the resulting au ..."
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Cited by 13 (1 self)
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The precise complexity of complementing Büchi automata is an intriguing and long standing problem. While optimal complementation techniques for finite automata are simple – it suffices to determinize them using a simple subset construction and to dualize the acceptance condition of the resulting automaton – Büchi complementation is more involved. Indeed, the construction of an EXPTIME complementation procedure took a quarter of a century from the introduction of Büchi automata in the early 60s, and stepwise narrowing the gap between the upper and lower bound to a simple exponent (of (6e) n for Büchi automata with n states) took four decades. While the distance between the known upper (O ` (0.96 n) n ´ ) and lower (Ω ` (0.76 n) n ´ ) bound on the required number of states has meanwhile been significantly reduced, an exponential factor remains between them. Also, the upper bound on the size of the complement automaton is not linear in the bound of its state space. These gaps are unsatisfactory from a theoretical point of view, but also because Büchi complementation is a useful tool in formal verification, in particular for the language containment problem. This paper proposes a Büchi complementation algorithm whose complexity meets, modulo a quadratic (O(n 2)) factor, the known lower bound for Büchi complementation. It thus improves over previous constructions by an exponential factor and concludes the quest for optimal Büchi complementation algorithms.
IMPROVED ALGORITHMS FOR THE AUTOMATABASED APPROACH TO MODELCHECKING
, 2009
"... We propose and evaluate new algorithms to solve the universality and language inclusion problems for nondeterministic Büchi automata. To obtain those new algorithms, we establish the existence of preorders that can be exploited to efficiently evaluate fixed points on the automata defined during th ..."
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Cited by 12 (6 self)
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We propose and evaluate new algorithms to solve the universality and language inclusion problems for nondeterministic Büchi automata. To obtain those new algorithms, we establish the existence of preorders that can be exploited to efficiently evaluate fixed points on the automata defined during the complementation step (that we keep implicit in our approach). We evaluate the performance of the new algorithm to check the universality of Büchi automata using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, our algorithm outperforms the standard ones by several orders of magnitude.
Antichains: Alternative Algorithms for LTL Satisfiability and ModelChecking
"... The linear temporal logic (LTL) was introduced by Pnueli as a logic to express properties over the computations of reactive systems. Since this seminal work, there have been a large number of papers that have studied deductive systems and algorithmic methods to reason about the correctness of reac ..."
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Cited by 12 (8 self)
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The linear temporal logic (LTL) was introduced by Pnueli as a logic to express properties over the computations of reactive systems. Since this seminal work, there have been a large number of papers that have studied deductive systems and algorithmic methods to reason about the correctness of reactive programs with regard to LTL properties. In this paper, we propose new efficient algorithms for LTL satisfiability and modelchecking. Our algorithms do not construct nondeterministic automata from LTL formulas but work directly with alternating automata using efficient exploration techniques based on antichains.
Complementation constructions for nondeterministic automata on infinite words
 In Proc. 11th International Conf. on Tools
, 2005
"... Abstract. The complementation problem for nondeterministic automata on infinite words has numerous applications in formal verification. In particular, the languagecontainment problem, to which many verification problems are reduced, involves complementation. Traditional optimal complementation cons ..."
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Cited by 8 (3 self)
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Abstract. The complementation problem for nondeterministic automata on infinite words has numerous applications in formal verification. In particular, the languagecontainment problem, to which many verification problems are reduced, involves complementation. Traditional optimal complementation constructions are quite complicated and have not been implemented. Recently, we have developed an analysis techniques for runs of coBüchi and generalized coBüchi automata and used the analysis to describe simpler optimal complementation constructions for Büchi and generalized Büchi automata. In this work, we extend the analysis technique to Rabin and Streett automata, and use the analysis to describe novel and simple complementation constructions for them. 1
Avoiding determinization
 In Proc. 21st IEEE Symp. on Logic in Computer Science
, 2006
"... Automata on infinite objects are extensively used in system specification, verification, and synthesis. While some applications of the automatatheoretic approach have been well accepted by the industry, some have not yet been reduced to practice. Applications that involve determinization of automat ..."
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Cited by 7 (2 self)
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Automata on infinite objects are extensively used in system specification, verification, and synthesis. While some applications of the automatatheoretic approach have been well accepted by the industry, some have not yet been reduced to practice. Applications that involve determinization of automata on infinite words have been doomed to belong to the second category. This has to do with the intricacy of Safra’s optimal determinization construction, the fact that the state space that results from determinization is awfully complex and is not amenable to optimizations and a symbolic implementation, and the fact that determinization requires the introduction of acceptance conditions that are more complex than the Büchi acceptance condition. Examples of applications that involve determinization and belong to the unfortunate second category include model checking of ωregular properties, decidability of branching temporal logics, and synthesis and control of open systems. We offer an alternative to the standard automatatheoretic approach. The crux of our approach is avoiding determinization. Our approach goes instead via universal coBüchi automata. Like nondeterministic automata, universal automata may have several runs on every input. Here, however, an input is accepted if all of the runs are accepting. We show how the use of universal automata simplifies significantly known complementation constructions for automata on infinite words, known decision procedures for branching temporal logics, known synthesis algorithms, and other applications that are now based on determinization. Our algorithms are less difficult to implement and have practical advantages like being amenable to optimizations and a symbolic implementation.
Antichain Algorithms for Finite Automata
"... We present a general theory that exploits simulation relations on transition systems to obtain antichain algorithms for solving the reachability and repeated reachability problems. Antichains are more succinct than the sets of states manipulated by the traditional fixpoint algorithms. The theory ju ..."
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Cited by 5 (3 self)
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We present a general theory that exploits simulation relations on transition systems to obtain antichain algorithms for solving the reachability and repeated reachability problems. Antichains are more succinct than the sets of states manipulated by the traditional fixpoint algorithms. The theory justifies the correctness of the antichain algorithms, and applications such as the universality problem for finite automata illustrate efficiency improvements. Finally, we show that new and provably better antichain algorithms can be obtained for the emptiness problem of alternating automata over finite and infinite words.