On the complexity of worst case and expected time in a circuit

  • Andreas Jakoby
  • Christian Schindelhauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


The computational delay of a circuit can be described by the natural concept of time [Jakoby et al. STOC94]. We show that for a given input x and circuit C the computation of timeC(x) is P-complete. Moreover, we show that it is NP-complete to decide whether there exists an input x such that timeC (x)≤t for a given time bound t.

We introduce the notion of worst time of a circuit and show that to decide whether a given time bound is the worst time of a circuit is BH2-complete. We also prove that the computation of an arbitrary worst case input is FP tt NP -hard, whereas the search of the lexicographically minimal worst case input is FP NP -complete and of the lex. middle worst case input is FP #P -complete.

Computation of the expected time E μD (timeC) of a circuit C with respect to a distribution μ D generated by circuit D is #P-complete under metric reducibility. Nevertheless we show that a polynomial time bounded probabilistic Turing machine approximates E μD (timeC) up to an arbitrary additive constant with high probability.

Key words

theory of parallel and distributed computation computational complexity average case analysis expected time worst case timed circuits 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Andreas Jakoby
    • 1
  • Christian Schindelhauer
    • 1
    • 2
  1. 1.Medizinische Universität zu LübeckDeutschland
  2. 2.Institut für Theoretische InformatikLübeckGermany

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