Abstract
It is shown that a variety of problems have computational complexity equivalent to that of finding a path through a directed graph. These results, which parallel those of Karp at a lower complexity level, concern satisfiability of propositional formulas with two literals per clause, generation of elements by an associative binary operation, solution of linear equations with two variables per equation, equivalence of generalized sequential machines with final states, and deciding theLL(k) andLR(k) conditions for context-free grammars. Finally, several problems are shown equivalent to reachability in undirected graphs, including bipartiteness and satisfiability of formulas with the “exclusive or” connective.
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References
Aho, A. V.;Ullman, J. D. The theory of parsing, translation and compiling. Vol. 1: Parsing. Prentice Hall, Englewood Cliffs, New Jersey. 1972.
Cook, S. A. The complexity of theorem proving procedures.Proceedings of 3rd Annual ACM Symposium on Theory of Computing, pp. 151–158, 1971.
Chang, C. L.;Lee, R. C. T. Symbolic logic and Mechanical theorem proving. Academic Press, New York, 1973.
Griffiths, T. V. The unsolvability of the equivalence problem forλ-free nondeterministic generalized sequential machines.Journal of the ACM 15 (1968), 409–413.
Hartmanis, J.; Hunt, H. B. III. The LBA problem and its importance in the theory of computing. Computer Science Technical Report TR-171, Cornell University, 1973.
Hartmanis, J.; Simon, J. On the structure of feasible computations. Computer Science Technical Report TR-74-210, Cornell University, 1974.
Hunt, H. B. III;Szymanski, T.; Ullman, J. D. On the complexity ofLR(k) testing.Proceedings of 2nd Annual ACM Symposium on Principles of Programming Languages, pp. 130–138, 1975.
Jones, N. D. Space-bounded reducibility among combinatorial problems.Journal of Computer and Systems Sciences 11 (1975), 68–75.
Jones, N. D.; Laaser, W. T. Problems complete for deterministic polynomial time. To appear inTheoretical Computer Science.
Karp, R. M. Reducibility among combinatorial problems. InComplexity of Computer Computations, edited by R. E. Miller and J. Thatcher, Plenum Press, New York, pp. 85–104, 1972.
Lynch, N. Personal communication.
Savitch, W. J. Relations between nondeterministic and deterministic tape complexities.Journal of Computer and Systems Sciences 4 (1970), 177–192.
Savitch, W. J. Nondeterministic LogN space.Proceedings of 8th Princeton Conference on Information Sciences and Systems. Princeton University, pp. 21–23, 1974.
Sudborough, I. H. Personal Communication.
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The work of this author was partly supported by Kansas General Research Grant 3756-5038. A preliminary version appears in the Proceedings of the Eighth Princeton Conference on Information Sciences and Systems, Princeton University, pp. 184–188, March 1974.
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Jones, N.D., Lien, Y.E. & Laaser, W.T. New problems complete for nondeterministic log space. Math. Systems Theory 10, 1–17 (1976). https://doi.org/10.1007/BF01683259
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DOI: https://doi.org/10.1007/BF01683259