Namio Honda

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.

The decidability of equivalence for deterministic stateless pushdown automata

It is proved that there is an algorithm for deciding whether two deterministic stateless pushdown automata are equivalent. It is shown that equivalence can be tested in double-exponential time.

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.

Homomorphisms that preserve star height

A homomorphism ƒ from the set of words over a finite alphabet Σ 1 to the set of words over another finite alphabet Σ 2 is said to preserve star height if for all regular events R ⊆ Σ 1 * , the star height of R is equal to that of ƒ ( R ). An algorithm is presented for deciding whether an arbitrary homomorphism preserves star height or not: in our result, the injectivity of homomorphisms plays an important role, and it is shown that all homomorphisms which preserve star height are injective.

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.

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.