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Visibly Pushdown Automata with Multiplicities: Finiteness and K-Boundedness

Mathieu Caralp 1, Pierre-Alain Reynier 1, Jean-Marc Talbot 1

(14/05/2012)

We propose an extension of visibly pushdown automata by means of weights (represented as positive integers) associated with transitions, called visi- bly pushdown automata with multiplicities. The multiplicity of a computation is the product of the multiplicities of the transitions used along this computation. The multiplicity of an input is the sum of the ones of all its successful compu- tations. Finally, the multiplicity of such an automaton is the supremum of multi- plicities over all possible inputs. We prove the problem of deciding whether the multiplicity of an automaton is finite to be in PTIME. We also consider the K-boundedness problem, i.e. deciding whether the multiplicity is bounded by K: we prove this problem to be EXPTIME- complete when K is part of the input and in PTIME when K is fixed. As visibly pushdown automata are closely related to tree automata, we discuss deeply the relationship of our extension with weighted tree automata.

1 :	Laboratoire d'informatique Fondamentale de Marseille (LIF)
	CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I

Domaine

:

Informatique/Théorie et langage formel

Mots Clés : Weighted tree automata – Visibly Pushdown Automata – Multiplicity – Boundedness

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Contributeur : Pierre-Alain Reynier <>

Soumis le : Lundi 14 Mai 2012, 15:07:39

Dernière modification le : Lundi 14 Mai 2012, 15:37:22