Esik and Maletti introduced the notion of a proper semiring and proved that some important (classes of) semirings – Noetherian semirings, natural numbers – are proper. Properness matters as the equivalence problem for weighted automata over a semiring which is proper and finitely and effectively presented is decidable. Milius generalised the notion of properness from a semiring to a functor. As...

Modern Statistical Machine Translation (SMT) systems make their decisions based on multiple information sources, which assess various aspects of the match between a source sentence and its possible translation(s). Tuning a SMT system consists in finding the right balance between these sources so as to produce the best possible output, and is usually achieved through Minimum Error Rate Training ...

In this paper, we propose a new signature scheme connecting two private keys and two public keys based on general non-commutative division semiring. The key idea of our technique engrosses three core steps. In the first step, we assemble polynomials on additive structure of non-commutative division semiring and take them as underlying work infrastructure. In the second step, we generate first s...

Statistical parsing algorithms are useful in structure predictions, ranging from NLP to biological sequence analysis. Currently, there are a variety of efficient parsing algorithms available for different grammar formalisms. Conventionally, different parsing descriptions are needed for different tasks; a fair amount of work is required to construct for each one. Semiring parsing is proposed to ...

A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.

Semiring is an algebraic structure of (S, +, ×). Similar to a ring, but without the condition that each element must have inverse adding operation. The forms +) and ×) are semigroups satisfy distributive law multiplication addition. In matrix theory, there term known as Kronecker product. This operation transforms two matrices into larger containing all possible products entries in matrices. pr...

We determine the automorphism group of zero-divisor digraph semiring matrices over an antinegative commutative with a finite number zero-divisors.

We suggest a version of Nullstellensatz over the tropical semiring, the real numbers equipped with operations of maximum and summation.