Showing papers on "ω-automaton published in 2018"
11 Apr 2018
TL;DR: It was recently shown that 2- state reversible Mealy automata cannot generate infinite Burnside groups, and this result is extended to connected 3-state reversible Meally automata, using new original techniques.
Abstract: The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, no such examples have been constructed in some classes, as groups generated by non reversible automata. It was recently shown that 2-state reversible Mealy automata cannot generate infinite Burnside groups. Here we extend this result to connected 3-state reversible Mealy automata, using new original techniques. The results rely on a fine analysis of associated orbit trees and a new characterization of the existence of elements of infinite order.
22 citations
TL;DR: This paper considers the case in which the predictor is an automaton and the emitted values are drawn from a finite set; i.e., the emitted sequence is an infinite word.
Abstract: In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the predictor’s guesses are correct. In this paper we consider the case in which the predictor is an automaton and the emitted values are drawn from a finite set; i.e., the emitted sequence is an infinite word. We examine the predictive capabilities of finite automata, pushdown automata, stack automata (a generalization of pushdown automata), and multihead finite automata. We relate our predicting automata to purely periodic words, ultimately periodic words, and multilinear words, describing novel prediction algorithms for mastering these sequences.
8 citations
09 Apr 2018
TL;DR: In this paper, the authors conjecture that Cerny's conjecture holds true for planar automata, if and only if, it holds true also for deterministic finite state automata.
Abstract: Planar automata seems to be representative of the synchronizing behavior of deterministic finite state automata. We conjecture that Cerny’s conjecture holds true, if and only if, it holds true for planar automata. We provide new (and old) evidence concerning the conjectured C erny-universality of planar automata.
6 citations
01 Feb 2018
TL;DR: In this article, the equivalence of Mealy-type and Moore-type weighted finite automata with output was proved with respect to various semantics which are defined in this paper.
Abstract: In this paper, we prove the equivalence of sequential, Mealy-type and Moore-type weighted finite automata with output, with respect to various semantics which are defined here.
3 citations
TL;DR: This paper defines a model of non-deterministic, 2-way, concurrent automata working on series–parallel graphs and communicating through shared registers on the nodes of the graph and shows that a bounded version is decidable, even though there is no bound on the sizes of series– parallel graphs generated by the GTS.
Abstract: Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization of automata-theoretic infinite-state verification from strings to labelled series–parallel graphs. We define a model of non-deterministic, 2-way, concurrent automata working on series–parallel graphs and communicating through shared registers on the nodes of the graph. We consider the following verification problem: given a family of series–parallel graphs described by a context-free graph transformation system (GTS), and a concurrent automaton over series–parallel graphs, is some graph generated by the GTS accepted by the automaton? The general problem is undecidable already for (one-way) multi-head automata over strings. We show that a bounded version, where the automata make a fixed number of reversals along the graph and use a fixed number of shared registers is decidable, even though there is no bound on the sizes of series–parallel graphs generated by the GTS. Our decidability result is based on establishing that the number of context switches can be bounded and on an encoding of the computation of bounded concurrent automata that allows us to reduce the reachability problem to the emptiness problem for pushdown automata.
2 citations