On Discretization of Delays in Timed Automata and Digital Circuits

In this paper we solve the following problem: \given a digital circuit composed of gates whose real-valued delays are in an integerbounded interval, is there a way to discretize time while preserving the qualitative behavior of the circuit?" This problem is described as open in BS94]. When \preservation of qualitative behavior" is interpreted in a strict sense, as having all original sequences of events with their original ordering we obtain the following two results: 1) For acyclic (combinatorial) circuits whose inputs change only once, the answer is positive: there is a constant , depending on the maximal number of possible events in the circuit, such that if we restrict all events to take place at multiples of , we still preserve qualitative behaviors. 2) 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 preservatio...

• Type: Conference
• Year: 1998
• Where: CONCUR
• Authors: Eugene Asarin, Oded Maler, Amir Pnueli
• Keywords: CONCUR 1998, Digital Circuit, Distributed And Parallel Computing, Qualitative Behavior, Real-valued Delays