Denis Thérien

Bio: Denis Thérien is an academic researcher from McGill University. The author has contributed to research in topics: Monoid & Regular language. The author has an hindex of 31, co-authored 121 publications receiving 3269 citations. Previous affiliations of Denis Thérien include University of Paris.

Finite monoids and the fine structure of NC1

Abstract: Recently a new connection was discovered between the parallel complexity class NC1 and the theory of finite automata in the work of Barrington on bounded width branching programs. There (nonuniform) NC1 was characterized as those languages recognized by a certain nonuniform version of a DFA. Here we extend this characterization to show that the internal structures of NC1 and the class of automata are closely related.In particular, using Therien's classification of finite monoids, we give new characterizations of the classes AC0, depth-kAC0, and ACC, the last being the AC0 closure of the mod q functions for all constant q. We settle some of the open questions in [3], give a new proof that the dot-depth hierarchy of algebraic automata theory is infinite [8], and offer a new framework for understanding the internal structure of NC1.

Over words, two variables are as powerful as one quantifier alternation

Abstract: We show a property of strings is expressible in the two-variable fragment of first-order logic if and only if it is express ible by both a 2 and a 2 sentence. We thereby establish: UTL = FO2 = 2 \ 2 = UL ; where UTL stands for the string properties expressible in th e temporal logic with ‘eventually in the future’ and ‘eventua lly in the past’ as the only temporal operators and UL stands for the class of unambiguous languages. This enables us to show that the problem of determining whether or not a given temporal string property belongs to UTL is decidable (in exponential space), which settles a hitherto open problem. Our proof of 2 \ 2 = FO2 involves a new combinatorial characterization of these two classes and introduce s a new method of playing Ehrenfeucht-Fraı̈ssé games to verif y identities in semigroups.

Non-uniform automata over groups

Abstract: A new model, non-uniform deterministic finite automata (NUDFA's) over general finite monoids, has recently been developed as a strong link between the theory of finite automata and low-level parallel complexity. Achievements of this model include the proof that width 5 branching programs recognize exactly the languages in non-uniform NC1, NUDFA characterizations of several important subclasses of NC1, and a new proof of the old result that the dot-dephth hierarchy is infinite, using M. Sipser's (1983, in “Proceedings, 15th ACM Symposium on the Theory of Computing,” Association for Computing Machinery, New York, pp. 61–69) work on constant depth circuits. Here we extend this theory to NUDFA's over solvable groups (NUDFA's over non-solvable groups have the maximum possible computing power). We characterize the power of NUDFA's over nilpotent groups and prove some optimal lower bounds for NUDFA's over certain groups which are solvable but not nilpotent. Most of these results appeared in preliminary form in ( D. A. Barrington and D. Therien, 1987 , in “Automata, Languages, and Programming: 14th International Colloquium,” Springer-Verlag, Berlin, pp. 163–173).

Handbook of Constraint Programming

Abstract: Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics. The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area. The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas. The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming. - Covers the whole field of constraint programming - Survey-style chapters - Five chapters on applications Table of Contents Foreword (Ugo Montanari) Part I : Foundations Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh) Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth) Chapter 3. Constraint Propagation (Christian Bessiere) Chapter 4. Backtracking Search Algorithms (Peter van Beek) Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang) Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel) Chapter 7. Tractable Structures for CSPs (Rina Dechter) Chapter 8. The Complexity of Constraint Languages (David Cohen, Peter Jeavons) Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex) Chapter 10. Symmetry in Constraint Programming (Ian P. Gent, Karen E. Petrie, Jean-Francois Puget) Chapter 11. Modelling (Barbara M. Smith) Part II : Extensions, Languages, and Applications Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace) Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte) Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson) Chapter 15. Operations Research Methods in Constraint Programming (John Hooker) Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers) Chapter 17. Constraints over Structured Domains (Carmen Gervet) Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh) Chapter 19. Temporal CSPs (Manolis Koubarakis) Chapter 20. Distributed Constraint Programming (Boi Faltings) Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel) Chapter 22. Constraint-Based Scheduling and Planning (Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten) Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw) Chapter 24. Configuration (Ulrich Junker) Chapter 25. Constraint Applications in Networks (Helmut Simonis) Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)

Languages, automata, and logic

Abstract: The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.

Elements of Finite Model Theory

Abstract: Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.

Bounded-width polynomial-size branching programs recognize exactly those languages in NC1

Abstract: We show that any language recognized by an NC 1 circuit (fan-in 2, depth O (log n )) can be recognized by a width-5 polynomial-size branching program. As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly nonuniform NC 1 . Further, following Ruzzo ( J. Comput. System Sci. 22 (1981), 365–383) and Cook ( Inform. and Control 64 (1985) 2–22) , if the branching programs are restricted to be ATIME(logn)-uniform, they recognize the same languages as do ATIME(log n )-uniform NC 1 circuits, that is, those languages in ATIME(log n ). We also extend the method of proof to investigate the complexity of the word problem for a fixed permutation group and show that polynomial size circuits of width 4 also recognize exactly nonuniform NC 1 .

Visibly pushdown languages

Abstract: We propose the class of visibly pushdown languages as embeddings of context-free languages that is rich enough to model program analysis questions and yet is tractable and robust like the class of regular languages. In our definition, the input symbol determines when the pushdown automaton can push or pop, and thus the stack depth at every position. We show that the resulting class Vpl of languages is closed under union, intersection, complementation, renaming, concatenation, and Kleene-*, and problems such as inclusion that are undecidable for context-free languages are Exptime-complete for visibly pushdown automata. Our framework explains, unifies, and generalizes many of the decision procedures in the program analysis literature, and allows algorithmic verification of recursive programs with respect to many context-free properties including access control properties via stack inspection and correctness of procedures with respect to pre and post conditions. We demonstrate that the class Vpl is robust by giving two alternative characterizations: a logical characterization using the monadic second order (MSO) theory over words augmented with a binary matching predicate, and a correspondence to regular tree languages. We also consider visibly pushdown languages of infinite words and show that the closure properties, MSO-characterization and the characterization in terms of regular trees carry over. The main difference with respect to the case of finite words turns out to be determinizability: nondeterministic Buchi visibly pushdown automata are strictly more expressive than deterministic Muller visibly pushdown automata.