The consistency, the composition and the causality of the asynchronous flows, Journal of Progressive Research in Mathematics, Volume 3, Issue 2, 2015, pp. 152-160



Mathematical Subject Classification (2010): 94C10

Keywords and phrases: consistency, composition, causality, asynchronous flow, asynchronous circuit

The Boolean autonomous deterministic regular asynchronous systems, shortly the asynchronous flows, have been defined by the author in 2007. The concept has its origin in switching theory, the theory of modeling the asynchronous (or switching) circuits from the digital electrical engineering. The attribute Boolean vaguely refers to the Boolean algebra with two elements, autonomous means that there is no input, determinism means the existence of a unique state function and regular indicates the existence of a Boolean function Φ:{0,1}n→{0,1}n that 'generates' the system, by iterating its coordinates Φi independently on each other. Time is discrete or continuous.

The purpose of the paper is that of showing that the previously defined flows fulfill the adaptation to this context of the properties of consistency, composition and causality contained in the definition of the dynamical systems from Rudolf E. Kalman, Peter L. Falb, Michael A. Arbib, Topics in mathematical system theory, McGraw-Hill, 1969. We add the remark that in the cited work the systems had an input, unlike here where it is convenient to omit this aspect.