Strategic programming on graph rewriting systems

We describe a strategy language to control the application of graph rewriting rules, and show how this language can be used to write high-level declarative programs in several application areas. This language is part of a graph-based programming tool built within the port-graph transformation and visualisation environment PORGY.Comment: In Proceedings IWS 2010, arXiv:1012.533

When Can An Equational Simple Graph Be Generated By Hyperedge Replacement?

Infinite hypergraphs with sources arise as the canonical solutions of certain systems of recursive equations written with operations on graphs. There are basically two different sets of such operations known from the literature, HR and VR. VR is strictly more powerful than HR on simple graphs. Necessary conditions are known ensuring that a VR-equational simple graph is also HR-equational. We prove that two of them, namely having finite treewidth or not containing all finite bipartite graphs, are also sufficient. This shows that equational graphs behave like context-free sets of finite graphs. Using an alternate characterization of VR-equational simple graphs [3], this result provides a (necessary and) sufficient condition and an effective procedure to translate a language-theoretic definition of an infinite graph [9] into an operational one based on substitution [11]

On Equational Simple Graphs

We consider simple graphs that can be obtained from the infinite complete binary tree B by some simple language-theoretic operations. Their decision problems for sentences in monadic second-order logic are reduced to those of B in a straightforward manner and therefore are solvable by the famous result of Rabin. Our goal is to provide a natural alternative characterization for these graphs. They are the canonical solutions of recursive systems of equations written with certain operations on simple graphs

How To Construct A Hyperedge Replacement System For A Context-Free Set Of Hypergraphs

. We give yet another proof for the fact that a context-free set of simple hypergraphs can be generated by hyperedge replacement if the connectivity of its elements is bounded in some way. Measures for connectivity are the maximum degree, the tree-width, or the number of hyperedges relative to the number of vertices. It all boils down to the question whether or not arbitrarily large bipartite graphs are subgraphs of the elements. We transform a system of equations in the form of [7] into a system of equations in the form of [1]. Our transformation is "direct" in the sense that the structure of the latter reflects the structure of the first. This distinguishes it from the approach in [9], which uses methods from automata theory, logic and graph theory, and employs several encodings in the transformation process. Our proof is more general than its other precursors [17] and [18, 2], which transform sets of rewriting rules. 1. Introduction The notion of context-freeness [3, 4, 5, 7] has p..

Linear Types for Higher Order Processes with First Class Directed Channels

We present a small programming language for distributed systems based on message passing processes. In contrast to similar languages, channels are one-to-one connections between a unique sender and a unique receiver process. Process definitions and channels are first class values and the topology of process systems can change dynamically. The operational semantics of the language is defined by means of graph rewriting rules. A static type system based on the notion of linear types ensures that channels are always used as one-to-one connections. Keywords: distributed programming, process algebras, linear types, operational semantics, graph rewriting 1 Introduction Since the beginning of the eighties, process algebras have been successfully used for specifying and verifying concurrent systems. In the past years, there have been several attempts to integrate the concepts of process algebras into programming languages, mostly extending functional languages, e.g. Facile [3,11], CML [8] or..

Local Normal Forms for First-Order Logic with Applications to Games and Automata

this paper are automata theory and descriptive complexity. Since Buchi's and Elgot's famous characterization of the regular string languages as the sets of models of (existential) monadic second-order (MSO) sentences, (existential) MSO logic has been used as a guideline in the search for reasonable automata models for other kinds of structures like trees or graphs. In descriptive complexity, since Fagin [Fag74] showed that the complexity class NP coincides with the sets of models of existential secondorder (

Local Normal Forms for First-Order Logic with Applications to Games and Automata

Building on work of Gaifman [Gai82] it is shown that every first-order formula is logically equivalent to a formula of the form 9x 1 ; : : : ; x l 8y' where ' is r-local around y, i. e. quantification in ' is restricted to elements of the universe of distance at most r from y. From this and related normal forms, variants of the Ehrenfeucht game for first-order and existential monadic second-order logic are developed that restrict the possible strategies for the spoiler, one of the two players. This makes proofs of the existence of a winning strategy for the duplicator, the other player, easier and can thus simplify inexpressibility proofs. As another application, automata models are defined that have, on arbitrary classes of relational structures, exactly the expressive power of firstorder logic and existential monadic second-order logic, respectively. 1 Introduction First-order (FO) logic and its extensions play an important role in many branches of (theoretical) computer science. ..