36 research outputs found
Classification of finite congruence-simple semirings with zero
Our main result states that a finite semiring of order >2 with zero which is
not a ring is congruence-simple if and only if it is isomorphic to a `dense'
subsemiring of the endomorphism semiring of a finite idempotent commutative
monoid.
We also investigate those subsemirings further, addressing e.g. the question
of isomorphy.Comment: 16 page
On the rank of semimodules over semirings
In this paper we investigate conditions on a semiring such that there are semimodules over with bases of different length. This includes and generalizes corresponding results on rings, in particular one due to P. Dubreil
Simulations of Weighted Tree Automata
Simulations of weighted tree automata (wta) are considered. It is shown how
such simulations can be decomposed into simpler functional and dual functional
simulations also called forward and backward simulations. In addition, it is
shown in several cases (fields, commutative rings, Noetherian semirings,
semiring of natural numbers) that all equivalent wta M and N can be joined by a
finite chain of simulations. More precisely, in all mentioned cases there
exists a single wta that simulates both M and N. Those results immediately
yield decidability of equivalence provided that the semiring is finitely (and
effectively) presented.Comment: 17 pages, 2 figure