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Using the hamiltonian path operator to capture NP

  • Iain A. Stewart
Theory Of Computing, Algorithms And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 468)

Abstract

In this paper, we define the language (FO + posHP), where HP is the Hamiltonian path operator, and show that a problem can be represented by a sentence of this language if and only if the problem is in NP. We also show that every sentence of this language can be written in a normal form, and so establish the fact that the problem of deciding whether there is a directed Hamiltonian path between two distinguished vertices of a digraph is complete for NP via projection translations: as far as we know, this is the first such problem discovered. We also give a general technique for extending existing languages using operators derived from problems.

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References

  1. [1]
    M.R. GAREY & D.S. JOHNSON, Computers and intractability, W.H.Freeman and Co., San Francisco, 1979.Google Scholar
  2. [2]
    N. IMMERMAN, Languages that capture complexity classes, SIAM J. Comput., Vol. 16, No. 4, 1987, pp.760–778.Google Scholar
  3. [3]
    N. IMMERMAN, Nondeterministic space is closed under complementation, SIAM J. Comput., Vol. 17, No. 5, 1988, pp.935–938.Google Scholar
  4. [4]
    I.A.STEWART, Complete problems for symmetric logspace involving free groups, Univ. Newcastle upon Tyne Tech. Rep., No. 300, 1989.Google Scholar
  5. [5]
    I.A.STEWART, Using the Hamiltonian path operator to capture NP, Univ. Newcastle upon Tyne Tech. Rep., 1989.Google Scholar
  6. [6]
    R. SOMMERHALDER & S.C. vAN WESTRHENEN, The theory of computability: programs, machines, effectiveness, and feasibility, Addison-Wesley, Wokingham, England, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Iain A. Stewart
    • 1
  1. 1.Computing LaboratoryUniversity of Newcastle upon Tyne Claremont TowerNewcastle upon TyneEngland

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