We survey the properties of sets of integers recognizable by automata when they are written in p-ary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of Cobham-Semenov, the original proof being published in Russian. 1

One of the new possibilities oered by EPIC architectures is to allow the compiler to direct the cache placement and replacement policy through cache hints. In this work, a method to generate these cache hints at compile time is presented. The generation of appropriate cache hints is based on the locality of the instructions they apply to, which is quanti ed by the reuse distance metric. Next to the static selection of the most appropriate cache hints, a dynamic selection of cache hints by predicates is proposed. The generation of static hints is based on a simple pro ling scheme, while the dynamic selection is based on an analytical model of the programs cache behavior.

Abstract. This paper describes the development of some decision procedures which are useful for the automatic verification of imperative algorithms manipulating arrays. Our approach—based on the superposition framework—consists of extending an available satisfiability for infinite arrays to procedures for finite arrays, finite arrays with permutations, and their extensions with user-defined symbols. The Nelson and Oppen combination schema is used to incorporate a form of arithmetic reasoning and we propose an heuristic extension whereby symbols—defined by using both the theory of arrays and arithmetic—can be handled. The procedures so obtained are successfully put to work to automatically discharge the proof obligations arising in the correctness of the algorithms Find, Insertion sort, and Heap sort. While much existing research on decision procedures has been done in isolation or in the context of combination problems, the work described in this paper seems to be one of the few attempts to widen the scope of decision procedures aimed at building more flexible and extensible tools for verification. 1