Julien Cervelle

On automata and language based grammar metrics

Grammar metrics have been introduced to measure the quality and the complexity of the formal grammars. The aim of this paper is to explore the meaning of these notions and to experiment, on several grammars of domain specific languages and of general-purpose languages, existing grammar metrics together with the new metrics that are based on grammar LR automaton and on the language recognized. We discuss the results of this experiment and focus on the comparison between grammars of domain specific languages as well as of general-purpose languages and on the evolution of the metrics between several versions of the same language.

Some results about the chaotic behavior of cellular automata

We study the behavior of cellular automata (CA for short) in the Cantor, Besicovitch and Weyl topologies. We solve an open problem about the existence of transitive CA in the Besicovitch topology. The proof of this result has some interest of its own since it is obtained by using Kolmogorov complexity. To our knowledge it is the first result about discrete dynamical systems obtained using Kolmogorov complexity. We also prove that in the Besicovitch topology every CA has either a unique periodic point (thus a fixed point) or an uncountable set of periodic points. This result underlines the fact that CA have a great degree of stability; it may be considered a further step towards the understanding of CA periodic behavior.Moreover, we prove that in the Besicovitch topology there is a special set of configurations, the set of Toeplitz configurations, that plays a role similar to that of spatially periodic configurations in the Cantor topology, that is, it is dense and has a central role in the study of surjectivity and injectivity. Finally, it is shown that the set of spatially quasi-periodic configurations is not dense in the Weyl topology.

Fundamental study: From sandpiles to sand automata

We introduce a new model for simulating natural phenomena. We address several issues: topology, basic set properties like injectivity and surjectivity, reversibility, and decidability questions about a special kind of conservation law called grain conservation and ultimate periodicity.

Tatoo: an innovative parser generator

This paper presents Tatoo, a new parser generator. This tool, written in Java 1.5, produces lexer and bottom-up parsers. Its design has been driven by three main concerns: the ability to use the parser with the non-blocking IO API; the possibility to simply deal with several language versions; a clean separation between the lexer definition, the parser definition and the semantics. Moreover, Tatoo integrates several other interesting features such as lookahead-based rule selection, pluggable error recovery mechanism, multiple character sets optimized support.

Towards a rice theorem on traces of cellular automata

The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram. We prove the undecidability of a rather large class of problems over trace subshifts of cellular automata.

Basic properties for sand automata

We prove several results about the relations between injectivity and surjectivity for sand automata. Moreover, we begin the exploration of the dynamical behavior of sand automata proving that the property of ultimate periodicity is undecidable. We believe that the proof technique used for this last result might turn out to be useful for many other results in the same context.

Sofic Trace Subshift of a Cellular Automaton

The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram. In this paper we study conditions for a sofic subshift to be the trace of a cellular automaton.

Periodicity and Transitivity for Cellular Automata in Besicovitch Topologies

We study cellular automata (CA) behavior in Besicovitch topology. We solve an open problem about the existence of transitive CA. The proof of this result has some interest in its own since it is obtained by using Kolmogorov complexity. At our knowledge it if the first result on discrete dynamical systems obtained using Kolmogorov complexity. We also prove that every CA (in Besicovitch topology) either has a unique fixed point or a countable set of periodic points. This result underlines that CA have a great degree of stability and may be considered a further step towards the understanding of CA periodic behavior.

Entropy Games and Matrix Multiplication Games

Two intimately related new classes of games are introduced and studied: entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on a finite arena by two-and-a-half players: Despot, Tribune and the non-deterministic People. Despot wants to make the set of possible Peoples behaviors as small as possible, while Tribune wants to make it as large as possible.An MMG is played by two players that alternately write matrices from some predefined finite sets. One wants to maximize the growth rate of the product, and the other to minimize it. We show that in general MMGs are undecidable in quite a strong sense.On the positive side, EGs correspond to a subclass of MMGs, and we prove that such MMGs and EGs are determined, and that the optimal strategies are simple. The complexity of solving such games is in NP\&coNP.

Ultimate Traces of Cellular Automata

A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing the sequence of states taken by some particular cell. In this paper we study the ultimate trace of CA and partial CA (a CA restricted to a particular subshift). The ultimate trace is the trace observed after a long time run of the CA. We give sufficient conditions for a set of infinite words to be the trace of some CA and prove the undecidability of all properties over traces that are stable by ultimate coincidence.