On the Inertia of the Asynchronous Circuits

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

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

Some first thoughts on the stability of the asynchronous systems

The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous circuits. Our purpose is to state the problem of the their stability.Comment: 12 pages, conferenc

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

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

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

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

Binary signals: a note on the prime period of a point

The 'nice' $x:\mathbf{R}\rightarrow\{0,1\}^{n}$ functions from the asynchronous systems theory are called signals. The periodicity of a point of the orbit of the signal x is defined and we give a note on the existence of the prime period.Comment: 6 pages, conference ICMA 201