Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that semiring complexity of a Schur polynomial sλ(x1, . . . , xk) labeled by a partition λ = (λ1 ≥ λ2 ≥ · · · ) is bounded by O(log(λ1)) provided the number of variables k is fixed.

Overview Diagnosis traditionally viewed as logical reasoning – (de Kleer and Williams 87), (Reiter 87), ... But more naturally viewed as constraint optimization – Minimal set of faulty components, most likely fault, ... Framework that unifies qualitative and quantitative notions of diagnosis using semiring-based CSP – Choose appropriate semiring and construct constraints Diagnosis algorithms ba...

In this paper we investgate some properties of fuzzy ideal extension of fuzzy ideal, fuzzy prime ideal, fuzzy semiprime ideal of a Γ−semiring. Among other results we have obtained a characterization of a prime ideal I of a Γ−semiring in terms of fuzzy ideal extension of its characteristic function λI . Mathematics Subject Classification[2000]:16Y60, 16Y99, 03E72

In the present paper we show that given a tree series S, which is accepted by (a) a deterministic bottom-up finite state weighted tree automaton (for short: bu-w-fta) or (b) a non-deterministic bu-w-fta over a locally finite semiring, there exists for every input tree t ∈ supp(S) a decomposition t = C′[C[s]] into contexts C, C′ and an input tree s as well as there exist semiring elements a, a′,...

1 0 Introduction The tropical semiring is the semiring denoted by M which has support Nf+1g and operations ab = minfa; bg and ab = a+b. It was rst introduced in the context of cost minimization in Operations Research. However it appeared that M plays in fact a central role in several decision problems concerning rational languages (see 15] for a survey of the tropical semiring theory and of its...

We prove a general lower bound on the size of switching-and-rectifier networks over any semiring of zero characteristic, including the (min,+) semiring. Using it, we show that the classical dynamic programming algorithm of Bellman, Ford and Moore for the shortest s-t path problem is optimal, if only Min and Sum operations are allowed.

The prime k-spectrum Speck(R) of a k-semiring R will be introduced. It will be proven that it is a topological space, and some properties of this space will be investigated. Connections between the topological properties of Speck(R) and possible algebraic properties of the k-semiring R will be established.

This note gives an explicit construction of the one-generated free domain semiring. In particular it is proved that the elements can be represented uniquely by finite antichains in the poset of finite strictly decreasing sequences of nonnegative integers. It is also shown that this domain semiring can be represented by sets of binary relations with union, composition and relational domain as op...

We show that the support of a recognizable series over a zero-sum free, commutative semiring is a recognizable language. We also give a sufficient and necessary condition for the existence of an effective transformation of a weighted automaton recognizing a series S over a zero-sum free, commutative semiring into an automaton recognizing the support of S.

We consider (subclasses of) polynomial bottom-up and top-down tree series transducers over a partially ordered semiring A = (A,⊕, ,0,1, ), and we compare the classes of tree-to-tree-series and o-tree-to-tree-series transformations computed by such transducers. Our main result states the following. If, for some a ∈ A with 1 a, the semiring A is a weak a-growth semiring and either (i) the semirin...