On discretization of delays in timed automata and digital circuits
For acyclic (combinatorial) circuits whose inputs change only once, the answer is positive: there is a constant δ, depending on the maximal number of possible events in the circuit, such that if we restrict all events to take place at multiples of δ, we still preserve qualitative behaviors.
For cyclic circuits the answer is negative: a simple circuit with three gates can demonstrate a qualitative behavior which cannot be captured by any discretization.
Nevertheless we show that a weaker notion of preservation, similar to that of [HMP92], allows in many cases to verify discretized circuits with δ=1 such that the verification results are valid in dense time.
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