On the decidability of semigroup freeness

On the decidability of semigroup freeness

This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness pr...

A ug 2 00 8 On the decidability of semigroup freeness ∗

This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness pr...

On the Decidability of the Freeness of Matrix Semigroups

new semigroup compactifications via the enveloping semigroups of associated flows

this thesis deals with the construction of some function algebras whose corresponding semigroup compactification are universal with respect to some properies of their enveloping semigroups. the special properties are of beigan a left zero, a left simple, a group, an inflation of the right zero, and an inflation of the rectangular band.

Matrix Semigroup Freeness Problems in $\mathrm{SL}(2,\mathbb{Z})$

In this paper we study decidability and complexity of decision problems on matrices from the special linear group SL(2,Z). In particular, we study the freeness problem: given a finite set of matrices G generating a multiplicative semigroup S, decide whether each element of S has at most one factorization over G. In other words, is G a code? We show that the problem of deciding whether a matrix ...