Conjugacy and Equivalence of Weighted Automata and Functional Transducers

International audienceWe show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) ¯eld and that the same holds true for functional tranducers as well

Simulations of Weighted Tree Automata

Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noetherian semirings, semiring of natural numbers) that all equivalent wta M and N can be joined by a finite chain of simulations. More precisely, in all mentioned cases there exists a single wta that simulates both M and N. Those results immediately yield decidability of equivalence provided that the semiring is finitely (and effectively) presented.Comment: 17 pages, 2 figure

Graph Spectral Properties of Deterministic Finite Automata

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces the notion of matrix rank into a regular language L, the minimal adjacency matrix rank of a deterministic automaton that recognises L. We then define and focus on rank-one languages: the class of languages for which the rank of minimal automaton is one. We also define the expanded canonical automaton of a rank-one language.Comment: This paper has been accepted at the following conference: 18th International Conference on Developments in Language Theory (DLT 2014), August 26 - 29, 2014, Ekaterinburg, Russi

10031 Abstracts Collection -- Quantitative Models: Expressiveness and Analysis

From Jan 18 to Jan 22, 2010, the Dagstuhl Seminar 10031 ``Quantitative Models: Expressiveness and Analysis \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available