Masakazu Nasu

Linear cellular automata over Zm

Abstract A subclass of cellular automata called linear cellular automata over Z m is studied. Criteria for surjectivity and injectivity of the global transition function of such a cellular automaton are presented. The question of reappearance of patterns for such cellular automata is also dealt with.

Local maps inducing surjective global maps of one-dimensional tessellation automata

In this paper, we investigate some combinatorial aspects ofC-surjective local maps, i.e., local maps inducing surjective global maps,CF-surjective local maps, i.e., local maps inducing surjective restrictions of global maps on the setCF of finite configurations, andC-injective local maps, i.e., local maps inducing injective local maps, of one-dimensional tessellation automata.We introduce a pair of right and left bundle-graphs and a pair of right and leftλ-bundle-graphs for everyC-surjective local map. We give characterizations forCF-surjectivity,C-injectivity and some other properties ofC-surjective local maps in relation to these bundle-graphs. We also establish some properties of the inverse of aC-injective local map.

Fuzzy events realized by finite probabilistic automata

In this paper the concept of probabilistic events is introduced and their closure properties under the operations on the set of all fuzzy events are studied. It is shown that the mean of probabilistic events is a probabilistic event and the set of all probabilistic events is closed under the transposition and the operation of the convex-combination. A sufficient condition for the union and the intersection of two probabilistic events to be probabilistic events in the sense of fuzzy sets is given. In the last two sections we showed some families of probabilistic events closed or approximately closed under the operation of the union and the intersection and the complementation.

A context-free language which is not acceptable by a probabilistic automaton

A linear context-free language which is not acceptable by a finite probabilistic automaton is given, and it is shown that the family of stochastic languages is not closed under concatenation and homomorphism.

Mappings induced by PGSM-mappings and some recursively unsolvable problems of finite probabilistic automata

A probabilistic event is a fuzzy set of tapes accepted by a finite probabilistic automation. In this paper, a mapping induced by a PGSM-mapping is introduced and is shown to be one of the operations which preserve a probabilistic event. Using mappings induced by a GSM-mapping, some recursively unsolvable problems with respect to rational finite probabilistic automata are studied.

Indecomposable local maps of tessellation automata

Indecomposable local maps of one-dimensional tessellation automata are studied. The main results of this paper are the following. (1) For any alphabet ∑ containing two or more symbols and for anyn≥ 1, there exist indecomposable scope-n local maps over ∑. (2) If ∑ is a finite field of prime order, then a linear scope-n local map over ∑ is indecomposable if and only if its associated polynomial is an irreducible polynomial of degreen − 1 over ∑, except for a trivial case. (3) Result (2) is no longer true if ∑ is a finite field whose order is not prime.

Left universal context-free grammars and homomorphic characterizations of languages

A context-free grammar G with terminal vocabulary σ is left universal for a class of languages uif110-1} with respect to a class of languages uif110-2} if for each language L ⊂ σ* in uif110-3}, a control language C in uif110-4} can be found such that G controlled by C generates L by leftmost derivations. We show that for a class of languages uif110-5} and a class of languages uif110-6}, if uifuscL}1 is closed under homomorphism and inverse homomorphism, then for each alphabet σ, the following two statements are equivalent. (1) There exists a context-free grammar with terminal vocabulary σ which is left universal for uif110-7} with respect to uif110-8}. (2) There exist a context-free language L1 and a homomorphism h such that each language L ⊂ σ* in uif110-9} equals uith(L1 ∩ L′)} for some L′ in uif110-10}. We also give some applications of this result.

RECOGNITION OF FUZZY LANGUAGES

In this paper, we propose the concept of recognition of fuzzy languages by machines such as Turing machines, linear bounded automata, pushdown automata and finite automata. It is shown that it is a reasonable extension of the ordinary concept of recognition of languages by machines. Basic results are given about the recognition theory of fuzzy languages.

An interconnection of local maps inducing onto global maps

Abstract “Local maps and the global maps induced by them” treated in this paper is a subject not only on cellular or tessellation automata but also on shift dynamical systems. We study an interconnection of local maps inducing onto global maps from a graph-theoretical viewpoint.

A completeness property of one-dimensional tessellation automata

In this paper, it is shown that if k>=3, any finite k-symbols pattern whose lengthis greater than 1 can be generted strictly monotonously from the primitive pattern by some sequence of parallel transformations of a k-symbols scope-n tessellation automaton for any n>=2. It is also shown that any nonzero finite binary pattern can be generated monotonously from the primitive pattern by some sequence of parallel transformations of a binary scope-n tessellation automaton for any n>=3.