Amalgams of finite inverse semigroups

reserved3We show that the word problem is decidable for an amalgamated free product of finite inverse semigroups (in the category of inverse semigroups). This is in contrast to a recent result of M. Sapir that shows that the word problem for amalgamated free products of finite semigroups (in the category of semigroups) is in general undecidable.A. Cherubini; J. Meakin; B. PiochiCherubini, Alessandra; J., Meakin; B., Pioch

Quasi-abelian and quasi-solvable regular semigroups

In this note quasi-abelian semigroups are studied and it is proved that they form an e-variety of orthodox semigroups. More, quasi-abelian regular Bruck-Reilly monoids are characterized as extensions of monoids which are (reverse) semidirect products of a group and a semilattice. At last, quasi-abelian congruences are studied and a definition of quasi-solvability is given which generalizes the notion of solvability to the class of regular semigroups

On the Length of Shortest 2-Collapsing Words

Let n be a positive integer, a word w is n-compressing for a finite deterministic automaton if its natural action reduces the image of the automaton state set by at least n states. A word w is n-collapsing if it is n-compressible for all deterministic finite automata that admit n-compressing words. We improve the known theoretical bound for the lenght of the shortest 2-collapsing word an a finite alphabet. Then we produce shorter 2-collapsing and 2-synchronizing words over alphabets of 4 and 5 elements