This paper,  applies the concept  of KM-fuzzy metric spaces and  introduces a novel concept of KM-fuzzy metric  graphs based on KM-fuzzy metric spaces.  This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to  extend   the concept of KM-fuzzy metric spaces to  a larger ...

We propose a new class of tree automata, called tree automata with normalization (TAN). This framework extends equational tree automata, and improved the results of them: recognized tree languages modulo the idempotency f(x, x) = x are closed under complement, besides we do not lose an important decidability result. In the paper, first we investigate the closure properties of this class for Boo...

The class TPA of true pairing algebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of TPA nor the first order theory of TPA are decidable. Moreover, we show that the set of all equations valid in TPA is exactly on the Π11 level. We consider the class TPA o...

The “semilattices of Mal’cev blocks”, for short SMB algebras, were defined by A. Bulatov. In a recently accepted paper P. Đapić, Marković, R. McKenzie, and Prokić, the class all algebras its subclass regular proved to be varieties algebras. this paper, we find an equational base first variety simplify previously known second variety.

This paper is a survey on the equational descriptions of languages. The first part is devoted to Birkhoff’s and Reiterman’s theorems on equational descriptions of varieties. Eilenberg’s variety theorem and its successive generalizations form the second part. The more recent results on equational descriptions of lattices of languages are presented in the third part of the paper. Equations have b...

Undecidability of the equational theory of the class RA of relation algebras can easily be proved using the undecidability of the word-problem for semigroups. With some eeort and ingenuity, one can push this proof through for the larger class SA. We provide another \cause" for undecidability which works for even larger classes than SA. The reason is that we can encode the tiling problem. In doi...

We propose a method for incrementally computing success patterns of logic programs with respect to a class of abstractions. The method is specialised for computing success patterns for depth and stump abstractions. Equational unification algorithms for these abstractions are presented.