Manuel Vázquez de Parga

Learning Regular Languages Using Nondeterministic Finite Automata

A new general method for inference of regular languages using nondeterministic automata as output has recently been developed and proved to converge. The aim of this paper is to describe and analyze the behavior of two implementations of that method and to compare it with two well known algorithms for the same task. A complete set of experiments has been carried out and the results of the new algorithms improve the existing ones both in recognition rates as in sizes of the output automata.

A family of algorithms for non deterministic regular languages inference

We present in this paper a new family of algorithms for regular languages inference from complete presentation. Every algorithm of this family, on input of the sets of words (D+,D−), obtains for every x in D+ at least a non deterministic finite automaton (NFA) which accepts x and is consistent with D−. This automaton is, besides, irreducible in the sense that any further merging of states accepts words of D−. The output of the algorithm is a NFA which consists of the collection of NFAs associated to each word of D+. Every algorithm of the family converges to a automaton for the target language. We also present the experiments done to compare one of the algorithms of the family with two other well known algorithms for the same task. The results obtained by our algorithm are better, both in error rate as in the size of the output.

Learning automata teams

We prove in this work that, under certain conditions, an algorithm that arbitrarily merges states in the prefix tree acceptor of the sample in a consistent way, converges to the minimum DFA for the target language in the limit. This fact is used to learn automata teams, which use the different automata output by this algorithm to classify the test. Experimental results show that the use of automata teams improve the best known results for this type of algorithms. We also prove that the well known Blue-Fringe EDSM algorithm, which represents the state of art in merging states algorithms, suffices a polynomial characteristic set to converge.

Bilateral locally testable languages

We give an algebraic characterization of a new variety of languages that will be called bilateral locally testable languages and denoted as BLT. Given k>0, the membership of a word x to a BLT (k-BT) language can be decided by means of exploring the segments of length k of x, as well as considering the order of appearance of those segments when we scan the prefixes and the suffixes of x. In this paper, we also characterize the syntactic semigroup of BLT languages in terms of the equations of the variety they belong to, as well as in terms of the join of two previously studied varieties.

A Split-Based Incremental Deterministic Automata Minimization Algorithm

We here study previous results due to Hopcroft and Almeida et al. to propose an incremental split-based deterministic automata minimization algorithm whose average running-time does not depend on the size of the alphabet. The experimentation carried out shows that our proposal outperforms the algorithms studied whenever the automata have more than a (quite small) number of states and symbols.

DFA minimization: Double reversal versus split minimization algorithms

“NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published inTheoretical Computer Science, [Volume 583, 7 June 2015, Pages 78–85] DOI 10.1016/j.tcs.2015.04.002

EFFICIENT DETERMINISTIC FINITE AUTOMATA SPLIT-MINIMIZATION DERIVED FROM BRZOZOWSKI'S ALGORITHM

Minimization of deterministic finite automata is a classic problem in Computer Science which is still studied nowadays. In this paper, we relate the different split-minimization methods proposed to date, or to be proposed, and the algorithm due to Brzozowski which has been usually set aside in any classification of DFA minimization algorithms. In our work, we first propose a polynomial minimization method derived from a paper by Champarnaud et al. We also show how the consideration of some efficiency improvements on this algorithm lead to obtain an algorithm similar to Hopcroft’s classic algorithm. The results obtained lead us to propose a characterization of the set of possible splitters.

DFA minimization

“NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published inTheoretical Computer Science, [Volume 583, 7 June 2015, Pages 78–85] DOI 10.1016/j.tcs.2015.04.002