We address highly dynamic distributed systems modeled by time-varying graphs (TVGs). We interest in proof of impossibility results that often use informal arguments about convergence. First, we provide a distance among TVGs to define correctly the convergence of TVG sequences. Next, we provide a general framework that formally proves the convergence of the sequence of executions of any deterministic algorithm over TVGs of any convergent sequence of TVGs. Finally, we illustrate the relevance of the above result by proving that no deterministic algorithm exists to compute the underlying graph of any connected-over-time TVG, i.e., any TVG of the weakest class of long-lived TVGs. *

is paper presents the first probabilistic Byzantine Agreement algorithm whose communication and time complexities are poly-logarithmic. So far, the most effective probabilistic Byzantine Agreement algorithm had communication complexityÕ n and time complexityÕ (1). Our algorithm is based on a novel, unbalanced, almost everywhere to everywhere Agreement protocol which is interesting in its own right.

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In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over Boolean variables. Such approaches partially expand one type of variable (either existential or universal) and pass the obtained formula to a SAT solver for deciding the QBF. State-of-the-art expansionbased solvers process the given formula quantifier-block wise and recursively apply expansion until a solution is found.In this paper, we present a novel algorithm for expansionbased QBF solving that deals with the whole quantifier prefix at once. Hence recursive applications of the expansion principle are avoided. Experiments indicate that the performance of our simple approach is comparable with the state of the art of QBF solving, especially in combination with other solving techniques.

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