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...

This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial, notions of regularity and invertibility arise naturally for matrices over this semiring; we show that a tropical matrix is invertible if and only if it is r...

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 ...

In theoretical computer science the connection between automata and logic is of fundamental importance. This connection was first considered by Büchi and Elgot in the 1960s, when they showed that the languages accepted by finite automata are precisely those languages that can be defined in monadic second-order logic (MSO). In this thesis we consider extensions of Büchi’s and Elgot’s theorem int...