Tetsuo Moriya

Accepting conditions for automata on Ω-languages

Abstract In this paper we study the ω-languages accepted by finite automata under a new type of accepting conditions which are based on whether the automaton enters all of its accepting states infinitely many times or not. We investigate the classes of ω-languages defined thereby in relation to other well-known subclasses of the class of ω-regular languages.

Topological characterizations of infinite tree languages

Abstract In this paper we define several types of acceptance of finite automata for infinite trees, and study the topological properties of the tree languages accepted thereby. As a consequence, we show that the two classes of tree languages accepted by (nondeterministic) tree automata in the following two types of acceptance coincide: 1. (1) an infinite tree τ is accepted iff there is a run for τ such that on each path an accepting state is contained; 2. (2) an infinite tree τ is accepted iff every run for τ contains an accepting state.

Some Results on Primitive Words, Square-Free Words, and Disjunctive Languages

In this paper, we give some resuts on primitive words, square-free words and disjunctive languages. We show that for a word u e Σ+, every element of λ(cp(u)) is d-primitive iff it is square-free, where cp(u) is the set of all cyclic-permutations of u, and λ(cp(u)) is the set of all primitive roots of it. Next we show that pm qn is a primitive word for every n, m ≥ 1 and primitive words p, q, under the condition that |p| = |q| and (m, n) ≠ (1, 1). We also give a condition of disjunctiveness for a language.

Closure properties of subclasses of ω-regular languages under morphism and inverse morphism

We study ω-languages by using morphism and inverse morphism. We investigate the closure properties of some subclasses of ω-regular languages under e-free morphism and inverse morphism (for e-free case and for arbitrary case). As one of the results, we have that the only R ω the class of all ω-regular languages, is closed under both e-free morphism and inverse (arbitrary) morphism.

A Class by Principal Congruence of a Syntactically Embedded Language

In this paper, we introduce a syntactically embedded (s-embedded) language, and consider its principal congruence. The following three results are proved, where PL is the principal congruence of a language L, and W(L) is the residual of L. (1) For a language K, s-embedded in M, K is equal to a PM class. (2) For a language K, s-embedded in an infix language M, K is equal to a PW(M) class. (3) For a nonempty s-embedded language L, if L is double-unitary, then L is equal to a PW(M) class. From the above results, we can obtain those for principal congruence of some codes. For example, Ln is equal to a PLn+1 class for an inter code L of index n.

Literal shuffle on Ω-languages

We consider literal shuffle on ω-languages. First, we show that a duo (a family of ω-languages closed under e-free morphisms and inverse e-free morphisms) is closed under literal shuffle if and only if it is closed under intersection. Next we investigate the closure properties of some classes of the ω-regular languages under literal shuffle and shuffle. Last the relation between literal shuffle and shuffle are presented.

Full coverability of ω-powers of codes

We give the necessary and sufficient condition for some types of ω-languages(ω-powers of codes) to represent the set {x|0 ≦ x ≦ 1} of real numbers written in binary notations.

Ω-languages accepted by finite automata whose structures are cascade products of resets

Abstract We study ω-languages accepted by finite automata whose structures are cascade products of resets. It is proved that the class of ω-languages accepted by these kinds of automata under Muller-type conditions coincides with the class of star-free ω-regular languages and that it properly includes the class of ω-languages accepted by these kinds of automata under Buch-type conditions. Furthermore we prove that the class of projective images of star-free ω-regular languages coincides with the class of ω-regular languages.

Closure property of principal cones under substitution

It is shown that a principal cone L is closed under substitution if and only if L is closed under syntactic substitution of cone generators of L.