Some properties of the regular asynchronous systems

The asynchronous systems are the models of the asynchronous circuits from the digital electrical engineering. An asynchronous system f is a multi-valued function that assigns to each admissible input u a set f(u) of possible states x in f(u). A special case of asynchronous system consists in the existence of a Boolean function \Upsilon such that for any u and any x in f(u), a certain equation involving \Upsilon is fulfilled. Then \Upsilon is called the generator function of f (Moisil used the terminology of network function) and we say that f is generated by \Upsilon. The systems that have a generator function are called regular. Our purpose is to continue the study of the generation of the asynchronous systems that was started in [2], [3].Comment: International Conference on Computers, Communications & Control 2008, May 15-17, Baile Felix, Romani

On the serial connection of the regular asynchronous systems

The asynchronous systems f are multi-valued functions, representing the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In real time, they map an 'admissible input' function u:R\rightarrow{0,1}^{m} to a set f(u) of 'possible states' x\inf(u), where x:R\rightarrow{0,1}^{m}. When f is defined by making use of a 'generator function' {\Phi}:{0,1}^{n}\times{0,1}^{m}\rightarrow{0,1}^{n}, the system is called regular. The usual definition of the serial connection of systems as composition of multi-valued functions does not bring the regular systems into regular systems, thus the first issue in this study is to modify in an acceptable manner the definition of the serial connection in a way that matches regularity. This intention was expressed for the first time, without proving the regularity of the serial connection of systems, in a previous work. Our present purpose is to restate with certain corrections and prove that result.Comment: 9 pages; ROMAI Journal, Vol. 7, Nr. 2, 201

Some properties of the regular asynchronous systems

The asynchronous systems are the models of the asynchronous circuits from the digital electrical engineering. An asynchronous system f is a multi-valued function that assigns to each admissible input u: R → {0, 1} m a set f(u) of possible states x ∈ f(u), x: R → {0, 1} n. A special case of asynchronous system consists in the existence of a Boolean function Υ: {0, 1} n × {0, 1} m → {0, 1} n such that ∀u, ∀x ∈ f(u), a certain equation involving Υ is fulfilled. Then Υ is called the generator function of f (Moisil used the terminology of network function) and we say that f is generated by Υ. The systems that have a generator function are called regular. Our purpose is to continue the study of the generation of the asynchronous systems that was started in [2], [3]