Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation techniques to the associated extended expressions called hairpin expressions. More precisely, we extend partial derivation of regular expressions to two-sided partial derivation of hairpin expressions and we show how to deduce a recognizer for a hairpin expression from its two-sided derived term automaton, providing an alternative proof of the fact that hairpin completions of regular languages are linear context-free.Comment: 28 page

FAdo and GUItar: tools for automata manipulation and visualization

Abstract. FAdo is an ongoing project which aims to provide a set of tools for symbolic manipulation of formal languages. To allow highlevel programming with complex data structures, easy prototyping of algorithms, and portability (to use in computer grid systems for example), are its main features. Our main motivation is the theoretical and experimental research, but we have also in mind the construction of a pedagogical tool for teaching automata theory and formal languages. For the graphical visualization and interactive manipulation a new interface application, GUItar, is being developed. In this paper, we describe the main components of the FAdo system as well as the basics of the graphical interface and editor, the export/import filters and its generic interface with external systems, such as FAdo.

Partial derivative automata formalized in Coq

In this paper we present a computer assisted proof of the correctness of a partial derivative automata construction from a regular expression within the Coq proof assistant. This proof is part of a for- malization of Kleene algebra and regular languages in Coq towards their usage in program certification.Fundação para a Ciência e Tecnologia (FCT) Program POSI, RESCUE (PTDC/EIA/65862/2006), SFRH/BD/33233/2007

Language, Life, Limits

Motivated by the desire to facilitate the implementation of interactive proof systems with rich sets of proof rules, we present a uniform system of rule schemata to generate proof rules for different styles of logical calculi. The system requires only one schema for each logical operator to generate introduction and elimination rules in natural deduction and sequent calculus style. In addition, the system supports program extraction from proofs by generating realizers for the proof rules automatically

Random Generation of Deterministic Tree (Walking) Automata

The original publication is a available at www.springerlink.comInternational audienceUniform random generators deliver a simple empirical means to estimate the average complexity of an algorithm. We present a general rejection algorithm that generates sequential letter-to-letter transducers up to isomorphism. We tailor this general scheme to randomly generate deterministic tree walking automata and deterministic top-down tree automata. We apply our implementation of the generator to the estimation of the average complexity of a deterministic tree walking automata to nondeterministic top-down tree automata construction we also implemented