In this paper the concept of anti fuzzy ideals of a Γsemigroup has been introduced and some important characterizations have been obtained. Among other results a regular Γ-semigroup has been characterized in terms of anti fuzzy ideals. Finally we show that the set of all the anti fuzzy ideals of a Γ-semigroup forms a semilattice. 2010 AMS Classification: 20M99, 08A72, 20M12

An ordered semigroup is a structure S = 〈S, ·,≤〉 with a binary operation · that is associative and a partial ordering ≤ that is compatible with the binary operation. For a given congruence relation θ of the semigroup S = 〈S, ·〉 the quotient structure S/θ = 〈S/θ, , 〉 is not in general an ordered semigroup. In this paper we study quotients of ordered semigroups. We first define a special type of ...

2-We have a group G or a semigroup S with a set of (semigroup) generators A. We have a natural mapping ! : A* " G. Various notions of classes of groups and semigroups give rise to (the possibility of) effective computation. In the cases we will consider, we have L # A + = A*-{$} such that L is regular and L! = G.

A kernel-trace description of right congruences on an inverse semigroup is developed. It is shown that the trace mapping is a complete nhomomorphism but not a V-homomorphism. However, the trace classes are intervals in the complete lattice of right congruences. In contrast, each kernel class has a maximum element, namely the principal right congruence on the kernel, but in general there is no m...

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 notion of communication complexity was introduced by Yao in his seminal paper [Yao79]. In [BFS86], Babai Frankl and Simon developed a rich structure of communication complexity classes to understand the relationships between various models of communication complexity. This made it apparent that communication complexity was a self-contained mini-world within complexity theory. In this thesis...