M.Y. Vardi. Alternating automata: Unifying truth and validity checking for temporal logics. In 14th International Conference on Automated Deduction, Lecture Notes in Arti cial Intelligence 1249, pages 191-206, 1997. 15  Home/Search   Document Not in Database   Summary   Related Articles   Check

....automaton, information logic, hybrid logic 1 Introduction From logic to automata. After the works of B uchi and Rabin [B uc62,Rab69] various classes of automata turned out to be well suited to solve decision procedures for logical problems, including some for temporal logics (see e.g. VW94,Var97,KVW00] for the calculus and its fragments (see e.g. EJ99,SE89,VW86,EJS01,Var98] and for description logics (see e.g. CDGL99,CGL02] to quote three families of logics. For instance, translating formulae in temporal logics to automata is a standard approach for implementing model ....

M. Vardi. Alternating automata: unifying truth and validity checking for temporal logics. In CADE'97, volume 1249 of Lecture Notes in Arti cial Intelligence, pages 191-206. Springer, 1997.

....if in the transition graph there are no cycles containing 2 or more states, and if along each path through the transition graph the colors of the states do not increase. A simple induction shows that a PLTL de nable language can also be recognized by an alternating linear automaton (see e.g. [Var97]) Here we show the other direction, which was independently shown by Rohde [Roh97] Theorem 6. Let A = Q; 0 ; c) be an alternating linear automaton. There is a PLTL formula such that L(A) L( Proof. For 2 B (Q) let A( Q; c) an automaton with an initial formula ....

M.Y. Vardi. Alternating automata: Unifying truth and validity checking for temporal logics. In 14th International Conference on Automated Deduction, Lecture Notes in Articial Intelligence 1249, pages 191-206, 1997. 15

....a bisimulation relation R with (s; s 0 ) 2 R. Coalgebras are often used to model transition systems and automata where the functor determines the kind of system that is being modelled. The following examples visualize this for Kripkestructures (cf. e.g. Gol87, Pop94] alternating automata ([Var97]) and deterministic transition systems (cf. Rut99] 1.3. Example (Kripke structures) Kripke structures are F coalgebras (S; ff) for the functor F = P(Id) Theta f0; 1g AtProp where 1 Functors and Coalgebras 5 AtProp denotes the set of atomic propositions: for each world s 2 S, ff(s) ....

....propositions that hold in s in its second component. 1.4. Example (alternating automata) Let B (S) denote the set of all positive Boolean formulas over S (i.e. Boolean formulas built from elements of S using and ) including the formulas and . Then an alternating Buchi word automaton ([Var97]) is a tuple ( Sigma; S; s 0 ; F in) where Sigma is a finite non empty alphabet, S is a finite non empty set of states, s 0 2 S is an initial state, F in S is a set of accepting states, and : S Theta Sigma B (S) is a partial transition function. Given a word w = a 0 a 1 : ....

M.Y. Vardi, Alternating automata: unifying truth and validity for temporal logics. In: Proc. 14th International Conference on Automated Deduction, W. McCune (ed.), LNCS 1249 (1997), 191-206.

....describes a set of allowed computation trees, which can be described by an automaton over infinite trees. By translating branching time specifications to alternating tree automata, we can reduce satisfiability to the nonemptiness problem and reduce verification to the membership problem [BVW94, Var97]. Solving the nonemptiness problem for an alternating tree automaton is done by translating the automaton to a nondeterministic tree automaton. Deciding the membership of a program in a language of an alternating tree automaton is done by taking the product of the program and the automaton. This ....

M.Y. Vardi. Alternating automata -- unifying truth and validity checking for temporal logics. In W. McCune, editor, Proc. 14th International Conference on Automated Deduction, volume 1249 of Lecture Notes in Artificial Intelligence, pages 191--206. Springer-Verlag, Berlin, july 1997.

....O(j j) such that L(A ) is exactly the set of computations satisfying the formula . 4. 2 Alternating Automata on Infinite Trees Alternating tree automata generalize nondeterministic tree automata and were first introduced in [26] They have recently found usage in computer aided verification [34]. An alternating tree automaton A = h Sigma ; Q; q0 ; ffi; ffi runs on Sigma labelled Upsilon trees (i.e. mappings from Upsilon to Sigma ) It consists of a finite set Q of states, an initial state q0 2 Q, a transition function ffi, and an acceptance condition ff (a condition that ....

M.Y. Vardi. Alternating automata -- unifying truth and validity checking for temporal logics. In W. McCune, editor, Proc. 14th International Conference on Automated Deduction, volume 1249 of Lecture Notes in Artificial Intelligence, pages 191--206. Springer-Verlag, Berlin, july 1997.

....automata theoretic approach used nondeterministic tree automata [9,39,51] The translation from formulas to nondeterministic automata is nontrivial; for example, the translation in [51] is exponential and consists of a sequence of successive translations. As argued in [28] and then utilized in [2,47], it is easier to translate formulas to alternating automata. Alternating tree automata generalize nondeterministic tree automata by allowing multiple successor states to go down along the same branch of the tree. It is known that while the translation from branching temporal logic formulas to ....

M.Y. Vardi. Alternating automata -- unifying truth and validity checking for temporal logics. In W. McCune, editor, Proc. 14th International Conference on Automated Deduction, volume 1249 of Lecture Notes in Artificial Intelligence, pages 191--206. Springer-Verlag, Berlin, july 1997.

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M.Y. Vardi. Alternating automata: Unifying truth and validity checking for temporal logics. In 14th International Conference on Automated Deduction, Lecture Notes in Arti cial Intelligence 1249, pages 191-206, 1997. 15

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Vardi, M., Alternating automata: Unifying truth and validity checking for temporal logics, in: W. McCune, editor, Proceedings of the 14th International Conference on Automated deduction, LNAI 1249 (1997), pp. 191-206. URL http://www.cs.rice.edu/~vardi/papers/cade97.ps.gz

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Vardi, M., Alternating automata: Unifying truth and validity checking for temporal logics, in: W. McCune, editor, Proceedings of the 14th International Conference on Automated deduction, LNAI 1249 (1997), pp. 191-206. URL http://www.cs.rice.edu/~vardi/papers/cade97.ps.gz

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