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There are several proofs now for the stability of Tooms example of a two-dimensional stable cellular automaton and its application to fault-tolerant computation. Simon and Berman simplified and strengthened Tooms original proof: the present report is a simplified exposition of their proof.
We present a very simple new bijective proof of Cayleys formula. The bijection is useful for the analysis of random trees, and we explain some of the ways in which it can be used to derive probabilistic identities, bounds, and growth procedures for s
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis.
The new multipurpose event-generation framework SHERPA, acronym for Simulation for High-Energy Reactions of PArticles, is presented. It is entirely written in the object-oriented programming language C++. In its current form, it is able to completely
We provide a direct proof of Agafonovs theorem which states that finite state selection preserves normality. We also extends this result to the more general setting of shifts of finite type by defining selections which are compatible the shift. A sli
Recently Cristian S. Calude, Sanjay Jain, Bakhadyr Khoussainov, Wei Li and Frank Stephan proposed a quasi-polynomial time algorithm for parity games. This paper proposes a short proof of correctness of their algorithm.