No abstract

Abstract. A real is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay 23 and Chaitin 10 we s a y that an r.e. real dominates an r.e. real if from a good approximation of from below one can compute a good approximation of from below. We shall study this relation and characterize it in terms of relations between r.e. sets. Solovay's 23 -like numbers are the maximal r.e. real numbers with respect to this order. They are random r.e. real numbers. The halting probability o f a universal self-delimiting Turing machine Chaitin's number, 9 is also a random r.e. real. Solovay showed that any Chaitin numberis -like. In this paper we show that the converse implication is true as well: any -like real in the unit interval is the halting probability of a universal self-delimiting Turing machine.

Abstract. Achieving secure communications in networks has been one of the most important problems in information technology. Dolev, Dwork, Waarts, and Yung have studied secure message transmission in one-way or two-way channels. They only consider the case when all channels are two-way or all channels are one-way. Goldreich, Goldwasser, and Linial, Franklin and Yung, Franklin and Wright, and Wang and Desmedt have studied secure communication and secure computation in multi-recipient (multicast) models. In a "multicast channel" (such as Ethernet), one processor can send the same message -simultaneously and privately -to a fixed subset of processors. In this paper, we shall study necessary and sufficient conditions for achieving secure communications against active adversaries in mixed one-way and two-way channels. We also discuss multicast channels and neighbor network channels.

No abstract

No abstract