TY - JOUR

T1 - Almost complete sets

AU - Ambos-Spies, Klaus

AU - Merkle, Wolfgang

AU - Reimann, Jan

AU - Terwijn, Sebastiaan A.

N1 - Funding Information:
∗Corresponding author. Tel.: +49-6221-54-5409. E-mail addresses: ambos@math.uni-heidelberg.de (K. Ambos-Spies), merkle@math.uni-heidelberg.de (W. Merkle), reimann@math.uni-heidelberg.de (J. Reimann),terwijn@cs.vu.nl (S.A. Terwijn). 1Supported by a Marie Curie Fellowship of the European Union under grant ERB-FMBI-CT98-3248.

PY - 2003/9/5

Y1 - 2003/9/5

N2 - We show that there is a set that is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2lin. Here a set in a complexity class C is almost complete for C under some given reducibility if the class of the problems in C that do not reduce to this set has measure 0 in C in the sense of Lutz's resource-bounded measure theory. We also show that the almost complete sets for E under polynomial time-bounded length-increasing one-one reductions and truth-table reductions of norm 1 coincide with the almost p-m-complete sets for E. Moreover, we obtain similar results for the class EXP of sets computable in deterministic time 2poly.

AB - We show that there is a set that is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2lin. Here a set in a complexity class C is almost complete for C under some given reducibility if the class of the problems in C that do not reduce to this set has measure 0 in C in the sense of Lutz's resource-bounded measure theory. We also show that the almost complete sets for E under polynomial time-bounded length-increasing one-one reductions and truth-table reductions of norm 1 coincide with the almost p-m-complete sets for E. Moreover, we obtain similar results for the class EXP of sets computable in deterministic time 2poly.

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U2 - 10.1016/S0304-3975(03)00262-7

DO - 10.1016/S0304-3975(03)00262-7

M3 - Article

AN - SCOPUS:0042508855

SN - 0304-3975

VL - 306

SP - 177

EP - 194

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1-3

ER -