We consider tree automata with costs over semirings in the sense of (Seidl, 1994). We de ne the concept of a nitely factorizing semiring and of a monotonic semiring, both as the generalization of well-known particular semirings, and show that the costniteness of tree automata with costs over nitely factorizing and monotonic semirings is decidable. We show that, for tree automata with costs over...

While the existence of inverses is a natural condition in Algebra it is seldom satissed in Computer Science applications. Since the group-theoretical orientation has to be abandoned we consider an advantage when the non-conventional structures needed are linked to an already existing knowledge. We propose semirings as a candidate and we aim at the Computer Science applications such as processes...

In continuation of a previous works on semirings [5], in the present paper we introduce the notions of a strong ternary semiring (ST-semiring) (that is a ternary semirings with an additional condition called the left invertive law). We prove that many results obtained in [5] for semirings are still valid in the present case. We establish some relationships between the idempotents for both the a...

The aim of this paper is to investigate the ideal theory of Γ-semirings based on intersectional soft sets. Some basic operations are investigated and some related properties are also studied. Finally, some characterizations of regular and intra-regular Γ-semirings are obtained by means of soft intersectional ideals (bi-ideals, quasi-ideals).

In this paper, we describe the relationships between pseudo MV algebras and semirings. We also give definitions of automata on lattice ordered semirings, prove that the family of K-Languages is closed under union, and discuss the conditions for the closedness of families of K-languages under intersection, generalized intersection and reversal operations.

In this note we describe conditions under which, in idempotent functional analysis (see [1–3]), linear operators have integral representations in terms of idempotent integral of V. P. Maslov. We define the notion of nuclear idempotent semimodule and describe idempotent analogs of the classical kernel theorems of L. Schwartz and A. Grothendieck (see, e.g., [4–6]). In [11], for the idempotent sem...

We study generalized fixed-point equations over idempotent semirings and provide an efficient algorithm for the detection whether a sequence of Kleene’s iterations stabilizes after a finite number of steps. Previously known approaches considered only bounded semirings where there are no infinite descending chains. The main novelty of our work is that we deal with semirings without the boundedne...

General automata are considered with respect to normal-ization over semirings. Possibilistic automata are deened as normal pessimistic fuzzy automata. Possibilistic automata are analogous to stochas-tic automata where stochastic (+=) semirings are replaced by possi-bilistic (_=^) semirings; but where stochastic automata must be normal, fuzzy automata may be (resulting in possibilistic automata)...

Conway hemirings are Conway semirings without a multiplicative unit. We also define iteration hemirings as Conway hemirings satisfying certain identities associated with the finite groups. Iteration hemirings are iteration semirings without a multiplicative unit. We provide an analysis of the relationship between Conway hemirings and (partial) Conway semirings and describe several free construc...

3 Dioids 4 3.1 Join Semilattices . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Join Semilattices with an Additive Unit . . . . . . . . . . . . 5 3.3 Near Semirings . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Variants of Dioids . . . . . . . . . . . . . . . . . . . . . . . . 6 3.5 Families of Nearsemirings with a Multiplicative Unit . . . . . 8 3.6 Families of Nearsemirin...