Author

# Maurice Nivat

Other affiliations: Lille University of Science and Technology

Bio: Maurice Nivat is an academic researcher from University of Paris. The author has contributed to research in topics: Discrete tomography & Polyomino. The author has an hindex of 22, co-authored 72 publications receiving 3036 citations. Previous affiliations of Maurice Nivat include Lille University of Science and Technology.

Topics: Discrete tomography, Polyomino, Time complexity, Rewriting, Finite set

##### Papers published on a yearly basis

##### Papers

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TL;DR: This contribution was made possible only by the miraculous fact that the first members of the Editorial Board were sharing the same conviction about the necessity of Theoretical Computer Science.

Abstract: The collection of TCS issues is about 1 meter high, 17,000 pages long and it contains 1100 papers. When in 1974 Einar Fredriksson and myself started talking about the creation of a journal dedicated to Theoretical Computer Science we were very far from even dreaming that it could take such an extension within twelve years. We were also a bit shy: what could such a journal, very theoretical indeed and hard to read, be useful to, and who would read it? Fortunately, some people encouraged us and indeed helped us a lot, Mike Paterson who was at that time President of EATCS and who accepted to become Associate Editor, Albert Meyer who was a very active editor at the beginning, Arto Salomaa, who was to become President of EATCS shortly afterwards. Indeed, I should mention all the first members of the Editorial Board, for TCS would never have come to existence without them. Theoretical Computer Science is not a clearly defined discipline with neat borderlines: it is more a state of mind, the conviction that the observed computation phenomena can be formally described and analysed as any physical phenomenon; the conviction that such a formal description helps to understand these phenomena and to master them in order to design better algorithms, better computers, better systems. Our fundamental activity is not to prove theorems in strange mathematical theories, it is to model a complicated reality and in this respect it has to be compared with theoretical physics or what we call in French “Mecanique rationnelle”. This comparison can be pursued rather far, for we also use all possible mathematical concepts and methods and when we do not find appropriate ones in traditional mathematics we create them. The aim is quite clear: using the compact and unambiguous language of mathematics brings to life concepts and methods which will be useful to all designers, builders and users of computer systems, exactly in the same way as matrix calculus or Fourier series and transforms are useful to all engineers and technicians in the electric and electronic industry. And when one thinks about the amount of time it took to build the mathematical theory of matrices and to polish and simplify it up to the state in which it could be taught to all future engineers and become a tool in daily use, we can be extremely satisfied by the development of Theoretical Computer Science. It is true that concepts and methods which were still vague and unclear when TCS was created became essential tools for all industrial designers and manufacturers, in algorithmics, in semantics, in automata theory and control, etc. . . . Certainly, TCS can be proud to have contributed to this development. Coming back to what I was saying a few minutes ago, this contribution was made possible only by the miraculous fact that the first members of the Editorial Board were sharing the same conviction about the necessity of Theoretical Computer Science

1,480 citations

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TL;DR: Some operations for recontructing convex polyominoes by means of vectors H's and V's partial sums allows a new algorithm to be defined whose complexity is less than O(n2m2).

Abstract: In [1], we studied the problem of reconstructing a discrete set 5 from its horizontal and vertical projections. We defined an algorithm that establishes the existence of a convex polyomino Λ whose horizontal and vertical projections are equal to a pair of assigned vectors (H,V), with H ∈ ℕ m and V ∈ ℕ n . Its computational cost is O(n4m4). In this paper, we introduce some operations for recontructing convex polyominoes by means of vectors H's and V's partial sums. These operations allows us to define a new algorithm whose complexity is less than O(n2m2).

201 citations

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120 citations

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TL;DR: It is proved that it can be decided whether translated copies of the polyomino can tile the plane, and every such tiling of the plane by translated Copy of the Polyomino is half-periodic.

Abstract: Given a polyomino, we prove that we can decide whether translated copies of the polyomino can tile the plane. Copies that are rotated, for example, are not allowed in the tilings we consider. If such a tiling exists the polyomino is called anexact polyomino. Further, every such tiling of the plane by translated copies of the polyomino is half-periodic. Moreover, all the possible surroundings of an exact polyomino are described in a simple way.

119 citations

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01 Jul 1992

TL;DR: Trees and Algebraic Semantics (I. Steinby), Interpretability and Tree Automata: A Simple Way to Solve Algorithmic Problems on Graphs Closely Related to Trees (D. Seese).

Abstract: Binary Tree Codes (M. Nivat). Suffix, Prefix and Maximal Tree Codes (P. Aigrain, M. Nivat). A Monoid Approach to Tree Automata (A. Podelski). A Theory of Tree Language Varieties (M. Steinby). Interpretability and Tree Automata: A Simple Way to Solve Algorithmic Problems on Graphs Closely Related to Trees (D. Seese). Computing Trees with Graph Rewriting Systems with Priorities (I. Litovsky, Y. Metivier). Recognizable Sets of Unrooted Trees (B. Courcelle). Fixed Point Characterization of Weak Monadic Logic Definable Sets of Trees (A. Arnold, D. Niwinski). Automata on Infinite Trees and Rational Control (A. Saoudi, P. Bonizzoni). Recognizing Sets of Labelled Acyclic Graphs (P. Bonizzoni et al.). Rational and Recognizable Infinite Tree Sets (A. Saoudi). Algebraic Specification of Action Trees and Recursive Processes (M. Grose-Rhode, C. Dimitrovici). Trees and Algebraic Semantics (I. Guessarian). A Survey of Tree Transductions (J.C. Raoult). Structural Complexity of Classes of Tree Languages (M. Dauchet, S. Tison). Ambiguity and Valuedness (H. Seidl). Decidability of the Inclusion in Monoids Generated by Tree Transformation Classes (Z. Fulop, S. Vagvolgyi). Tree-adjoining Grammars and Lexicalized Grammars (A.K. Joshi, Y. Schabes). A Short Proof of the Factorization Forest Theorem (I. Simon). Unification Procedures in Automated Deduction Methods based on Matings: A Survey (J.H. Gallier).

96 citations

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01 Jan 1984TL;DR: This is the second edition of an account of the mathematical foundations of logic programming, which collects, in a unified and comprehensive manner, the basic theoretical results of the field, which have previously only been available in widely scattered research papers.

Abstract: This is the second edition of an account of the mathematical foundations of logic programming. Its purpose is to collect, in a unified and comprehensive manner, the basic theoretical results of the field, which have previously only been available in widely scattered research papers. In addition to presenting the technical results, the book also contains many illustrative examples and problems. The text is intended to be self-contained, the only prerequisites being some familiarity with PROLOG and knowledge of some basic undergraduate mathematics. The material is suitable either as a reference book for researchers or as a textbook for a graduate course on the theoretical aspects of logic programming and deductive database systems.

4,500 citations

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TL;DR: In this paper, the control of a class of discrete event processes, i.e., processes that are discrete, asynchronous and possibly non-deterministic, is studied. And the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language, where the control process is described as the generator of a formal language, while the supervisor is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior.

Abstract: This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.

3,432 citations

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01 Jan 1989TL;DR: The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered.

Abstract: A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence, at possibly unknown irregular intervals, of physical events. Such systems arise in a variety of contexts ranging from computer operating systems to the control of complex multimode processes. A control theory for the logical aspects of such DESs is surveyed. The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered. Automata and formal language models for DESs are surveyed. >

2,829 citations

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02 Jan 1991TL;DR: This chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree.

Abstract: Publisher Summary This chapter focuses on finite automata on infinite sequences and infinite trees. The chapter discusses the complexity of the complementation process and the equivalence test. Deterministic Muller automata and nondeterministic Buchi automata are equivalent in recognition power. Any nonempty Rabin recognizable set contains a regular tree and shows that the emptiness problem for Rabin tree automata is decidable. The chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree. A short overview of the work that studies the fine structure of the class of Rabin recognizable sets of trees is also presented in the chapter. Depending on the formalism in which tree properties are classified, the results fall in three categories: monadic second-order logic, tree automata, and fixed-point calculi.

1,475 citations

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TL;DR: Maude as discussed by the authors is a programming language whose modules are rewriting logic theories, which is defined and given denotational and operational semantics, and it provides a simple unification of concurrent programming with functional and object-oriented programming and supports high level declarative programming of concurrent systems.

Abstract: Rewriting with conditional rewrite rules modulo a set E of structural axioms provides a general framework for unifying a wide variety of models of concurrency. Concurrent rewriting coincides with logical deduction in conditional rewriting logic , a logic of actions whose models are concurrent systems. This logic is sound and complete and has initial models. In addition to general models interpreted as concurrent systems which provide a more operational style of semantics, more restricted semantics with an incresingly denotational flavor such as preorder, poset, cpo, and standard algebraic models appear as special cases of the model theory. This permits dealing with operational and denotational issues within the same model theory and logic. A programming language called Maude whose modules are rewriting logic theories is defined and given denotational and operational semantics. Maude provides a simple unification of concurrent programming with functional and object-oriented programming and supports high level declarative programming of concurrent systems.

1,345 citations