Hidenosuke Nishio

Fault tolerant cellular spaces

This paper treats the problem of designing a fault tolerant cellular space which simulates an arbitrary given cellular space in real time. A cellular space is called fault tolerant if it behaves normally even when its component cells misoperate. First such notions as simulation, misoperation, and K-separated misoperation are defined. Then a new multidimensional coding of configurations is introduced and explained using as typical example the two-dimensional space. The first main result is Theorem 1, which states that the introduced coding method is useful for correcting errors occurring at most once in every K=5x5 rectangle. The general theory is given in Section 6, where the second main result is given in the form of Theorem 8. It gives a necessary and sufficient condition for testing whether or not a given coding is adequate for error correction.

How does the neighborhood affect the global behavior of cellular automata

The neighborhood is a fundamental constituent of the cellular automaton (CA) and has been investigated in its own right by H.Nishio, M.Margenstern and F.von Haeseler(2004,2005) In this paper we ask a new question how the neighborhood affects the global behavior of CA and particularly gives some instances of CA where the global behavior does not depend on the neighborhood We also discuss the conjectures that the injectivity is generally preserved from changing the neighborhood but the surjectivity is not.

Some regular state sets in the system of one-dimensional iterative automata ☆

Abstract For the system of one-dimensional iterative automata, each set of all passive, Garden-of-Eden, and branching point state configurations is defined and shown to constitute a regular set. This regularity is proved to hold for the fixed, cyclic, open and reflexive boundary conditions. For proving theorems, a new device called N -automaton is introduced. Relationship with the gsm mapping is also discussed.

Changing the neighborhood of cellular automata

In place of the traditional definition of a cellular automaton CA = (S, Q,N, f), a new definition (S, Q, fn, υ) is given by introducing an injection called the neighborhood function v : {0, 1, ..., n - 1} → S, which provides a connection between the variables of local function fn of arity n and neighbors of CA: image(v) is a neighborhood of size n. The new definition allows new analysis of cellular automata. We first show that from a single local function countably many CA are induced by changing v and then prove that equivalence problem of such CA is decidable. Then we observe what happens if we change the neighborhood. As a typical research topics, we show that reversibility of 2 states 3 neighbors CA is preserved from changing the neighborhood, but that of 3 states CA is not.

Variations on neighborhoods in CA

We show how an arbitrary finite number of CA with different local rules can be simulated by CA using the same local rule by just changing the (shape of the) neighborhood. In that way one can even achieve universality.

Cell lineage system for describing growths of filamentous organisms

For describing and analyzing the growth process of filamentous organisms, the L system was originated by A. Lindenmayer in 1968, and since then it has been investigated by many authors intensively. We define here a new formal system, the cell lineage (CL) system, for the same purpose, and prove its fundamental relationships to the L system. Among other things, we show that in general the CL system is more powerful than the PDIL system in describing filamentous growths, but in a restricted case the finite regular CL system is equivalent to the PDOL system.

HEURISTIC USE OF IMAGE PROCESSING TECHNIQUE FOR THEORETICAL STUDIES OF AUTOMATA

Publisher Summary This chapter discusses the heuristic use of image processing technique for theoretical studies of automata. The relationship between the study of pattern recognition and the theoretical study of automata is two folds: (1) Theory of automata will be a base or a background for pattern recognition. (2) Pattern recognition (processing) technique will help the theoretical study of complex systems such as cellular automata. The field of pattern recognition has two distinct goals. One is to construct an effective machine for classifying given images into certain preassigned categories. The other is to know the mechanism of image perception and pattern recognition in a human being or other living organisms. The classification problem is new in the study of cellular automata. The interactive graphic display system with image processing ability seems effective in this study, though definite results have not yet been obtained. The simulation method using unknown variables has been newly devised for visualizing the information transmission. New theoretical results are expected from this kind of man–machine communication, and from two-fold relationship between pattern recognition and theory of automata.

Structural and behavioral equivalence relations in automata networks

Abstract We formulate the automata network as an edge- and vertex-labeled directed graph. A vertex-label corresponds to the finite automaton which is placed at the vertex and an edge-label corresponds to the label of the input terminal of a finite automaton on the vertex. In this paper, we define, on the set of vertices, the structural equivalence relation induced by the structure of the graph and the behavioral equivalence relation induced by the behavior (i.e., state transition) of the finite automaton on each vertex and discuss the structure and behavior of the network by investigating the relationships between these relations. We have obtained some interesting results, in particular about the element-uniform system.

On Polynomial Rings in Information Dynamics of Linear CA

In this article we are considering linear cellular automata with states in the ring of maps from a finite field in itself. We are particularly interested in the structure of the subrings generated by the coefficients of powers of polynomials with coefficients in the above mentioned ring. We present results on the equality of these subrings together with an upper bound on the number of different subrings generated by this procedure.

Automorphissm Classification of Cellular Automata

A new classification of arbitrary cellular automata (CA for short) in Z d is studied considering the set (group) of all permutations of the neighborhood ν and state set Q. Two CA (Z d, Q, f A, ν A) and (Z d, Q, f B, ν B) are called automorphisc, if there is a pair of permutations (π, p) of ν and Q, respectively, such that (f B, ν B) = (p −1 f A πp, ν A π), where ν π denotes a permutation of ν and f π denotes a permutation of arguments of local function f corresponding to ν π. This automorphissm naturally induces a classification of CA, such that it generally preserves the global properties of CA up to permutation. As a typical example of the theory, the local functions of 256 ECA (1-dimensional 3-nearest neighbors 2-states CA) are classified into 46 classes. We also give a computer test of surjectivity, injecitivity and reversibility of the classes.