Examples of undecidable problems for 2-generator matrix semigroups

Examples of Undecidable Problems for 2-Generator Matrix Semigroups

Decidable and Undecidable Problems in Matrix Theory

This work is a survey on decidable and undecidable problems in matrix theory. The problems studied are simply formulated, however most of them are undecidable. The method to prove undecidabilities is the one found by Paterson [Pat] in 1970 to prove that the mortality of nitely generated matrix monoids is undecidable. This method is based on the undecidability of the Post Correspondence Problem....

Computational problems in matrix semigroups

This thesis deals with computational problems that are defined on matrix semigroups, which play a pivotal role in Mathematics and Computer Science in such areas as control theory, dynamical systems, hybrid systems, computational geometry and both classical and quantum computing to name but a few. Properties that researchers wish to study in such fields often turn out to be questions regarding t...

Cancellativity is undecidable for automatic semigroups

Via an encoding of the Modified Post’s Correspondence Problem, this paper shows that it is undecidable whether an automatic semigroup is cancellative.

Examples of non-quasicommutative semigroups decomposed into unions of groups

Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied...