ThÄ› CernÂ´y's conjecture states that for every synchronizing automaton with n states there exists a reset word of length not exceeding (nâˆ’1) 2. We prove this conjecture for a class of automataâ€¦ (More)

We prove that every abelian permutation group, but known exceptions , is the symmetry group of a boolean function. This solves the problem posed in the book by Clote and Kranakis. In fact, our resultâ€¦ (More)

In this article, we improve known results, and, with one exceptional case, prove that when kâ‰¥3, the direct product of the automorphism groups of graphs whose edges are colored using k colors, isâ€¦ (More)

is called a Boolean function. By Aut(f) we denote the set of all symmetries of f , i.e., these permutation Ïƒ âˆˆ Sn for which f(xÏƒ(1), . . . , xÏƒ(n)) = f(x1, . . . , xn). We show the solution of aâ€¦ (More)

When a particle beam travels through an accelerator structure like the LHC, energy is lost to the structure itself. This phenomenon is described through the beam-coupling impedance and is ideallyâ€¦ (More)

In this paper we study representations of permutation groups as automorphism groups of colored graphs and supergraphs. In particular, we consider how such representations for various products ofâ€¦ (More)

In this paper we consider the Cerny conjecture in terminology of colored digraphs corresponding to finite automata. We define a class of colored digraphs having a relatively small number of junctionsâ€¦ (More)