The complexity of semilinear sets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)


In this paper we shall characterize the computational complexity of two decision problems: the inequality problem and the uniform word problem for semilinear sets. It will be proved that the first problem is log-complete in the second class (Σp2) of the polynomial-time hierarchy and the second problem is log-complete in NP. Moreover we shall show that these problems restricted to the 1-dimensional case have the ‘same’ computational complexity as the general case.


Interior Point Generate Vector Inequality Problem Boundary Plane Face Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E.Cardoza, R.Lipton and A.R.Meyer: "Exponential Space Complete Problem for Petri Nets and Commutative Semigroups", in "Proc. of the 8-th Annual ACM Symposium on the Theory of Computing" (1976), pp. 50–54.Google Scholar
  2. 2.
    S.Eilenberg and M.P.Schützenberger: "Rational Sets in Commutative Monoids", Journal of Algebra, No 13, 1969, pp. 173–191.Google Scholar
  3. 3.
    J. Von Zur Gathen and M. Sieveking: "A bound on Solutions of Linear Integer Equalities and Inequalities", Proc. of the AMS, Vol. 72, No 1, 1978, pp. 155–158.Google Scholar
  4. 4.
    M. Gerstenhaber: "Theory of Convex Polyhedral Cones", in Proc. of a Conference on "Activity Analysis of Production and Allocation", Ed. T.C. Koopmans, John Willey & Sons — Chapman & Hall, 1951.Google Scholar
  5. 5.
    S.Ginsburg: "The Mathematical Theory of Context-free Languages", Mc Graw-Hill, 1966.Google Scholar
  6. 6.
    F. Glover and R.E.D. Woolsey: "Aggregating Diophantine Equations", Zeitschrift für Operations Researchs, Vol. 16, 1972, pp. 1–10.Google Scholar
  7. 7.
    G.Hotz: "Eine Neue Invariante Kontext-freier Grammatiken", 1978, to appear in Theoretical Computer Science.Google Scholar
  8. 8.
    G.Hotz: "Verschränkte Homomorphismen Formaler Sprachen", 1979, to appear in RAIRO.Google Scholar
  9. 9.
    W.J.Paul: "Komplexitätstheorie", Teubner Verlag, 1979.Google Scholar
  10. 10.
    L.Stockmeyer and A.R.Meyer: "Word Problem Requiring Exponential Time", in Proc. of the 5-th Annual Symposium on the Theory of Computing, 1973, pp. 1–9.Google Scholar
  11. 11.
    L. Stockmeyer: "The Polynomial-Time Hierarchy", Theoretical Computer Science, Vol. 3, 1977, pp. 1–12.Google Scholar
  12. 12.
    J.Stoer and C.Witzgall: "Convexity and Optimization in Finite Dimension I", Springer Verlag, 1970.Google Scholar
  13. 13.
    C. Wrathall: "Complete Sets and the Polynomial-Time Hierarchy", Theoretical Computer Science, Vol. 3, 1977, pp. 23–33.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  1. 1.Fachbereich InformatikUniversität SaarbrückenGermany

Personalised recommendations