Graph Automata Research Articles

L-graph Automata And Some Applications

Abstract This paper defines a novel graph constructed on a residuated lattice using a specific definition of the fuzzy graph (called $L$-graph). These types of graphs also have applications in libraries, pharmacies and machine facilities. Among these applications, this research presents the $L$-graph automaton related to the $L$-graph constructed by a minimum zero forcing set. The $L$-graph automaton is used to find efficient searching for diseases that have the most similar symptoms. It has been demonstrated that if two $L$-graphs are isomorphic, then the related $L$-graph automata are isomorphic but not necessarily vice versa. New notions, $L^{\prime\prime}$-graph automata, pseudo-isomorphism and self-sufficiency are proved. Besides, by taking advantage of the properties of the residuated lattice, it has been proven that the two $L$-graph automata are equivalent if and only if the $L^{\prime}$-graph automata contracted of $L$-graph automata are equivalent. Ultimately, in light of the above, some related theorems are proved and several examples are provided to illustrate these new notions.

Treewidth, pathwidth and cospan decompositions with applications to graph-accepting tree automata

We will revisit the categorical notion of cospan decompositions of graphs and compare it to the well-known notions of path decomposition and tree decomposition from graph theory. More specifically, we will define several types of cospan decompositions with appropriate width measures and show that these width measures coincide with pathwidth and treewidth. Such graph decompositions of small width are used to efficiently decide graph properties, for instance via graph automata. Hence we will give an application by defining graph-accepting tree automata, thus integrating previous work by Courcelle into the setting of cospan decompositions. Furthermore we will show that regardless of whether we consider path or tree decompositions, we arrive at the same notion of recognizability.

Incorporating Graph Automata into Plant Growth Simulation with Nutrients Transport

In this paper we model the growth of living plants in a discrete approach, the graph automata based plant model representing each metamer of the plant as node of the automata. The allocation and transport of carbon, water and nitrogen among metamers, as an emergent property, resulted from the strategy of local pressure equilibrium between adjacent neighbors using discrete pressure-flow kinetics which were found to be suitable to describe mass flow in discrete space. Simulation results show that the graph automata based parallel approach can deal with carbon transport and allocation effectively.

AUTOMATIC GENERATION OF SELF-REPLICATING PATTERNS IN GRAPH AUTOMATA

Graph automata define symbol dynamics of graph structures, which are capable of generating structures in addition to describing state transition. Rules of the graph automata are uniform and are therefore suitable for evolutionary computation. This paper shows that various self-replications are possible in graph automata, and that evolutionary computation is applicable to automatic rule generation to obtain self-replicating patterns of graph automata.

グラフオートマタ

A variety of models of self-reproduction process have been proposed since von Neumann initiated this field. Almost all of them are described within the framework of two-dimensional cellular automata. They are heavily dependent on or limited by the peculiar properties of the two dimensional lattice spaces, but such properties are irrelevant to the essential nature of self-reproduction. In this paper, we introduce a new framework called “graph automata” to obtain a natural description of complicated spatio-temporal developmental processes. As an illustrative example, a self-reproduction of Turing machine, which requires very long description by conventional cellular automata, is shown in a simple and straightforward formulation.

Graph automata: natural expression of self-reproduction

A variety of models of self-reproduction process have been proposed since von Neumann initiated this field with his self-reproducing automata. Almost all of them are described within the framework of two-dimensional cellular automata. They are heavily dependent on or limited by the peculiar properties of the two-dimensional lattice spaces. But such properties are irrelevant to the essential nature of self-replication. In this paper, we introduce a new framework called “graph automata” to obtain a natural description of complicated spatio-temporal developmental processes such as self-reproduction. The most advantageous point of this methodology is that it is not restricted to particular lattice space. As an illustrative example, a self-reproduction of Turing machine, which requires very long description by conventional cellular automata, is shown in a simple and straightforward formulation. Graph automata provide a new tool to approach important scientific problems such as evolution of morphology, and also to give the basis of self-reproducing and self-repairing artifacts.

Time--Space Tradeoffs For Undirected st-Connectivity on a Graph Automata

Undirected st-connectivity is an important problem in computing. There are algorithms for this problem that use O(n) time and ones that use O(log n) space. The main result of this paper is that, in a very natural structured model, these upper bounds are not simultaneously achievable. Any probabilistic jumping automaton for graphs (JAG) requires either space $\Omega( \log^2 n / \log log n )$ or time $n^{(1 + \Omega ( 1 / \log \log n )) }$ to solve undirected st-connectivity.

Time-Space Tradeoffs for Undirected Graph Traversal by Graph Automata

We investigate time-space tradeoffs for traversing undirected graphs, using a variety of structured models that are all variants of Cook and Rackoff's “Jumping Automata for Graphs.” Our strongest tradeoff is a quadratic lower bound on the product of time and space for graph traversal. For example, achieving linear time requires linear space, implying that depth-first search is optimal. Since our bound in fact applies to nondeterministic algorithms for non connectivity, it also implies that closure under complementation of nondeterministic space-bounded complexity classes is achieved only at the expense of increased time. To demonstrate that these structured models are realistic, we also investigate their power. In addition to admitting well known algorithms such as depth-first search and random walk, we show that one simple variant of this model is nearly as powerful as a Turing machine. Specifically, for general undirected graph problems, it can simulate a Turing machine with only a constant factor increase in space and a polynomial factor increase in time.

A branching time logic with past operators

An expressive branching time logic is introduced. Its power allows us to describe the local structure of the underlying graph of the computation. The logic's linear operators correspond to all the relations definable by finite automata and are able to express the computations in the past, in addition to the computations in the future. In particular the logic contains as a fragment the ordinary temporal logic of branching time. It is shown that the logic is decidable. The proof is based on reduction to the emptiness problem for graph automata.

Nondeterminism versus determinism of finite automata over directed acyclic graphs

Three types of nite-state graph automata are compared over directed acyclic graphs (where vertices and edges are labelled). The automata are distinguished by the way how states are attached to an input graph (\vertexmarking, \edge-marking, and \1-sphere-marking). We note the equivalence of these models, relate them to logical denability notions, and show that deterministic versions are strictly weaker (thus correcting an error of [9]).

Sequential and cellular graph automata

Labeled graphs of bounded degree, with numbers assigned to the arcs at each node, are called d-graphs. Sequential and cellular d-graph automata are defined, and it is shown that they can simulate each other and are also equivalent to web-bounded automata.

Cellular graph automata. II. graph and subgraph isomorphism, graph structure recognition

This paper deals with cellular automata in which the intercell connections define a graph of bounded degree. It discusses acceptance tasks that involve the detection of graph or subgraph isomorphism in time proportional to the diameter of the given graph. In some of the algorithms, special assumptions are made about the “homogeneity” of the graph; these assumptions hold for many important classes of graphs, including trees and arrays. The paper also examines types of graph structures that can be recognized by these automata. Diameter-time algorithms are presented for the recognition of cycles, strings, trees, cliques, rectangular and square arrays, Eulerian graphs, bipartite and complete bipartite graphs, stars, and wheels. The recognition of planar graphs is also discussed.

Acceptors for the derivation languages of phrase-structure grammars

This paper studies the representation of the derivations in phrase-structure grammars by the use of “derivation languages.” The words in the derivation language of a grammar correspond exactly to the “syntactical graphs” of Loeckx (1970) . Furthermore, the derivation languages generalize the representation of context-free derivation trees in prefix form. “Graph automata” are developed as acceptors of the derivation languages. The graph automata generalize the theory of tree automata as studied in connection with contextfree grammars.