This paper furthers the study of quasi-linear time complexity initiated by Schnorr and Gurevich and Shelah [GS89]. We show that the fundamental properties of the polynomial-time hierarchy carry over to the quasilineartime hierarchy. Whereas all previously known versions of the Valiant-Vazirani reduction from NP to parity run in quadratic time, we give a new construction using error-correcting codes that runs in quasilinear time. We show, however, that the important equivalence between search problems and decision problems in polynomial time is unlikely to carry over: if search reduces to decision for SAT in quasi-linear time, then all of NP is contained in quasi-polynomial time. Other connections to work by Stearns and Hunt [SH86, SH90, HS90] on “power indices” of NP languages are made.
CITATION STYLE
Naik, A. V., Regan, K. W., & Sivakumar, D. (1994). Quasilinear time complexity theory. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 775 LNCS, pp. 97–108). Springer Verlag. https://doi.org/10.1007/3-540-57785-8_134
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