Using a result of Gurevich and Lewis on the word problem for finite semigroups, we give short proofs that the following theories are hereditarily undecidable: (1) finite graphs of vertex-degree at most 3; (2) finite nonvoid sets with two distinguished permutations; (3) finitedimensional vector spaces over a finite field with two distinguished endomorphisms.

The purpose of this paper is towards the algebraic study of rough finite state machines, i.e., to introduce the concept of homomorphisms between two rough finite state machines, to associate a rough transformation semigroup with a rough finite state machine and to introduce the concept of coverings of rough finite state machines as well as rough transformation semigroups.

Combining the the results of A.R. Meyer and L.J. Stockmeyer " The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space " , and K.S. Booth " Iso-morphism testing for graphs, semigroups, and finite automata are polynomiamlly equivalent problems " shows that graph isomorphism is PSPACE-complete. The equivalence problem for regular expressions was shown to be PSPACE-...

Let a be a non-invertible transformation of a finite set and let G be a group of permutations on that same set. Then 〈G, a 〉 \G is a subsemigroup, consisting of all non-invertible transformations, in the semigroup generated by G and a. Likewise, the conjugates ag = g−1ag of a by elements g ∈ G generate a semigroup denoted 〈ag | g ∈ G〉. We classify the finite permutation groups G on a finite set...

A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating set. This paper considers the natural generalizations of these concepts to semigroups and monoids. Two distinct potential generalizations to monoids are shown...

Anumerical semigroup is a subset ofN containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of algebraic geometry codes, Weierstrass semigroups are crucial for defining bounds on the minimum distance as well as for defining improvements on the dimension of codes...

We prove that every strongly commuting pair of CP0-semigroups has a minimal E0-dilation. This is achieved in two major steps, interesting in themselves: 1: we show that a strongly commuting pair of CP0semigroups can be represented via a two parameter product system representation; 2: we prove that every fully coisometric product system representation has a fully coisometric, isometric dilation....

This paper introduces the concept of ultimately periodic functions for nite semigroups. Ultimately periodic functions are shown to be the same as regularity-preserving functions in automata theory. This characterization reveals the true algebraic nature of regularity-preserving functions. It makes it possible to prove properties of ultimately periodic functions through automata-theoretic method...

We call a pseudovariety finite join irreducible if V ≤ V1 ∨V2 =⇒ V ≤ V1 or V ≤ V2. We present a large class of group mapping semigroups generating finite join irreducible pseudovarieties. We show that many naturally occurring pseudovarieties are finite join irreducible including: S, DS, CR, CS and H, where H is a group pseudovariety containing a non-nilpotent group.

This paper revisits the solution of the word problem for ω-terms interpreted over finite aperiodic semigroups, obtained by J. McCammond. The original proof of correctness of McCammond’s algorithm, based on normal forms for such terms, uses McCammond’s solution of the word problem for certain Burnside semigroups. In this paper, we establish a new, simpler, correctness proof of McCammond’s algori...