In the literature, there exist several interesting hybrid models of finite automata which have both quantum and classical states. We call them semi-quantum automata. In this paper, we compare the descriptional power of these models with that of DFA. Specifically, we present a uniform method that gives a lower bound on the size of the three existing main models of semi-quantum automata, and this...

Let X, d be a metric space and S a closed and nonempty subset of X. Denote by 2 resp., C X the family of all nonempty resp., nonempty and closed subsets of X. A mapping T : S → 2 is said to satisfy condition P if, for every closed ball B of S with radius r ≥ 0 and any sequence {xn} in S for which d xn, B → 0 and d xn, T xn → 0 as n → ∞, there exists x0 ∈ B such that x0 ∈ T x0 where d x, B inf{d...

We are given a set of identical machines and a sequence of jobs from which we know the sum of the job weights in advance. The jobs have to be assigned on-line to one of the machines and the objective is to minimize the makespan. An algorithm with performance ratio 1.6 and a lower bound of 1.5 is presented. This improves recent results by Azar and Regev who published an algorithm with performanc...