## 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 Φ_{1},...,Φ_{n} 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.