Efficient Reductions from NP to Parity using Error-Correcting Codes (preliminary version)
by Kenneth W. Regan
ftp://ftp.cs.buffalo.edu/pub/tech-reports/93-24.ps.Z
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Abstract:
This paper proves that every language in NP is recognized by an RP [ \Phi P] machine whose time complexity is quasilinear, apart from the time to verify witnesses. The results significantly improve the number of random bits, success probability, and running time of Valiant and Vazirani's original construction [VV86], and beat both the 2n random bits and time/success tradeoff in subsequent methods based on universal hashing. Questions of further improvements are connected to open problems in the theory of error-correcting codes. 1.
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