Alternating automata on infinite trees

David, E. Muller; Paul, Erik

doi:10.1016/0304-3975(87)90133-2

Cited by 200 publications

(118 citation statements)

References 6 publications

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“…Alternating tree automata are a generalization of nondeterministic tree automata [19]. Intuitively, while a nondeterministic tree automaton that visits a node of the input tree sends exactly one copy of itself to each of the successors of the node, an alternating automaton can send several copies of itself to the same successor.…”

Section: Alternating Parity Tree Automatamentioning

confidence: 99%

Improved Model Checking of Hierarchical Systems

Aminof

Kupferman

Murano

2010

Lecture Notes in Computer Science

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We present a unified game-based approach for branching-time model checking of hierarchical systems. Such systems are exponentially more succinct than standard state-transition graphs, as repeated sub-systems are described only once. Early work on model checking of hierarchical systems shows that one can do better than a naive algorithm that "flattens" the system and removes the hierarchy.Given a hierarchical system S and a branching-time specification ψ for it, we reduce the model-checking problem (does S satisfy ψ?) to the problem of solving a hierarchical game obtained by taking the product of S with an alternating tree automaton A ψ for ψ. Our approach leads to clean, uniform, and improved model-checking algorithms for a variety of branching-time temporal logics. In particular, by improving the algorithm for solving hierarchical parity games, we are able to solve the model-checking problem for the µ-calculus in Pspace and time complexity that is only polynomial in the depth of the hierarchy. Our approach also leads to an abstraction-refinement paradigm for hierarchical systems. The abstraction maintains the hierarchy, and is obtained by merging both states and sub-systems into abstract states.

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Section: Alternating Parity Tree Automatamentioning

confidence: 99%

Improved Model Checking of Hierarchical Systems

Aminof

Kupferman

Murano

2010

Lecture Notes in Computer Science

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“…Alternating automata on infinite trees generalize nondeterministic tree automata and were first introduced in [22]. Here we describe two-way alternating tree automata Let B+(X) be the set of positive Boolean formulas over X (i.e., boolean formulas built from elements in X using/~ and V), where we also allow the formulas true and false, and, as usual,/~ has precedence over V. A run of an alternating automaton A over a labeled tree (T, V) is a labeled tree (Tr, r} in which every node is labeled by an element of T • Q.…”

Section: Alternating Tree Automatamentioning

confidence: 99%

“…Similarly, there is a simple translation from p-calculus formulas to alternating tree automata [1,5]. Alternating tree automata as defined in [22], however, cannot easily handle backwards modalities, since they are one-way automata. To deal with backward modalities we introduce two-way alternating automata on infinite trees, based on an analogous notion of two-way automata on finite trees in [29].…”

Section: Introductionmentioning

confidence: 99%

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Reasoning about the past with two-way automata

Vardi

1998

Lecture Notes in Computer Science

244

249

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Abstract. The p-calculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the p-calculus is EXPTIMEcomplete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result in this paper is an exponential time upper bound for the satisfiability problem of the p-calculus with both forward and backward modalities. To get this result we develop a theory of two-way alternating automata on infinite trees.

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“…In the early 90s, researchers started to base the automata-theoretic approach on alternating automata [19,20]. In an alternating automaton, the transition function maps a state and a letter to a formula over the set of states, indicating by which states the suffix of the word should be accepted.…”

Section: Introductionmentioning

confidence: 99%

Alternation Removal in Büchi Automata

Boker

Kupferman

Rosenberg

2010

Automata, Languages and Programming

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Abstract. Alternating automata play a key role in the automata-theoretic approach to specification, verification, and synthesis of reactive systems. Many algorithms on alternating automata, and in particular, their nonemptiness test, involve removal of alternation: a translation of the alternating automaton to an equivalent nondeterministic one. For alternating Büchi automata, the best known translation uses the "breakpoint construction" and involves an O(3 n ) state blowup. The translation was described by Miyano and Hayashi in 1984, and is widely used since, in both theory and practice. Yet, the best known lower bound is only 2 n . In this paper we develop and present a complete picture of the problem of alternation removal in alternating Büchi automata. In the lower bound front, we show that the breakpoint construction captures the accurate essence of alternation removal, and provide a matching Ω(3 n ) lower bound. Our lower bound holds already for universal (rather than alternating) automata with an alphabet of a constant size. In the upper-bound front, we point to a class of alternating Büchi automata for which the breakpoint construction can be replaced by a simpler n2 n construction. Our class, of ordered alternating Büchi automata, strictly contains the class of very-weak alternating automata, for which an n2 n construction is known.

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Alternating automata on infinite trees

Cited by 200 publications

References 6 publications

Improved Model Checking of Hierarchical Systems

Improved Model Checking of Hierarchical Systems

Reasoning about the past with two-way automata

Alternation Removal in Büchi Automata

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