Reasoning about the past with two-way automata

Vardi, Moshe Y.

doi:10.1007/bfb0055090

Cited by 244 publications

(253 citation statements)

References 37 publications

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“…As in the linear framework, one can strengthen these extensions by using more powerful automata, in particular two-way and alternating ones. Since it is possible to remove bidirectionality and alternation also in the branching framework [Var98], our treatment of ETL £ ¡ should work here as well. Its implementation, however, is going to be much more complicated in the branching framework.…”

Section: Discussionmentioning

confidence: 99%

“…So, ETL £ ¢ extends ETLc in two important aspects. On the other hand, the two succinctness results are not additive: there is an exponential translation of two-way alternating Büchi automata to one-way nondeterministic Büchi automata [Var98].…”

mentioning

confidence: 99%

“…For that, we first remove the hesitation and get a Büchi automaton, and then combine techniques for removing alternation [MS95] with techniques for removing bidirectionality [Var88]. The fact we deal with hesitant word automata makes the procedure much simpler than the one required for the translation of two-way alternating parity tree automata to one-way nondeterministic parity tree automata [Var98]. All in all, given an ETL can be solved in polynomial space.…”

mentioning

confidence: 99%

“…We describe how to transform the intermediate 2AHW to 1NBW. In [Var98], Vardi translates 2-way alternating parity tree automata to 1-way nondeterministic parity tree automata. Since £ ¡ can be defined as a parity automaton, and since words are a special case of trees, one could use the transformation in [Var98].…”

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confidence: 99%

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Extended Temporal Logic Revisited

Kupferman

Piterman

Vardi

2001

Lecture Notes in Computer Science

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Abstract.A key issue in the design of a model-checking tool is the choice of the formal language with which properties are specified. It is now recognized that a good language should extend linear temporal logic with the ability to specify all -regular properties. Also, designers, who are familiar with finite-state machines, prefer extensions based on automata than these based on fixed points or propositional quantification. Early extensions of linear temporal logic with automata use nondeterministic Büchi automata. Their drawback has been inability to refer to the past and the asymmetrical structure of nondeterministic automata. In this work we study an extension of linear temporal logic, called ETL © , that uses two-way alternating automata as temporal connectives. Two-way automata can traverse the input word back and forth and they are exponentially more succinct than one-way automata. Alternating automata combine existential and universal branching and they are exponentially more succinct than nondeterministic automata. The rich structure of two-way alternating automata makes ETL © a very powerful and convenient logic. We show that ETL © formulas can be translated to nondeterministic Büchi automata with an exponential blow up. It follows that the satisfiability and model-checking problems for ETL © are PSPACEcomplete, as are the ones for LTL and its earlier extensions with automata. So, in spite of the succinctness of two-way and alternating automata, the advantages of ETL © are obtained without a major increase in space complexity. The recent acceptance of alternating automata by the industry and the development of symbolic procedures for handling them make us optimistic about the practicality of ETL © .

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Section: Discussionmentioning

confidence: 99%

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Extended Temporal Logic Revisited

Kupferman

Piterman

Vardi

2001

Lecture Notes in Computer Science

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“…This kind of reasoning enables conversion of alternating tree automata to nondeterministic tree automata and complementation of nondeterministic tree automata (cf. [Rab72,Tho90,Var98]). …”

Section: Determinization Of Büchi and Streett Automatamentioning

confidence: 99%

From Nondeterministic B\"uchi and Streett Automata to Deterministic Parity Automata

Piterman¹

2007

Logical Methods in Computer Science

175

232

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Abstract. In this paper we revisit Safra's determinization constructions for automata on infinite words. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Determinization is used in numerous applications, such as reasoning about tree automata, satisfiability of CTL * , and realizability and synthesis of logical specifications. The upper bounds for all these applications are reduced by using the smaller deterministic automata produced by our construction. In addition, the parity acceptance conditions allows to use more efficient algorithms (when compared to handling Rabin or Streett acceptance conditions).

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An Automata-Theoretic Approach to Reasoning about Infinite-State Systems

Kupferman

Vardi

2000

Computer Aided Verification

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Abstract.We develop an automata-theoretic framework for reasoning about infinitestate sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way tree automaton that navigates through the tree. As has been the case with finite-state systems, the automatatheoretic framework is quite versatile. We demonstrate it by solving several versions of the model-checking problem for § -calculus specifications and prefixrecognizable systems, and by solving the realizability and synthesis problems for § -calculus specifications with respect to prefix-recognizable environments.

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Reasoning about the past with two-way automata

Cited by 244 publications

References 37 publications

Extended Temporal Logic Revisited

Extended Temporal Logic Revisited

From Nondeterministic B\"uchi and Streett Automata to Deterministic Parity Automata

An Automata-Theoretic Approach to Reasoning about Infinite-State Systems

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