On the complexity of worst case and expected time in a circuit
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 wordstheory of parallel and distributed computation computational complexity average case analysis expected time worst case timed circuits
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