Abstract
In this paper we report preliminary results of experiments with finding efficient circuits (over binary bases) using SAT-solvers. We present upper bounds for functions with constant number of inputs as well as general upper bounds that were found automatically. We focus mainly on MOD-functions. Besides theoretical interest, these functions are also interesting from a practical point of view as they are the core of the residue number system. In particular, we present a circuit of size 3n + c over the full binary basis computing \({\rm MOD}_3^n\).
The first two authors are supported in part by RFBR (grant 08-01-00640-a) and RAS Program for Fundamental Research (”Modern Problems of Theoretical Mathematics”).
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Kojevnikov, A., Kulikov, A.S., Yaroslavtsev, G. (2009). Finding Efficient Circuits Using SAT-Solvers . In: Kullmann, O. (eds) Theory and Applications of Satisfiability Testing - SAT 2009. SAT 2009. Lecture Notes in Computer Science, vol 5584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02777-2_5
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DOI: https://doi.org/10.1007/978-3-642-02777-2_5
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