Abstract
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-log2 n 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.”
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References
A. Adachi, S. Iwata and T. Kasai, Combinatorial game problems require Ω (n i) time,J. Assoc. Comput. Mach., 31, 361–376 (1984).
O. H. Ibarra, On two-way multi head automata,J. Comput. System Sci., 7, 28–36 (1973).
S. Iwata and T. Kasai, Problem requiringk logn deterministic space,Congressus Numerantium, 44, 161–174 (1984).
N. Jones, Space-bounded reducibility among combinatorial problems,J. Comput. System Sci., 11, 68–85 (1975).
N. Jones, Y. E. Lien and W. T. Laaser, New problems complete for nondeterministic log space,Math. System Theory, 10, 1–17 (1976).
T. Kasai, A. Adachi, and S. Iwata, Classes of pebble games and complete problems,SIAM J. Comput., 8, 574–586 (1979).
B. Monien, Transformational methods and their application to complexity problems,Acta Informatica, 6, 95–108 (1976).
J. L. Peterson, Petri Nets,Computing Surveys, 9, 223–252 (1977).
J. I. Seiferas, Relating refined space complexy classes,J. of Comput. System Sci., 14, 100–129 (1977).
J. I. Seiferas, Techniques for separating space complexity classes,J. of Comput. System Sci., 14, 73–99 (1977).
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Kasai, T., Iwata, S. Gradually intractable problems and nondeterministic log-space lower bounds. Math. Systems Theory 18, 153–170 (1985). https://doi.org/10.1007/BF01699467
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DOI: https://doi.org/10.1007/BF01699467