Upper and Lower Bounds on Unrestricted Black-Box Complexity of Jump\(_{n,\ell }\)

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9026)

Abstract

We analyse the unrestricted black-box complexity of \(\textsc {Jump}_{n,\ell }\) functions. For upper bounds, we present three algorithms for small, medium and extreme values of \(\ell \). We present a matrix lower bound theorem which is capable of giving better lower bounds than a general information theory approach if one is able to assign different types to queries and define relationships between them. Using this theorem, we prove lower bounds for Jump separately for odd and even values of \(n\). For several cases, notably for extreme Jump, the first terms of lower and upper bounds coincide.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.ITMO UniversitySaint-PetersburgRussia
  2. 2.LIXÉcole PolytechniquePalaiseau CedexFrance

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