Multipass automata and group word problems

We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean closure of the class of deterministic context-free languages while the class of languages accepted by nondeterministic multipass automata is exactly the class of poly-context-free languages, that is, languages which are the intersection of finitely many context-free languages. We illustrate the use of these automata by studying groups whose word problems are in the above classes

Representation Theory of Finite Semigroups, Semigroup Radicals and Formal Language Theory

In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are given to obtain many new results, as well as easier proofs of several results in the literature, involving: triangularizability of finite semigroups; which semigroups have (split) basic semigroup algebras, two-sided semidirect product decompositions of finite monoids; unambiguous products of rational languages; products of rational languages with counter; and \v{C}ern\'y's conjecture for an important class of automata

On the Uniform Random Generation of Non Deterministic Automata Up to Isomorphism

In this paper we address the problem of the uniform random generation of non deterministic automata (NFA) up to isomorphism. First, we show how to use a Monte-Carlo approach to uniformly sample a NFA. Secondly, we show how to use the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism. Using labeling techniques, we show that in practice it is possible to move into the modified Markov Chain efficiently, allowing the random generation of NFAs up to isomorphism with dozens of states. This general approach is also applied to several interesting subclasses of NFAs (up to isomorphism), such as NFAs having a unique initial states and a bounded output degree. Finally, we prove that for these interesting subclasses of NFAs, moving into the Metropolis Markov chain can be done in polynomial time. Promising experimental results constitute a practical contribution.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223, pp.12, 2015, Implementation and Application of Automata - 20th International Conferenc