## 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 Φ_{i} 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.