Two-Way Cost Automata and Cost Logics over Infinite Trees

Achim Blumensath (1) , Thomas Colcombet (2) , Denis Kuperberg (2) , Paweł Parys (3) , Michael Vanden Boom (4)

1 TU Darmstadt - Technische Universität Darmstadt - Technical University of Darmstadt
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
4 Department of Computer Science [Oxford]

Regular cost functions provide a quantitative extension of regular languages that retains most of their important properties, such as expressive power and decidability, at least over finite and infinite words and over finite trees. Much less is known over infinite trees. We consider cost functions over infinite trees defined by an extension of weak monadic second-order logic with a new fixed-point-like operator. We show this logic to be decidable, improving previously known decidability results for cost logics over infinite trees. The proof relies on an equivalence with a form of automata with counters called quasi-weak cost automata, as well as results about converting two-way alternating cost automata to one-way alternating cost automata.

Domaines: Théorie et langage formel [cs.FL]

Achim Blumensath, Thomas Colcombet, Denis Kuperberg, Paweł Parys, Michael Vanden Boom. Two-Way Cost Automata and Cost Logics over Infinite Trees. JOINT MEETING OF the Twenty-Third EACSL Annual Conference on COMPUTER SCIENCE LOGIC (CSL) AND the Twenty-Ninth Annual ACM/IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS), 2014, Vienne, Austria. ⟨10.1145/2603088.2603104⟩. ⟨hal-02070744⟩