The time reversal symmetry vs. the technical condition of proper operation of the asynchronous flows, International Journal of Computer Research Volume 23, Number 4, pp. 329–348, 2017



Mathematical Subject Classification (2010): 94C10

Keywords and phrases: Boolean function; time-reversal symmetry; the technical condition of proper operation; predecessor; successor

The asynchronous flows are generated by Boolean functions Φ:{0,1}n→{0,1}n whose coordinates Φ1,...,Φn are iterated independently on each other. The order and the time instants of these iterations are not known. The flows are the models of the asynchronous circuits from the digital electronics. Time-reversal symmetry is one of the fundamental symmetries discussed in natural science and our main purpose is to adapt this concept, by analogy with mechanics, to the asynchronous flows. The technical condition of proper operation, also known as race-freedom, is a special case of work in asynchronicity which ’softens’ the non-determinism of the models. We prove that when it is fulfilled, the flow behaves like a dynamical system. Finally, we relate the time-reversal symmetry and the fulfillement of the technical condition of proper operation.