arXiv subjects

Julien Provillard

Publications and source records attributed to Julien Provillard.

3 recordsLinked to original sources

arXiv2013

Acceptance conditions for omega-languages and the Borel hierarchy

This paper investigates acceptance conditions for finite automata recognizing omega-regular languages. As a first result, we show that, under any acceptance condition that can be defined in the MSO logic, a finite automaton can recognize at most omega-regular languages. Starting from this, the paper aims at classifying acceptance conditions according to their expressive power and at finding the exact position of the classes of omega-languages they induced according to the Borel hierarchy. A new interesting acceptance condition is introduced and fully characterized. A step forward is also made in the understanding of the expressive power of (fin, =).

cs.FL↗

arXiv2011

Non-uniform cellular automata and distributions of rules

In this paper we study $ν$-CA on one-dimensional lattice defined over a finite set of local rules. The main goal is to determine how the local rules can be mixed to ensure the produced $ν$-CA has some properties. In a first part, we give some background for the study of $ν$-CA. Then surjectivity and injectivity are studied using a variant of DeBruijn graphs. The next part is dedicated to the number-conserving property.

cs.FL↗

arXiv2011

Non-Uniform Cellular Automata: classes, dynamics, and decidability

The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like surjectivity and injectivity is also established. The final part studies a strong form of equicontinuity property specially suited for non-uniform cellular automata.

cs.FL↗