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Journals ACM SIGACT News Volume 27 Issue 3

Complexity Theory Newsflash Stephen A. Fenner* Lance J. Fortnow t August 2, 1996 The following people have independently proved that P = NP. Here axe the titles of their papers. A. Selman. SAT is P-selective. R. Beigel. ppNP _--pp. L. Hemaspaandra. T h e weak exponential hierarchy collapses. S. Toda. P H _ P P . M. K u m m e r . T h e b o u n d e d query hierarchy over NP collapses. R. Solovay. Con(PA) --~ C o n ( P A + "P = NP"). S. Homer. The m-complete degree for N E X P is a 1-Ii degree. K.-I Ko, T. Long, and D.-Z. Du. All 1-Ii degrees collapse. L. Berman. All EXP-complete sets are isomorphic. R. Ladner. There axe no NP-intermediate sets. J. Feigenbaum. S A T is random-self-reducible. E. Allender and R. Rubinstein. Every sparse set in P is P-printable. J. Torah. GI is in co-NP. S. Arora. A (1 + e)-approximation scheme for general TSP. A. Razborov. A generalization of monotone lower bounds. W . Gasarch. S A T is not P-superterse. M. Sipser. Clique has uniform polynomial-size nonmonotone circuits. J. Goldsmith. Limited nondeterminism does not help. J. Hartmanis. Berman's conjecture fails. J. Lutz. N P has measure 0 in E. S. Fenner. The N P - j u m p is not invertible. N. Nisan. B P P can be simulated in polynomial deterministic time. U. SchSning. Vertex cover is in the low hierarchy. J. KSbler. Vertex cover is in the extended low hierarchy. N. Immerman. S O = FO_< + LFP. L. Fortnow. P ---N P with respect to a finite oracle. S. Mahaney. S A T many-one reduces to a sparse set. M. Ogihara and O. Watanabe. S A T btt reduces to a sparse set. M. Kearns. Circuits are PAC-learnable. M. Sudan. N P = PCP(0, 0). C. Lund. The constant is 0. S. Kurtz, S. Mahaney, and J. Royer. Even further results on collapsing degrees. A. Condon. Every N P set has an interactive proof with a prover in P. L. Longpre. S o m e new results on time-bounded Kolgraorov complexity. William I. Gasarch ~ "Department of Computer Science, University of Southern Maine, 96 Falmouth St., Portland, ME 04103, USA. E-maih adu. The authors are somewhat, coy about acknowledging any financial support for this. tDepartment of Computer Science, University of Chicago, 1100 E. 58th St., Chicago, IL 60637, USA. E-maih ~orl:novOcs. uch$cago, edu. SDepartment of Computer Science, University of Maryland, College Park, MD, 20742, USA. E-mail: gasarch@ca .trod. edu. fenner@cs .usm.maine.

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Complexity Theory Newsflash

Fenner, Stephen A.; Fortnow, Lance J.; Gasarch, William J.
ACM SIGACT News , Volume 27 (3)
Association for Computing Machinery – Sep 1, 1996

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