## Exact algorithms for MAX-2SAT and MAX-3SAT via multidimensional matrix multiplication

##### Type

Master thesis###### Not peer reviewed

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##### Date

2015-06-01##### Author

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In this thesis it is showed how an $O(n^{4-\epsilon})$ algorithm for the cube multiplication problem (that is defined in the thesis) would imply a faster than naive $O^{*}(2^{n(1-\frac{\epsilon}{4})})$ algorithm for the MAX-3SAT problem; this algorithm for MAX-3SAT is a generalization of the algorithm for the MAX-2SAT problem which was proposed by Ryan Williams; and cube multiplication, in turn, is defined as a generalization of the matrix multiplication problem for three-dimensional arrays. Approaches to find a faster than naive algorithm for cube multiplication are considered. Though no such algorithm was found using these approaches, it is showed how a variant of the Strassen algorithm for matrix multiplication could be found using the same approaches. Implementations of these approaches using computer programming and results of computational experiments are discussed.