We present pumping lemmas for five classes of functions definable by fragments weighted automata over the min-plus semiring, max-plus semiring and natural numbers. As a corollary we show that hierarchy unambiguous, finitely-ambiguous, polynomially-ambiguous automata, full class is strict semirings.

There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of ΓI(R) for some ideal I of R. We also show tha...

Let be a commutative semiring. A semimodule over semiring is fully prime if each proper subsemimodule of prime. This research aims to investigate the relationship between direct sum subsemimodules and , semimodule.

The tropical semiring M consists of the set of natural numbers extended with innnity, equipped with the operations of taking minimums (as semiring addition) and addition (as semiring multiplication). We use factorization forests to prove niteness results related to semi-groups of matrices over M. Our method is used to recover results of Hashiguchi, Leung and the author in a uniied combinatorial...

We introduce the notion of a generalized semi-ideal in a ternary semiring. Various examples to establish a relationship between ideals, bi-ideals, quasi-ideals and generalized semi-ideals are furnished. A criterion for a commutative ternary semiring without any divisors of zero to a ternary division semiring is given. AMS Mathematics Subject Classification (2010): 16Y60, 16Y99

The paradigm of pattern discovery based on constraints was introduced with the aim of providing to the user a tool to drive the discovery process towards potentially interesting patterns, with the positive side effect of achieving a more efficient computation. So far the research on this paradigm has mainly focussed on the latter aspect: the development of efficient algorithms for the evaluatio...

Weighted languages and weighted automata over multi-hemirings are capable of expressing quantitative properties of systems such as its average or discounted costs. We study the applicability of well-known semiring theory and algorithms in the field of multi-hemirings. To this end, we embed multi-hemirings into semirings and extend this embedding for weighted languages and weighted automata. We ...

Cost register automata (CRAs) are one-way finite automata whose transitions have the side effect that a register is set to the result of applying a state-dependent semiring operation to a pair of registers. Here it is shown that CRAs over the tropical semiring (N∪{∞},min,+) can simulate polynomial time computation, proving along the way that a naturally defined width-k circuit value problem ove...

The semiring-based constraint satisfaction problems (semiring CSPs), proposed by Bistarelli, Montanari and Rossi [3], is a very general framework of soft constraints. In this paper we propose an abstraction scheme for soft constraints that uses semiring homomorphism. To find optimal solutions of the concrete problem, the idea is, first working in the abstract problem and finding its optimal sol...