For exploring the meaning of power set in evidence theory, a possible explanation is proposed from view Pascal’s triangle and combinatorial number. Here comes question: what would happen if number replaced by permutation number? To address this issue, new kind set, named as random (RPS), paper, which consists event space (PES) mass function (PMF). The PES certain considers all that set. element...

In this paper we investigate the existence of permutation polynomials of the form F(x) = xd + L(x) over GF(2n), L being a linear polynomial. The results we derive have a certain impact on the long-term open problem on the nonexistence of APN permutations over GF(2n), when n is even. It is shown that certain choices of exponent d cannot yield APN permutations for even n. When n is odd, an infini...

In this paper we prove that if the congruence lattice of an automaton A is finite then the endomorphism semigroup E(A) of A is finite. Moreover, if A is commutative then A is A-finite. We prove that if 3 ≤ |A| then a commutative automaton A is simple if and only if it is a cyclic permutation automaton of prime order. We also give some results concerning cyclic, strongly connected and strongly t...