Dominique Perrin

Dominique Perrin
Name	Dominique Perrin
Alma mater	Université Paris-Sud
Nationality	French
Fields	Mathematics, Theoretical Computer Science, Probability
Known for	Automata theory, formal languages, stochastic processes
Influences	Marcel-Paul Schützenberger
Workplaces	Université Paris-Sud, CNRS

Dominique Perrin — French mathematician and theoretical computer scientist known for foundational work in automata theory, formal language theory, and connections between combinatorics on words and probability theory. Perrin contributed to the structural theory of rational languages, the algebraic characterization of regular languages, and the study of sturmian sequences and substitution systems. His research intersects with the work of figures such as Marcel-Paul Schützenberger, Jean Berstel, and Miklós Laczkovich and has influenced developments in symbolic dynamics, coding theory, and computability theory.

Early life and education

Perrin was educated in France, obtaining his doctorate at Université Paris-Sud where he studied under influences from researchers at institutions such as the Centre National de la Recherche Scientifique (CNRS). During his formative years he engaged with the mathematical communities centered at Institut des Hautes Études Scientifiques, École Normale Supérieure (Paris), and conferences like the International Colloquium on Automata, Languages and Programming and meetings of the Société Mathématique de France. His early exposure included contact with the work of Marcel-Paul Schützenberger, Noam Chomsky, Dana Scott, Michael Rabin, and John Myhill through seminars and collaborations that shaped his focus on algebraic and combinatorial aspects of languages.

Academic career and positions

Perrin held academic appointments at Université Paris-Sud and research positions associated with the Centre National de la Recherche Scientifique. He collaborated with colleagues at institutions including CNRS Laboratoire groups, visited departments such as Massachusetts Institute of Technology, University of California, Berkeley, and University of Warwick, and participated in exchanges with research centers like Institut Henri Poincaré and Université Paris Diderot. He contributed to editorial boards for journals associated with the Association for Symbolic Logic, European Association for Theoretical Computer Science, and served on program committees for conferences including STOC, FOCS, ICALP, and DLT.

Research contributions and notable results

Perrin made significant contributions to the algebraic theory of rational languages and the classification of regular languages via syntactic monoids, building on concepts introduced by Schützenberger and Samuel Eilenberg. He worked on the characterization of varieties of finite monoids and their correspondence with classes of regular languages, linking with results from Eilenberg's variety theorem and extensions studied by Alfred Tarski-era algebraists. Perrin investigated the structure of codes and unique decipherability, developing combinatorial criteria related to the Grundy theorem lineage and connecting with research by Berstel and Perrin coauthors in code theory.

In combinatorics on words, Perrin explored properties of sturmian words, morphic sequences, and substitution dynamical systems, relating low-complexity sequences to symbolic dynamics phenomena studied by Marcel Mossé and Berstel. His work addressed return words, balance properties, and the critical exponent for classes of infinite words, with implications for quasicrystals modeling and Tilings studied by researchers such as Roger Penrose.

Perrin also examined probabilistic models on words and automata, treating stochastic processes on free monoids and probabilistic automata, with connections to Markov chain theory, information theory pioneers like Claude Shannon, and learning theory topics advanced by Leslie Valiant and Valiant coauthors. He contributed to decidability results for language equivalence problems and complexity classifications that relate to computational frameworks from Alan Turing-inspired computability and complexity theory advanced at INRIA and CNRS centers.

His collaborative monographs synthesized algebraic, combinatorial, and algorithmic perspectives, influencing subsequent work on separation problems, profinite methods in language theory, and automata minimization techniques linked with algorithms from Hopcroft and Moore traditions.

Awards and honors

Perrin received recognition within the French and international mathematical community, including honors from organizations such as the Société Mathématique de France and fellowships or visiting positions at institutions like Institut des Hautes Études Scientifiques and Collège de France. He was invited to speak at major venues including plenary and invited sessions of ICALP, Automata, Languages and Programming (ICALP), and international congresses related to symbolic dynamics and formal methods. His contributions were acknowledged in festschrifts and dedicated conference volumes produced by colleagues from Université Paris-Sud, CNRS, and partner universities.

Selected publications and books

- D. Perrin and J. Berstel, "Theory of Codes and Languages" (coauthored works and edited volumes), surveys linking algebraic and combinatorial language theory with applications in coding theory and cryptography contexts. - D. Perrin, research articles on sturmian sequences, substitution systems, and return words in journals associated with the European Mathematical Society and American Mathematical Society. - D. Perrin, contributions to collections on automata theory, syntactic semigroups, and profinite methods, appearing alongside works by Jean Berstel, Alain Lascoux, Imre Simon, and J.-E. Pin. - Collaborative papers on decidability and complexity for automata and language equivalence, cited in proceedings of ICALP, STACS, and DLT.

Category:French mathematicians Category:Theoretical computer scientists