Automata for the modal μ-calculus and related results

Janin, David; Walukiewicz, Igor

doi:10.1007/3-540-60246-1_160

Cited by 114 publications

(104 citation statements)

References 8 publications

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“…(3) The labelled transition systems from [12] can be represented as coalgebras for the functor PΦ × P A , i.e. for the functor that maps a set S to the set PΦ × (PS) A .…”

mentioning

confidence: 99%

Coalgebraic Automata Theory: Basic Results

Kupke¹,

Venema²

2008

Logical Methods in Computer Science

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Abstract. We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects.Let F be any set functor that preserves weak pullbacks. We show that the class of recognizable languages of F-coalgebras is closed under taking unions, intersections, and projections. We also prove that if a nondeterministic F-automaton accepts some coalgebra it accepts a finite one of the size of the automaton. Our main technical result concerns an explicit construction which transforms a given alternating F-automaton into an equivalent nondeterministic one, whose size is exponentially bound by the size of the original automaton.

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“…(3) The labelled transition systems from [12] can be represented as coalgebras for the functor PΦ × P A , i.e. for the functor that maps a set S to the set PΦ × (PS) A .…”

mentioning

confidence: 99%

Coalgebraic Automata Theory: Basic Results

Kupke¹,

Venema²

2008

Logical Methods in Computer Science

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“…As a corollary of this result and Proposition 3.5, MSO (see Example 2.9) is in fact a coalgebraic fixpoint logic. Theorem 3.10 below can be seen as a more precise formulation of Fact 1.3; as mentioned there, the two statements can be found in Walukiewicz [23] and Janin & Walukiewicz [12], respectively. Theorem 3.10 1.…”

Section: Qedmentioning

confidence: 93%

“…This link between logic and automata theory essentially goes back to the work of Rabin and Büchi on stream and tree automata. The two statements in Fact 1.3 below can be found in Walukiewicz [23] and Janin & Walukiewicz [12], respectively. Fact 1.3 1.…”

Section: Introductionmentioning

confidence: 93%

Expressiveness Modulo Bisimilarity: A Coalgebraic Perspective

Venema

2014

Outstanding Contributions to Logic

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“…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. A Symmetric alternating tree automaton [15,25] does not distinguish between the different successors of a node, and can send copies of itself only in a universal or an existential manner, possibly with ε-transitions. We use a partition of the state space of the automaton in order to denote the type of transitions from it.…”

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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Automata for the modal μ-calculus and related results

Cited by 114 publications

References 8 publications

Coalgebraic Automata Theory: Basic Results

Coalgebraic Automata Theory: Basic Results

Expressiveness Modulo Bisimilarity: A Coalgebraic Perspective

Improved Model Checking of Hierarchical Systems

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