Separable graphs, planar graphs and web grammars

This paper is concerned with the class of “web grammars,≓ introduced by Pfaltz and Rosenfeld, whose languages are sets of labelled graphs. A slightly modified definition of web grammar is given, in which the rewriting rules can have an applicability condition, and it is proved that, in general, this extension does not increase the generative power of the grammar. This extension is useful, however, for otherwise it is not possible to incorporate negative contextual conditions into the rules, since the context of a given vertex can be unbounded. A number of web grammars are presented which define interesting classes of graphs, including unseparable graphs, unseparable planar graphs and planar graphs. All the grammars in this paper use “normal embeddings≓ in which the connections between the web that is written and the host web are conserved, so that any rewriting rule affects the web only locally

A system of graph grammars which generates all recursively enumerable sets of labelled graphs

The aim of this paper is to prove that the system of simple graph grammars (Einfache Graph-Grammatiklen) in [1] is complete. A graph grammar is generakization of a Chomsky-grammar which defines a graph language, i.e. a language composed of a set of directed graphs with labelled nodes and arcs. ..

Program Understanding through Cliché Recognition

We propose research into automatic program understanding via recognition of common data structures and algorithms (clichés). Our goals are two-fold: first, to develop a theory of program structure which makes such recognition tractable; and second, to produce a program (named Inspector) which, given a Lisp program and a library of clichés, will construct a hierarchical decomposition of the program in terms of the clichés it uses. Our approach involves assuming constraints on the possible decompositions of programs according to the teleological relations between their parts. Programs are analyzed by translating them into a language-independent form and then parsing this representation in accordance with a context-free web grammar induced by the library of clichés. Decompositions produced by this analysis will in general be partial, since most programs will not be made up entirely of clichés. This work is motivated by the belief that identification of clichés used in program, together with knowledge of their properties, provides a sufficient basis for understanding large parts of that program's behavior. Inspector will become one component of a system of programs known as a programmer's apprentice, in which Inspector's output will be used to assist a programmer with program synthesis, debugging, and maintenance.MIT Artificial Intelligence Laborator

Logic and Automata

Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field

Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing

This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to represent a collection of processes, depicted as "boxes" with multiple (typed) inputs and outputs, depicted as "wires". If we allow plugging input and output wires together, we can intuitively represent complex compositions of processes, formalised as morphisms in a monoidal category. [...] The first major contribution of this dissertation is the introduction of a discretised version of a string diagram called a string graph. String graphs form a partial adhesive category, so they can be manipulated using double-pushout graph rewriting. Furthermore, we show how string graphs modulo a rewrite system can be used to construct free symmetric traced and compact closed categories on a monoidal signature. The second contribution is in the application of graphical languages to quantum information theory. We use a mixture of diagrammatic and algebraic techniques to prove a new classification result for strongly complementary observables. [...] We also introduce a graphical language for multipartite entanglement and illustrate a simple graphical axiom that distinguishes the two maximally-entangled tripartite qubit states: GHZ and W. [...] The third contribution is a description of two software tools developed in part by the author to implement much of the theoretical content described here. The first tool is Quantomatic, a desktop application for building string graphs and graphical theories, as well as performing automated graph rewriting visually. The second is QuantoCoSy, which performs fully automated, model-driven theory creation using a procedure called conjecture synthesis.Comment: PhD Thesis. Passed examination. Minor corrections made and one theorem added at the end of Chapter 5. 182 pages, ~300 figures. See full text for unabridged abstrac