M.Y. Vardi. Nontraditional applications of automata theory. In Proc. International Symp. on Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 575--597. Springer-Verlag, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....their expressiveness, in that we cannot express sets of trees with real relationship between subtrees, such as sets of the form ff(a ; c )jn 2 Ng. They become very complex when we want to add infinite trees, whereas considering infinite behaviors is known to be important in static analysis [21, 24, 6]. When we look closely at those analysis, we see that, due to some lack of expressiveness in the representations, the actual behavior of programs is always approximated in practice. We know a theory to deal smartly with approximations, namely abstract interpretation [7, 8] And in this framework, ....

Vardi, M. Y. Nontraditional applications of automata theory. In Theoretical Aspects of Computer Software (April 1994), M. Hagiya and J. C. Mitchell, Eds., vol. 789 of Lecture Notes in Computer Science, Springer-Verlag, pp. 575--597.

.... about acceptance of sequences by a Buchi automaton (Buchi Theorem) The resulting theory is fundamental for those areas in computer science where non terminating computations are studied, for instance modal logics of programs and specification and verification of concurrent systems (e.g. see [15]) This paper is an attempt to set a correspondence between languages accepted by systolic automata and suitable (proper) extensions of MSO[ Systolic automata (see [8] for a survey) are synchronous networks of (memoryless) processors working in discrete time. These automata have been the main ....

M.Y. Vardi, Nontraditional applications of automata theory, LNCS Vol. 789 (Springer, Berlin,1994), 575--597.

....and Rabin [12] introduced this theory, which, more recently, turned out to be an important source of tools for synthesis and veri cation of nonterminating computer programs. A recent survey on automata on in nite objects is [15] Connections with Temporal Logic have been particularly successful [4,7,16,17]. The main results in this perspective consist of reducing temporal logic problems to decidable problems in the automata theory eld. To model and verify real time systems (that is, systems that interact with physical processes and whose correct running crucially depends upon real time ....

M.Y. Vardi. Nontraditional applications of automata theory. In Proceedings of the International Symposium TACS'94, LNCS 789, pages 575-597. SpringerVerlag, 1994.

....theory of finite automata on sequences and trees has been an important source of tools for the specification and verification of computer programs. In particular, the connections between the theory of automata on objects and Temporal Logic have been extensively and profitably investigated ([6, 11, 24, 25, 26]) These connections rely on the consideration that sequences and trees whose symbols are truth values of a finite set of atomic propositions can represent nonterminating computations and sets of nonterminating computations. On the other hand, given a formula in a linear time or branching time ....

M.Y. Vardi, "Nontraditional Applications of Automata Theory", Proc. of the International Symposium TACS'94, Lecture Notes in Computer Science, Vol. 789 (Springer-Verlag, 1994) 575 - 597.

....of stochastic systems may shed some new light on these issues. Beyond VLSI Many of the ideas that we have put forth in this dissertation have a very broad applicability. For example, there may be applications of the paradigms developed for hardware verification to database query optimization [116]. Similarly, results from finite state CHAPTER 9. CONCLUSIONS 110 machine synthesis can be used in control theory [5] the analysis of stochastic systems may lead to a better understanding of performance optimization. Many engineers and scientists are not aware of the power of logic. In order to ....

M. Vardi. Non-traditional Applications of Automata Theory. In Theoretical Aspects of Computer Science, 1994.

....than even nondeterminism. The idea is to allow the requirement of several successor states (going on to produce accepting runs) after a given state as well as just the existence of one accepting continuation. Many of the useful results for alternating automata on structures are presented in [Var94] For a set S, let B (S) be the set of positive Boolean formulae over S, that is the set of formulae built from atoms in S via and . We also allow truth and false. Given a subset R S we say that R satisfies OE 2 B (S) iff the propositional truth assignment V satisfies OE where V ....

....the truth of the quantified variable at each step. The overall complexity is determined by the determinization procedure and, as shown in [Saf88] it is single exponential. 5.2. 2 Via alternating automata The easy translation from PLTL to an alternating Buchi automaton is described in [MSS88] Var94] and [Var96] Suppose that we are given a formula OE using only atoms from the finite set P . The alternating Buchi automaton A = S; s 0 ; ae; F ) recognizes sequences of elements of 2 P . The set S of states of the corresponding automaton is just the set of subformulae of OE and their ....

M. Vardi. Nontraditional applications of automata theory. In Proceedings of International Symposium on the Theoretical Aspects of Computer Software, volume 789 of LNCS, pages 575--597. Springer-Verlag, 1994.

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M.Y. Vardi. Nontraditional applications of automata theory. In Proc. International Symp. on Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 575--597. Springer-Verlag, 1994.

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M. Vardi. Nontraditional applications of automata theory. In Proc. STACS, LNCS 789, pages 575--597, 1994.

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M.Y. Vardi. Nontraditional applications of automata theory. In Proc. International Symp. on Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 575--597. Springer-Verlag, 1994.

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M.Y. Vardi. Nontraditional applications of automata theory. In Proc. Inte'l Symp. on Theoretical Aspects of Computer Software, volume 789, pages 575--597. LNCS, 1994.

.... approach did not seem to be applicable to branching time truth checking, which in many cases can be done in linear running time [CES86, QS81, Cle93] Recently it has been shown that if one uses alternating automata rather than nondeterministic automata, then these problems can be solved [Var94, BVW94]. Alternating automata generalize the standard notion of nondeterministic automata by allowing several successor states to go down along the same word or the same branch of the tree. In this paper we show that alternating automata offer the key to a comprehensive and satisfactory ....

....be used to derive truth and validity checking algorithms for both linear and branching temporal logics. The key observation is that while the translation from temporal logic formulas to nondeterministic automata is exponential [VW86b, VW94] the translation to alternating automata is linear [MSS88, EJ91, Var94, BVW94]. Thus, the advantage of alternating automata is that they enable one to decouple the logic from the algorithmics. The translations from formulas to automata handle the logic, and the algorithms are then applied to the automata. 2 Automata Theory 2.1 Words and Trees We are given a finite ....

[Article contains additional citation context not shown here]

M.Y. Vardi. Nontraditional applications of automata theory. In Theoretical Aspects of Computer Software, Proc. Int. Symposium (TACS'94), volume 789 of Lecture Notes in Computer Science, pages 575--597. Springer-Verlag, Berlin, 1994.

....that the automaton should accept the suffix of the word either from state q1 or from both states q2 and q3 . Since the combinatorial structure of alternating automata is rich, translating specifications to alternating automata is much simpler than translating them to nondeterministic automata [Var94]. Alternating automata enable a complete partition between the logical and the algorithmic aspects of reasoning about programs, and they give rise to cleaner and simpler verification algorithms [Var96] The rich structure of alternating automata also makes them more succinct. For example, ....

M.Y. Vardi. Nontraditional applications of automata theory. In Proc. Int'l Symp. on Theoretical Aspects of Computer Software, volume 789, pages 575--597. Lecture Notes in Computer Science, Springer-Verlag, 1994.

.... approach did not seem to be applicable to branching time model checking, which in many cases can be done in linear running time [CES86, QS81, Cle93] Recently it has been shown that if one uses alternating automata rather than nondeterministic automata, then these problems can be solved [Var94, BVW94]. Alternating automata generalize the standard notion of nondeterministic automata by allowing several successor states to go down along the same word or the same branch of the tree. In this paper we argue that alternating automata offer the key to a comprehensive and satisfactory ....

....automata can be used to derive modelchecking algorithms for both linear and branching temporal logics. The key observation is that while the translation from temporal logic formulas to nondeterministic automata is exponential [VW86b, VW94] the translation to alternating automata is linear [MSS88, EJ91, Var94, BVW94]. Thus, the advantage of alternating automata is that they enable one to decouple the logic from the combinatorics. The translations from formulas to automata handle the logic, and the algorithms that handle the automata are essentially combinatorial. 2 Automata Theory 2.1 Words and Trees We are ....

[Article contains additional citation context not shown here]

M.Y. Vardi. Nontraditional applications of automata theory. In TheoreticalAspects of Computer Software, Proc. Int. Symposium (TACS'94), volume 789 of Lecture Notes in Computer Science, pages 575--597. Springer-Verlag, Berlin, 1994.

....is nonelementary, i.e. it may involve an unbounded stack of exponentials (that is, the complexity bound is of the form 2 : 2 n ; where the height of the stack is n. The following theorem establishes a very simple translation between LTL and alternating Buchi automata. Theorem 22. [MSS88, Var94] Given an LTL formula , one can build an alternating B uchi automaton A = Sigma; S; s 0 ; ae; F ) where Sigma = 2 Prop and jSj is in O(j j) such that L (A ) is exactly the set of computations satisfying the formula . Proof: The set S of states consists of all subformulas of and ....

M.Y. Vardi. Nontraditional applications of automata theory. In TheoreticalAspects of Computer Software, Proc. Int. Symposium (TACS'94), volume 789 of Lecture Notes in Computer Science, pages 575--597. Springer-Verlag, Berlin, 1994.

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M. Y. Vardi. Nontraditional applications of automata theory. In Proceedings of the International Conference on Theoretical Aspects of Computer Software (TACS 1994.

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Moshe Y. Vardi. Nontraditional applications of automata theory. In Theoretical Aspects of Computer Software, vol. 789 of LNCS, pp. 575--597, 1994. 40

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Moshe Y. Vardi. Nontraditional applications of automata theory. In Theoretical Aspects of Computer Software, vol. 789 of LNCS, pp. 575--597, 1994.

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Moshe Y. Vardi. Nontraditional applications of automata theory. In Theoretical Aspects of Computer Software, vol. 789 of LNCS, pp. 575--597, 1994. 37

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