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.

Foundations of logic programming

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.

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Supervisory control of a class of discrete event processes

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. >

The control of discrete event systems

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.

Automata on infinite objects

Conditional rewriting logic as a unified model of concurrency

Fiftieth volume of theoretical computer science

https://link.springer.com/content/pdf/10.1007%2F3-540-62005-2_25.pdf

Reconstructing convex polyominoes from horizontal and vertical projections

The metric space of infinite trees. Algebraic and topological properties

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.

/pdf/on-translating-one-polyomino-to-tile-the-plane-4cgyephhqw.pdf

On translating one polyomino to tile the plane

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).

Maurice Nivat

Papers

Fiftieth volume of theoretical computer science

Reconstructing convex polyominoes from horizontal and vertical projections

The metric space of infinite trees. Algebraic and topological properties

On translating one polyomino to tile the plane

Tree Automata and Languages