Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

Abstract Isothermic surfaces are which allow a conformal curvature line parametrisation. They form an integrable system, and Darboux transforms of isothermic obey Bianchi permutability: for two distinct spectral parameters, the corresponding have common transform can be computed algebraically. In this paper, we discuss two-step with same parameter, show that these obtained by Sym-type construct...

Let ~ be a property which can be attributed to 0, 1-sublattices of Eq (X), X arbitrary. (Eq (X) is the lattice of all equivalence relations on X.) For example, could be modularity or permutability. It was proved in [3] that for every integer k 2 there is an n -> 1 such that for every algebra A of cardinality k, if Con (A m) satisfies ~ for all m -< n then Con (A m) satisfies ~ for all m. Let ne...

Abstract We study permutability properties of matrix semigroups over commutative bipotent semirings (of which the best-known example is tropical semiring ). prove that every such semigroup weakly permutable (a result previous stated in literature, but with an erroneous proof) and then proceed to depth question when they are strongly (which turns out depend heavily on semiring). Along way we cla...