In this paper we prove that the congruence classes of A associated to the Burnside semigroup with jAj generators deened by the equation x n = x n+m , for n 4 and m 1, are recognizable. This problem was originally formulated by Brzozowski in 1969 for m = 1 and n 2. De Luca and Varricchio solved the problem for n 5 in 90. A little later, McCammond extended the problem for m 1 and solved it indepe...

The semigroup of binary relations on {1, . . . , n} with the relative product is isomorphic to the semigroup Bn of n×n matrices over {0, 1} with the Boolean matrix product. Over any field F , we prove that there is an ideal Kn in FBn of dimension (2n−1)2, and we construct an explicit isomorphism of Kn with the matrix algebra M2n−1(F ). Let Zn = {1, . . . , n} (n ≥ 1); then P (Z n), the power se...

The implicit operation ω is the unary operation which sends each element of a finite semigroup to the unique idempotent contained in the subsemigroup it generates. Using ω there is a well-defined algebra which is known as the free aperiodic semigroup. In this article we show that for each n, the ngenerated free aperiodic semigroup is defined by a finite list of pseudoidentities and has a decida...

Evolutionary inference methods that assume equal DNA base compositions and symmetric nucleotide substitution matrices, where these assumptions do not hold, are likely to group species on the basis of similar base compositions rather than true phylogenetic relationships. We propose an invariants-based method for dealing with this problem. An invariant QT of a tree T under a k-state Markov model,...

We relate two measures of complexity of regular languages. The first is syntactic complexity, that is, the cardinality of the syntactic semigroup of the language. That semigroup is isomorphic to the semigroup of transformations of states induced by non-empty words in the minimal deterministic finite automaton accepting the language. If the language has n left quotients (its minimal automaton ha...

The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...

Given the infinitesimal generator A of a C0-semigroup on the Banach space X which satisfies the Kreiss resolvent condition, i.e., there exists an M > 0 such that ‖(sI−A)‖ ≤ M Re(s) for all complex s with positive real part. We show that for general Banach spaces this condition does not give any information on the growth of the associated C0-semigroup. For Hilbert spaces the situation is less dr...

We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. The Julia set of such a semigroup may not be connected in general. We show that for such a polynomial semigroup, if A and B are two connected components of the Julia set, then one of A and B surrounds the other. From this, it is...

This paper concerns the structure of strongly continuous one parameter semigroups of completely positive contractions of B(H) = B(K⊗L(0,∞)) which are intertwined by translation. These are called CP -flows over K. Using Bhat’s dilation result each unital CP -flow over K dilates to an Eo-semigroup of B(H1) where H1 can be considered to contain B(K⊗L(0,∞)). Every spatial Eo-semigroup is cocycle co...

1 Abstract. Let S ={si}i∈IN ⊆ IN be a numerical semigroup. For each i ∈ IN, let ν(si) denote the number of pairs (si−sj , sj) ∈ S: it is well-known that there exists an integer m such that the sequence {ν(si)}i∈IN is non-decreasing for i > m. The problem of finding m is solved only in special cases. By way of a suitable parameter t, we improve the known bounds for m and in several cases we dete...