Notes on congruence relations and factor pumping conditions for rational languages

Congruence Relations on Multilattices

On Congruence Conditions for Primality

For any k ≥ 0, all primes n satisfy the congruence nσk(n) ≡ 2 mod φ(n). We show that this congruence in fact characterizes the primes, in the sense that it is satisfied by only finitely many composite n. This characterization generalizes the results of Lescot and Subbarao for the cases k = 0 and k = 1. For 0 ≤ k ≤ 14, we enumerate the composite n satisfying the congruence. We also prove that an...

NOTES ON CONGRUENCE n-PERMUTABILITY AND SEMIDISTRIBUTIVITY

In [1] T. Dent, K. Kearnes and Á. Szendrei define the derivative, Σ′, of a set of equations Σ and show, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutable for some n, and for congruence semidistributivity. In a recent paper [1] T. Dent, K. Kearne...

On Rational Series and Rational Languages

We study the connections between rational series with coeecients in a semiring and their languages.

turkish-israeli relations and their implication on iranian national security

this dissertation has six chapter and tree appendices. chapter 1 introduces the thesis proposal including description of problem, key questions, hypothesis, backgrounds and review of literature, research objectives, methodology and theoretical concepts (key terms) taken the literature and facilitate an understanding of national security, national interest and turkish- israeli relations concepts...