The Complexity of Computing the Size of an Interval

  • Lane A. Hemaspaandra
  • Sven Kosub
  • Klaus W. Wagner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)


We study the complexity of counting the number of elements in intervals of feasible partial orders. Depending on the properties that partial orders may have, such counting functions have different complexities. If we consider total, polynomial-time decidable orders then we obtain exactly the #P functions. We show that the interval size functions for polynomial-time adjacency checkable orders are tightly related to the class FPSPACE(poly): Every FPSPACE(poly) function equals a polynomial-time function subtracted from such an interval size function. We study the function #DIV that counts the nontrivial divisors of natural numbers, and we show that #DIV is the interval size function of a polynomial-time decidable partial order with polynomial-time adjacency checks if and only if primality is in polynomial time.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Lane A. Hemaspaandra
    • 1
  • Sven Kosub
    • 2
  • Klaus W. Wagner
    • 2
  1. 1.Department of Computer ScienceUniversity of RochesterRochesterUSA
  2. 2.Theoretische InformatikJulius-Maximilians-Universität WürzburgAm HublandGermany

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