Mathematical systems theory

, Volume 18, Issue 1, pp 153–170 | Cite as

Gradually intractable problems and nondeterministic log-space lower bounds

  • Takumi Kasai
  • Shigeki Iwata


The paper places five different problems (thek-pebble game problem, two problems aboutk finite automata, the reachability problem for Petri nets withk tokens, and the teachability problem for graphs whose “k-dimensional” edge sets are described by Cartesian products ofk factors) into the hierarchyNL k of problems solvable by nondeterministic Turing machines ink-log2n space (and binary tape alphabet, to avoid tape “speed-up”). The results, when combined with the conjecture thatNL i contains problems that requireO(n k ) deterministic time, show that these problems, while inP for every fixed value ofk, have polynomial deterministic time complexities with the degree of the polynomial growing linearly with the parameterk, and hence are, in this sense, “gradually intractable.”


Lower Bound Computational Mathematic Time Complexity Turing Machine Finite Automaton 
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Copyright information

© Springer-Verlag New York Inc 1985

Authors and Affiliations

  • Takumi Kasai
    • 1
  • Shigeki Iwata
    • 2
  1. 1.Department of Computer ScienceUniversity of Electro-CommunicationsChofuJapan
  2. 2.Information Science LaboratoryTokai UniversityHiratsukaJapan

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