Skip to main content
SpringerLink
Log in

Hierarchies of complete problems

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

An attempt is made to present a framework for the diverse complete problems that have been found. A new concept—a Hierarchy of Complete Problems is defined. Several hierarchies in various domains such as graph theory, automata theory, theorem proving and games are established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cook, S. A.: The complexity of theorem proving procedures. Proceedings of 3rd Annual ACM Symposium of Theory of Computing, Sheiker Heights (Ohio) 1971, p. 151–158

  2. Cook, S. A.: An observation on time-storage trade off. Proceedings of 5th Annual ACM Symposium on Theory of Computing, Austin (Tex.) 1973, p. 29–33

  3. Even, S., Tarjan, R. E.: A combinational problem which is complete in polynomial space. Proceedings of 7th Annual ACM Symposium on Theory of Computing, Albuquerque (New Mexico) 1975, p. 66–71

  4. Galil, Z.: On some direct encodings of nondeterministic Turing machines operating in polynomial time into P-complete problems. SIGACT News 6, 19–24 January 1974

    Article  Google Scholar 

  5. Gardner, M.: The fantastic combinations of John Conway's new solitaire game ‘Life’. Scientific American 223, 120–123 (1970)

    Article  Google Scholar 

  6. Garey, M. R., Johnson, D. S., Stockmeyer, L. J.: Some simplified NP-complete problems. Proceedings of 6th ACM Symposium on Theory of Computing, Seattle (Wash.) 1974, p. 91–95

  7. Gill, J. T.: Computational complexity of probabilistic Turing machines. Proceedings 6th Annual ACM Symposium on Theory of Computing, Seattle (Wash.) 1974, p. 91–95

  8. Greibach, S. A.: Checking automata and one-way stack languages. J. Computer and System Sciences 3, 196–217 (1969)

    Article  MathSciNet  Google Scholar 

  9. Hartmanis, J., Hunt, III., H. B.: The LBA problem and its importance in the theory of computing. Cornell University, Technical Report 73–171, 1973

  10. Hopcroft, J. E., Ullman, J. D.: Formal languages and their relation to automata. Reading (Mass.): Addison-Wesley 1969

    MATH  Google Scholar 

  11. Jones, N. D.: Reducibility among combinatorial problems in logn space. Proceedings of 7th Annual Princeton Conference on Information Sciences and Systems, 1973, p. 547–551

  12. Jones, N. D., Laaser, W. T.: Complete problems for deterministic polynomial time. Proceedings of 6th Annual ACM Symposium on Theory of Computing, Seattle (Wash.) 1974, p. 40–46

  13. Karp, R. M.: Reducibilities among combinatorial problems. In: Miller, R., Thatcher, J. (eds): Complexity of computer computations. New York: Plenum Press 1972, p. 85–104

    Chapter  Google Scholar 

  14. Ladner, R., Lynch, N., Selman, A.: Comparison of polynomial time reducibilities. Proceedings of 6th Annual ACM Symposium on Theory of Computing, Seattle (Wash.) 1974, p. 110–121

  15. Meyer, A. R., Stockmeyer, L. J.: Word problems requiring exponential time. Proceedings of 5th Annual ACM Symposium on Theory of Computing, Austin (Tex.) 1973, p. 1–9

  16. Rogers, J., Jr.: Theory of recursive functions and effective computability. New York: McGraw-Hill 1967

    MATH  Google Scholar 

  17. Savitch, W. J.: Relationship between nondeterministic and deterministic tape complexities. J. Computer and System Sciences 4, 177–192 (1970)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Sciences Department, IBM T. J. Watson Research Center, 10598, Yorktown Heights, New York, USA

    Zvi Galil

Authors
  1. Zvi Galil
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Some of the results in this paper were presented in the John Hopkins Conference on Information Sciences and Systems, April 1975.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Galil, Z. Hierarchies of complete problems. Acta Informatica 6, 77–88 (1976). https://doi.org/10.1007/BF00263744

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00263744

Keywords

Search

Navigation