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Serban E. Vlad

Publications and source records attributed to Serban E. Vlad.

At least 19 recordsLinked to original sources
arXiv2015

The consistency, the composition and the causality of the asynchronous flows

Let $Φ:\{0,1\}^{n}\longrightarrow\{0,1\}^{n}$. The asynchronous flows are (discrete time and real time) functions that result by iterating the coordinates $Φ_{i}$ independently on each other. The purpose of the paper is that of showing that the asynchronous flows fulfill the properties of consistency, composition and causality that define the dynamical systems. The origin of the problem consists in modelling the asynchronous circuits from the digital electrical engineering.

math.GM↗
arXiv2014

Binary periodic signals and flows

The concept of boolean autonomous deterministic regular asynchronous system has its origin in switching theory, the theory of modeling the switching circuits from the digital electrical engineering. The attribute boolean vaguely refers to the Boole 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 function $Φ:\{0,1\}^{n}\rightarrow\{0,1\}^{n},Φ=(Φ_{1},...,Φ_{n})$ whose coordinates iterate independently on each other. Time is discrete or continuous. The flows are these that result by analogy with the dynamical systems. The 'nice' discrete time and real time functions that the (boolean) asynchronous systems work with are called signals and periodicity is a very important feature in Nature. In the first two Chapters we give the most important concepts concerning the signals and periodicity. The periodicity properties are used to characterize the eventually constant signals in Chapter 3 and the constant signals in Chapter 4. Chapters 5,...,8 are dedicated to the eventually periodic points, eventually periodic signals, periodic points and periodic signals. Chapter 9 shows constructions that, given an (eventually) periodic point, by changing some values of the signal, change the periodicity properties of the point. The book addresses to researchers in systems theory and computer science, but it is also interesting to those that study periodicity itself. From this last perspective, the binary signals may be thought of as functions with finitely many values.

math.DS↗
arXiv2013

On the basins of attraction of the regular autonomous asynchronous systems

The Boolean autonomous dynamical systems, also called regular autonomous asynchronous systems are systems whose 'vector field' is a function Φ:{0,1}^{n}{\to}{0,1}^{n} and time is discrete or continuous. While the synchronous systems have their coordinate functions Φ_{1},...,Φ_{n} computed at the same time: Φ,Φ{\circ}Φ,Φ{\circ}Φ{\circ}Φ,... the asynchronous systems have Φ_{1},...,Φ_{n} computed independently on each other. The purpose of the paper is that of studying the basins of attraction of the fixed points, of the orbits and of the ω-limit sets of the regular autonomous asynchronous systems. The bibliography consists in analogies.

cs.OH↗
arXiv2013

Universal Regular Autonomous Asynchronous Systems: Fixed Points, Equivalencies and Dynamic Bifurcations

The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In the autonomous version, such a system is a set of functions x:R{\to}{0,1}^{n} called states (R is the time set). If an asynchronous system is defined by making use of a so called generator function Φ:{0,1}^{n}{\to}{0,1}^{n}, then it is called regular. The property of universality means the greatest in the sense of the inclusion. The purpose of the paper is that of defining and of characterizing the fixed points, the equivalencies and the dynamical bifurcations of the universal regular autonomous asynchronous systems. We use analogies with the dynamical systems theory.

cs.OH↗
arXiv2012

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.

math.GM↗
arXiv2012

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' Φ:{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.

cs.GL↗
arXiv2012

The decomposition of the regular asynchronous systems as parallel connection of regular asynchronous systems

The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering, where non-determinism is a consequence of the fact that modelling is made in the presence of unknown and variable parameters. Such a system is a multi-valued function f that assigns to an (admissible) input u:R{\to}{0,1}^{m} a set f(u) of (possible) states x:R{\to}{0,1}^{n}. When this assignment is defined by making use of a so-called generator function Φ:{0,1}^{n}{\times}{0,1}^{m}{\to}{0,1}^{n}, then the asynchronous system f is called regular. The generator function Φ acts in this asynchronous framework similarly with the next state function from a synchronous framework. The parallel connection of the asynchronous systems f' and f" is the asynchronous system (f'||f")(u)=f'(u){\times}f"(u). The purpose of the paper is to give the circumstances under which a regular asynchronous system f may be written as a parallel connection of regular asynchronous systems.

cs.OH↗
arXiv2011

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 element

cs.OH↗
arXiv2010

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' Φ:{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 ω-limit sets, the invariance and the basins of attraction of the universal regular autonomous asynchronous systems.

cs.OH↗
arXiv2008

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 Υsuch that for any u and any x in f(u), a certain equation involving Υis fulfilled. Then Υis 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].

cs.OH↗
arXiv2008

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.

cs.GL↗
arXiv2008

The equations of the ideal latches

The latches are simple circuits with feedback from the digital electrical engineering. We have included in our work the C element of Muller, the RS latch, the clocked RS latch, the D latch and also circuits containing two interconnected latches: the edge triggered RS flip-flop, the D flip-flop, the JK flip-flop, the T flip-flop. The purpose of this study is to model with equations the previous circuits, considered to be ideal, i.e. non-inertial. The technique of analysis is the pseudoboolean differential calculus.

cs.GL↗
arXiv2006

Relatively inertial delays

The paper studies the relatively inertial delays that represent one of the most important concepts in the modeling of the asynchronous circuits.

cs.OH↗
arXiv2006

The intersection and the union of the asynchronous systems

The asynchronous systems $f$ are the models of the asynchronous circuits from digital electrical engineering. They are multi-valued functions that associate to each input $u:\mathbf{R}\to \{0,1\}^{m}$ a set of states $x\in f(u),$ where $x:\mathbf{R}\to \{0,1\}^{n}.$ The intersection of the systems allows adding supplementary conditions in modeling and the union of the systems allows considering the validity of one of two systems in modeling, for example when testing the asynchronous circuits and the circuit is supposed to be 'good' or 'bad'. The purpose of the paper is that of analyzing the intersection and the union against the initial/final states, initial/final time, initial/final state functions, subsystems, dual systems, inverse systems, Cartesian product of systems, parallel connection and serial connection of systems.

cs.GL↗
arXiv2005

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].

cs.OH↗