Universal regular autonomous asynchronous systems: omega-limit sets, invariance and basins of attraction

The asynchronous systems are the non-deterministic real time-binary models of the asynchronous circuits from electrical engineering. Autonomy means that the circuits and their models have no input. Regularity means analogies with the dynamical systems, thus such systems may be considered to be the real time dynamical systems with a 'vector field' {\Phi}:{0,1}^2 \rightarrow {0,1}^2. Universality refers to the case when the state space of the system is the greatest possible in the sense of the inclusion. The purpose of the paper is that of defining, by analogy with the dynamical systems theory, the {\omega}-limit sets, the invariance and the basins of attraction of the universal regular autonomous asynchronous systems.Comment: accepted to be published in Mathematics and its Applications/Annals of the Academy of the Romanian Scientist

Examples of Models of the Asynchronous Circuits

We define the delays of a circuit, as well as the properties of determinism, order, time invariance, constancy, symmetry and the serial connection

Defining the Delays of the Asynchronous Circuits

We define the delays of a circuit, as well as the properties of determinism, order, time invariance, constancy, symmetry and the serial connection

Topics in asynchronous systems

In the paper we define and characterize the asynchronous systems from the point of view of their autonomy, determinism, order, non-anticipation, time invariance, symmetry, stability and other important properties. The study is inspired by the models of the asynchronous circuits.Comment: 40 page

Selected Topics in Asynchronous Automata

The paper is concerned with defining the electrical signals and their models. The delays are discussed, the asynchronous automata - which are the models of the asynchronous circuits - and the examples of the clock generator and of the R-S latch are given. We write the equations of the asynchronous automata, which combine the pure delay model and the inertial delay model; the simple gate model and the complex gate model; the fixed, bounded and unbounded delay model. We give the solutions of these equations, which are written on R->{0,1} functions, where R is the time set. The connection between the real time and the discrete time is discussed. The stability, the fundamental mode of operation, the combinational automata, the semi-modularity are defined and characterized. Some connections are suggested with the linear time and the branching time temporal logic of the propositions

The non-anticipation of the asynchronous systems

The asynchronous systems are the models of the asynchronous circuits from the digital electrical engineering and non-anticipation is one of the most important properties in systems theory. Our present purpose is to introduce several concepts of non-anticipation of the asynchronous systems.Comment: the 6-th Congress of the Romanian mathematicians, Bucharest, June 28 - July 4, 200

Introductory Topics in Distributions over Binary Test Functions

We note with B2 the Boole algebra with two elements. We define for the R->B2 functions the limits, the derivatives, the differentiability, the test functions, the integrals. We also define the distributions over the space of these test functions, the regular and the singular distributions, the support sets of the distributions. We also define for the RxR->{0,1} functions the test functions and the distributions over them. The direct product of the distributions is presented, as well as the convolution algebras of distributions. Generalizations of the binary test functions and of the distributions over them are given.Comment: the MSC-class was chosen by analogy: we refer to binary valued functions here, not to real valued function

The model of the ideal rotary element of Morita

Reversible computing is a concept reflecting physical reversibility. Until now several reversible systems have been investigated. In a series of papers Kenichi Morita defines the rotary element RE, that is a reversible logic element. By reversibility, he understands that 'every computation process can be traced backward uniquely from the end to the start. In other words, they are backward deterministic systems'. He shows that any reversible Turing machine can be realized as a circuit composed of RE's only. Our purpose in this paper is to use the asynchronous systems theory and the real time for the modeling of the ideal rotary elementComment: presented at the 12-th Symposium of Mathematics and its Applications, "Politehnica" University of Timisoara, Timisoara, 200

On the Inertia of the Asynchronous Circuits

We present the bounded delays, the absolute inertia and the relative inertia

Asynchronous pseudo-systems

The paper introduces the concept of asynchronous pseudo-system. Its purpose is to correct/generalize/continue the study of the asynchronous systems (the models of the asynchronous circuits) that has been started in [1], [2].Comment: 28 page