Abstract
Recently, an interest in constructing pseudorandom or hitting set generators for restricted branching programs has increased, which is motivated by the fundamental problem of derandomizing space bounded computations. Such constructions have been known only in the case of width 2 and in very restricted cases of bounded width. In our previous work, we have introduced a so-called richness condition which is, in a certain sense, sufficient for a set to be a hitting set for read-once branching programs of width 3. In this paper, we prove that, for a suitable constant C, any almost Clogn-wise independent set satisfies this richness condition. Hence, we achieve an explicit polynomial time construction of a hitting set for read-once branching programs of width 3 with the acceptance probability greater than \(\sqrt{12/13}\) by using the result due to Alon et al. (1992).
This research was partially supported by projects GA ČR P202/10/1333, MŠMT ČR 1M0545, and AV0Z10300504.
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Šíma, J., Žák, S. (2011). Almost k-Wise Independent Sets Establish Hitting Sets for Width-3 1-Branching Programs. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_10
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DOI: https://doi.org/10.1007/978-3-642-20712-9_10
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