The signals from digital electrical engineering are modeled by discrete time and real time functions, whose values are binary n-tuples and which are also called signals. The asynchronous circuits, representing the devices that work with such signals, are modeled by Boolean autonomous deterministic regular asynchronous systems, shortly by asynchronous flows. The attribute Boolean' vaguely refers to the binary Boole algebra; autonomous' means that there is no input; deterministic' means the existence of a unique state function; and regular' indicates the existence of a Boolean function that iterates its coordinates independently on each other (ie: asynchronously). Strong analogies exist with the real, usual dynamical systems. The purpose of this research monograph is to study the periodicity of the signals and of their values, as well as the periodicity of the asynchronous flows. The monograph addresses systems theory and computer science that apply to researchers, but it is also interesting to those that study periodicity itself. From this last perspective, the signals may be thought of as functions with many finite values. At the same time, the asynchronous flows may be considered as special cases of variable structure systems. The bibliography consists of works of real, dynamical systems that produce analogies.
Serban E Vlad was born in 1959 in Oradea, Romania and he works at present as analyst-programmer. He is a member of ROMAI and GAMM, the Romanian and the German societies of industrial and applied mathematics. He is the author of more than fifty papers and a chapter in a book. His research monograph Asynchronous Systems Theory' was published in several editions. His main fields of interest are binary valued analysis and asynchronous systems theory. In binary valued analysis, he defined for the real argument, binary functions the notions of integral and derivative. He studied also the periodicity of the real argument and discrete argument binary functions. In systems theory, he was concerned with modeling the asynchronous circuits from electronics. He defined the concept of delay and he wrote differential equations that model the ideal latches and other circuits. He introduced the regular asynchronous systems that, by some analogy with the (real, usual) dynamical systems, are generated by Boolean functions which iterate their coordinates independently on each other.
