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  • Khrapchenko's classical lower bound n(2) on the formula size of the parity function f can be interpreted as designing a suitable measure of sub-rectangles of the combinatorial rectangle f(-1)(0) x f(-1)(1). Trying to generalize this approach we arrived at the concept of convex measures. We prove the negative result that convex measures are bounded by O(n(2)) and show that several measures considered for proving lower bounds on the formula size are convex. We also prove quadratic upper bounds on a class of measures that are not necessarily convex.
  • Khrapchenko's classical lower bound n(2) on the formula size of the parity function f can be interpreted as designing a suitable measure of sub-rectangles of the combinatorial rectangle f(-1)(0) x f(-1)(1). Trying to generalize this approach we arrived at the concept of convex measures. We prove the negative result that convex measures are bounded by O(n(2)) and show that several measures considered for proving lower bounds on the formula size are convex. We also prove quadratic upper bounds on a class of measures that are not necessarily convex. (en)
Title
  • On convex complexity measures
  • On convex complexity measures (en)
skos:prefLabel
  • On convex complexity measures
  • On convex complexity measures (en)
skos:notation
  • RIV/67985840:_____/10:00342826!RIV11-AV0-67985840
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  • P(IAA1019401), Z(AV0Z10190503)
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  • 16-18
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  • 276680
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  • RIV/67985840:_____/10:00342826
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  • boolean formula; complexity measure; combinatorial rectangle; convexity (en)
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  • NL - Nizozemsko
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  • [FA3B9856F03A]
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  • Theoretical Computer Science
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  • 411
http://linked.open...iv/tvurceVysledku
  • Pudlák, Pavel
  • Hrubeš, P.
  • Jukna, S.
  • Kulikov, A.
http://linked.open...ain/vavai/riv/wos
  • 000276167000016
http://linked.open...n/vavai/riv/zamer
issn
  • 0304-3975
number of pages
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