Bruno Courcelle

Bio: Bruno Courcelle is an academic researcher from L'Abri. The author has contributed to research in topics: Monadic predicate calculus & Clique-width. The author has an hindex of 43, co-authored 180 publications receiving 11012 citations. Previous affiliations of Bruno Courcelle include Centre national de la recherche scientifique & University of Bordeaux.

The monadic second-order logic of graphs. I. recognizable sets of finite graphs

Abstract: The notion of a recognizable set of finite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable.

Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-Width

Abstract: Hierarchical decompositions of graphs are interesting for algorithmic purposes There are several types of hierarchical decompositions Tree decompositions are the best known ones On graphs of tree-width at most k , ie, that have tree decompositions of width at most k , where k is fixed, every decision or optimization problem expressible in monadic second-order logic has a linear algorithm We prove that this is also the case for graphs of clique-width at most k , where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer allowed to use edge set quantifications We develop applications to several classes of graphs that include cographs and are, like cographs, defined by forbidding subgraphs with ``too many'' induced paths with four vertices

Graph Rewriting: An Algebraic and Logic Approach.

Abstract: Publisher Summary This chapter presents three mathematical tools that can be used to describe graph-grammars and the sets generated by them. The chapter describes graph properties by logical formulas and presents a comparison of the powers of several logical languages. The chapter discusses first-order logic, second-order logic, and monadic second-order logic, together with a few variants and restrictions of these three languages. It presents algebraic techniques that are useful for defining and studying graph rewriting rules and context-free graph-grammars. The chapter also presents the use of category theory for specifying graph rewriting rules in a precise and concise way, and for properly defining the least or rather the initial solution of a system of graph equations. It presents some links between the context-free graph-grammars and monadic second-order logic. Some applications to the definition of sets of graphs by forbidden configurations and to the theory of NP-completeness are also presented in the chapter.

Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach

Abstract: The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Phd by thesis

Abstract: Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

The Semantics of a Simple Language for Parallel Programming.

Abstract: In this paper, we describe a simple language for parallel programming. Its semantics is studied thoroughly. The desirable properties of this language and its deficiencies are exhibited by this theoretical study. Basic results on parallel program schemata are given. We hope in this way to make a case for more formal (i.e. mathematical) approach to the design of languages for systems programming and the design of operating systems. There is a wide disagreement among systems designers as to what are the best primitives for writing systems programs. In this paper, we describe a simple language for parallel programming and study its mathematical properties. 1. A SIMPLE LANGUAGE FOR PARALLEL PROGRAMMING The features of our mini-language are exhibited on the sample program S on Figure 1. The conventions are close to Algol1 and we only insist upon the new features. The program S consists of a set of declarations and a body. Variables of type integer channel are declared at line (1), and for any simple type σ (boolean, real, etc. . . ) we could have declared a σ channel. Then processes f , g and h are declared, much like procedures. Aside from usual parameters (passed by value in this example, like INIT at line (3)), we can declare in the heading of the process how it is linked to other processes : at line (2) f is stated to communicate via two input lines that can carry integers, and one similar output line. The body of a process is an usual Algol program except for invocation of wait until something on an input line (e.g. at (4)) or send a variable on a line of compatible type (e.g. at (5)). The process stays blocked on a wait until something is being sent on this line by another process, but nothing can prevent a process from performing a send on a line. In others words, processes communicate via first-in first-out (fifo) queues. Calling instances of the processes is done in the body of the main program at line (6) where the actual names of he channels are bound to the formal parameters of the processes. The infix operator par initiates the concurrent activation of the processes. Such a style of programming is close to may systems using EVENT mechanisms ([1, 2, 3, 4]). A pictorial representation of the program is the schema P on Figure 2, where the nodes represent processes and the arcs communication channels between these processes. What sort of things would we like to prove on a program like S? Firstly, that all processes in S run forever. Secondly, Begin (1) In t eg e r channel X, Y, Z , T1 , T2 ; (2 ) Process f ( i n t e r g e r in U,V; i n t e r g e r out W) ; Begin i n t e g e r I ; l o g i c a l B; B := true ; Repeat Begin (4 ) I := i f B then wait (U) e l s e wait (V) ; (7 ) p r in t ( I ) ; (5 ) send I on W; B := not B; End ; End ; Process g ( i n t e g e r in U ; i n t e g e r out V, W) ; Begin i n t e g e r I ; l o g i c a l B; B := true ; Repeat Begin I := wait (U) ; i f B then send I on V e l s e send I on W : B := not B; End ; End ; (3 ) Process h( i n t e g e r in U; i n t e g e r out V; i n t e g e r INIT ) ; Begin i n t e g e r I ; send INIT on V; Repeat Begin I := wait (U) ; send I on V; End ; End ; Comment : body o f mainprogram ; (6 ) f (X,Y,Z) par g (X,T1 ,T2) par h(T1 ,Y, 0 ) par h(T2 , Z , 1 ) ; End ; Figure 1: Sample parallel program S. more precisely, that S prints out (at line (7)) an alternating sequence of 0’s and 1’s forever. Third, that if one of the processes were to stop at some time for an extraneous reason, the whole systems would stop. The ability to state formally this kind of property of a parallel program and to prove them within a formal logical framework is the central motivation for the theoretical study of the next sections. 2. PARALLEL COMPUTATION Informally speaking, a parallel computation is organized in the following way: some autonomous computing stations are connected to each other in a network by communication lines. Computing stations exchange information through these lines. A given station computes on data coming along

Handbook of Formal Languages

Abstract: The theory of formal languages is the oldest and most fundamental area of theoretical computer science. It has served as a basis of formal modeling from the early stages of programming languages to the recent beginnings of DNA computing. This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field. Best specialists of various subareas, altogether 50 in number, are among the authors. The maturity of the field makes it possible to include a historical perspective in many presentations. The individual chapters can be studied independently, both as a text and as a source of reference. The Handbook is an invaluable aid for advanced students and specialists in theoretical computer science and related areas in mathematics, linguistics, and biology.

A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth

Abstract: In this paper, we give for constant $k$ a linear-time algorithm that, given a graph $G=(V,E)$, determines whether the treewidth of $G$ is at most $k$ and, if so, finds a tree-decomposition of $G$ with treewidth at most $k$. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at most some constant $k$.