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Qualitative Tree Languages

By Arnaud Carayol, Axel Haddad and Olivier Serre

Abstract

International audienceWe study finite automata running over infinite binary trees and we relax the notion of accepting run by allowing a negligible set (in the sense of measure theory) of non-accepting branches. In this qualitative setting, a tree is accepted by the automaton if there exists a run over this tree in which almost every branch is accepting. This leads to a new class of tree languages, called the qualitative tree languages that enjoys many properties. Then, we replace the existential quantification --a tree is accepted if there exists some accepting run over the input tree-- by a probabilistic quantification --a tree is accepted if almost every run over the input tree is accepting. Together with the qualitative acceptance and the Büchi condition, we obtain a class of probabilistic tree automata with a decidable emptiness problem. To our knowledge, this is the first positive result for a class of probabilistic automaton over infinite trees

Topics: Tree Automata, Probabilistic Automata, Markov Decision Process, [ INFO.INFO-CL ] Computer Science [cs]/Computation and Language [cs.CL]
Publisher: HAL CCSD
Year: 2011
DOI identifier: 10.1109/LICS.2011.28
OAI identifier: oai:HAL:hal-00616304v1
Provided by: Hal-Diderot

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