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TR21-044 | 14th February 2021 13:11

SAT-based Circuit Local Improvement


Authors: Alexander Kulikov, Nikita Slezkin
Publication: 22nd March 2021 18:50
Downloads: 341


Finding exact circuit size is a notorious optimization problem in practice. Whereas modern computers and algorithmic techniques allow to find a circuit of size seven in blink of an eye, it may take more than a week to search for a circuit of size thirteen. One of the reasons of this behavior is that the search space is enormous: the number of circuits of size $s$ is $s^{\Theta(s)}$, the number of Boolean functions on $n$ variables is $2^{2^n}$.

In this paper, we explore the following natural heuristic idea for decreasing the size of a given circuit: go through all its subcircuits of moderate size and check whether any of them can be improved by reducing to SAT. This may be viewed as a local search approach: we search for a smaller circuit in a ball around a given circuit. We report the results of experiments with various symmetric functions.

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