In this paper, we present and analyze a variant of Burmester-Desmedt group key agreement protocol (BD) and enhance it to dynamic setting where a set of users can leave or join the group at any time during protocol execution with updated keys. In contrast to BD protocol, let us refer to our protocol as DB protocol. Although the DB protocol is similar to BD protocol, there are subtle differences between them: 1) Key computation in DB protocol is different and simpler than in BD protocol with same complexity of BD protocol; 2) Number of rounds required in our authenticated DB protocol is one less than that in authenticated BD protocol introduced by Katz-Yung; 3) DB protocol is more flexible than BD protocol in the sense that DB protocol is dynamic. The reusability of user's precomputed data in previous session enables the join and leave algorithms of our DB protocol to reduce most user's computation complexities which can be useful in real life applications; and 4) DB protocol has the ability to detect the presence of corrupted group members, although one can not detect who among the group members are behaving improperly.

Abstract. This paper presents a completeness result, with respect to a possible world semantics, for a combination of a first-order temporal logic and neighbourhood logic. This logic was considered by Qiu and Zhou (1998, Proceedings of the PROCOMET ‘98 , pp 444–461) to define semantics of a real-time OCCAM-like programming language.

Abstract- Recently, it has been shown that the simple bi-nary arithmetic and logical operations can be computed by the process of self assembly of DNA tiles, where arti-ficially constructed 2-D DNA nanostructures called tiles attach with one-another to form complex superstruc-tures, and in the process compute the result of these op-erations. We show how the DNA self assembly process can be used for computing finite field multiplication and addition. Our method can be used to efficiently execute multiple computation of finite field arithmetic, parallely and at very low cost. 1

This paper presents a completeness result for a first-order interval temporal logic, called Neighbourhood Logic (NL) which has two neighbourhood modalities. NL can support the specification of liveness and fairness properties of computing systems as well as formalisation of many concepts of real analysis. These two modalities are also adequate in the sense that they can derive other important unary and binary modalities of interval temporal logic. We prove the completeness result for NL by giving a Kripke model semantics and then mapping the Kripke models to the interval models for NL.

The σ-game, introduced by Sutner, is a combinatorial game played on a graph G and is closely related to the σ-automaton first studied by Lindenmayer. A related game is the σ+-game. In this article, we study the σ-game σ+-game played on the rectangular grid {1, 2, …, m} × {1, 2, …, n}. We analyse the σ+-game by studying the divisibility properties of the polynomials Pn(λ) which we have introduced here. (Similar polynomials were earlier studied by Sutner). We give a simple algorithm for finding the number of solutions for the σ+-game and also give a necessary and sufficient condition for the existence of a unique solution for the σ+-game, thus partially answering a question posed by Sutner. Further, we compute the number of solutions of the σ+-game when one of n, m is of the form 2k − 1. Finally, we look at the σ-game and the σ+-game played on cylinders and tori and give necessary and sufficient conditions for the existence of unique solutions for these games.