# Serban E. VladIndependent Researcher · Oradea City Hall, Department of Computers

Serban E. Vlad

## About

62

Publications

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103

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Introduction

Serban E. Vlad currently works at the Oradea City Hall, Department of Computers, Independent Researcher. Serban does research in Applied Mathematics.

**Skills and Expertise**

## Publications

Publications (62)

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 o...

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 o...

Let Φ:{0,1}ⁿ→{0,1}ⁿ a function whose coordinates Φ_{i},i∈{1,...,n} are iterated independently on each other, in discrete time or real time. The resulted flows, called asynchronous, model the asynchronous circuits from the digital electrical circuits. The concept of double eventual periodicity refers to two eventually periodic simultaneous phenomena...

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.

A discrete time Boolean asynchronous system consists in a function Φ : {0, 1} n → {0, 1} n which iterates its coordinates Φ 1 , ..., Φ n independently of each other. The durations of computation of Φ 1 , ..., Φ n are supposed to be unknown. The analysis of such systems has as main challenge characterizing their dynamics in conditions of uncertainty...

The theory of Daizhan Cheng [1] replaces B = {0, 1} with D = { (1,0) , (0,1) }, and Boolean functions with logical matrices. Interesting and very important algebraical opportunities result, which can be used in systems theory. Our purpose is to give a hint on the theory of Cheng and its application to asynchronicity. 2010 Mathematics Subject Classi...

The coordinates Φ 1 , ..., Φ n of the functions Φ : {0, 1} n −→ {0, 1} n are iterated independently on each other, in general, generating the so called Boolean asynchronous systems. The dynamics of these systems is unpredictable, since the computation durations of Φ 1 , ..., Φ n are not known and variable. The generalized technical condition of pro...

The asynchronous flows are defined by Boolean functions Φ : {0, 1} n → {0, 1} n that iterate their coordinates Φ 1 , ..., Φ n independently on each other. We define for the set A ⊂ {0, 1} n the properties of invariance, connectedness, path connectedness and we initiate a study of these concepts.

Let $\Phi:\{0,1\}^{n}\longrightarrow\{0,1\}^{n}$. The asynchronous flows are
(discrete time and real time) functions that result by iterating the
coordinates $\Phi_{i}$ 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...

The asynchronous flows are given by Boolean functions Φ : {0, 1} n −→ {0, 1} n that iterate their coordinates Φ 1 , ..., Φ n independently on each other. In the study of the asynchronous sequential circuits, the situation when multiple coordinates of the state can change at the same time in called a race. When the outcome of the race affects critic...

The regular autonomous asynchronous systems are the non-deterministic Boolean
dynamical systems and universality means the greatest in the sense of the
inclusion. The paper gives four definitions of symmetry of these systems in a
slightly more general framework, called semi-regularity and also many examples.

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 u...

The Boolean autonomous dynamical systems, also called regular autonomous
asynchronous systems are systems whose 'vector field' is a function
{\Phi}:{0,1}^{n}{\to}{0,1}^{n} and time is discrete or continuous. While the
synchronous systems have their coordinate functions {\Phi}_{1},...,{\Phi}_{n}
computed at the same time:
{\Phi},{\Phi}{\circ}{\Phi},...

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 {\Phi}:{0,1}^{n}{\to}...

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}^{...

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...

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' {...

The asynchronous systems are non-deterministic real time, binary valued models of the asynchronous circuits from electronics. Autonomy means that there is no input and regularity means analogies with the (real) dynamical systems. We introduce the concepts of dependence on the initial states and of transitivity for these systems. Comment: presented...

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...

Asynchronous systems are used as nondeterministic models for asynchronous circuits from digital electrical engineering. In the autonomous version, such a system is a set of functions x:ℝ→{0,1} n called states (ℝ is the time set). If an autonomous asynchronous system is defined by making use of a so-called generator function Φ:{0,1} n →{0,1} n , the...

An n-signal is a function x:R→{0,1}n that fulfills certain inertia requirements and an autonomous asynchronous system is a non-empty subset of the set of the n-signals. The autonomous asynchronous systems are the (real time, binary spaces, no input and non- deterministic) models of the autonomous asynchronous circuits from the digital electrical en...

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.

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 fo...

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...

Asynchronous systems represent the models of asynchronous circuits from digital electrical engineering. A delay is an asynchronous system that models the delay circuit. The purpose of the paper is that of defining and characterising the absolute inertia of the delays. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The asynchronous circuits from the digital electrical engineering are modeled by the so-called asynchronous systems. An autonomous asynchronous system consists in a set X of 'nice' R → {0, 1} n functions n ≥ 1, called signals, representing non-deterministically the models of the tensions that describe the behavior of an asynchronous circuit without...

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

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...

The asynchronous systems are multivalued applications f from the set ℝ→{0,1} m functions, called (admissible) inputs, to sets of ℝ→{0,1} n functions, called (possible) states. The fundamental (operating) mode of f consists in an input u and a sequence (μ k ) k∈N ∈{0,1} n of binary vectors so that μ 0 ,μ 1 ,μ 2 ,··· are accessed by all the states x∈...

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].

The delays are the R->{0,1} models of the delay circuits and delay theory is the theory of modeling the asynchronous circuits from digital electrical engineering that has as fundamantal concept the delay. We define the signals and give some useful properties on them. We define the delays, as well as their determinism, order, time invariance, consta...

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. This concept is inspired by the modeling of asynchronous circuits. Our purpose is to state the problem of the their stability.

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...

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.

The inequations of the delays of the asynchronous circuits are written, by making use of pseudo-Boolean differential calculus. We consider these efforts to be a possible starting point in the semi-formalized reconstruction of the digital electrical engineering (which is a non-formalized theory).

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

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

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

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 th...

The paper presents the differential equations that characterize an asynchronous automaton and gives their solution x:R->{0,1}x...x{0,1}. Remarks are made on the connection between the continuous time and the discrete time of the approach. The continuous and the discrete time, the linear and the branching temporal logics have the semantics depending...

We write the relations that characterize the simpliest timed automaton, the inertial delay buffer, in two versions: the non-deterministic and the deterministic one, by making use of the derivatives of the R->{0,1} 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 t...

Let X be a non-empty set and U a ring of subsets of X. The countable additive functions U->{0,1} are called measures. The paper gives some definitions (derivable measures, the Lebesgue-Stieltjes measures) and properties of these functions, its purpose being that of reconstruction of the measure theory within this frame, by analogy with the real mea...

This paper defines and characterizes the delay-insensitivity, the hazard-freedom, the semi-modularity and the technical condition of good running of discrete time asynchronous automata.

We write the relations that characterize the simpliest timed automaton, the inertial delay buffer, in two versions: the non-deterministic and the deterministic one, by making use of the derivatives of the R → {0,1} functions.

B2 is the Boole algebra with two elements. The paper defines the Riemann integrals and the derivatives of the R->B2 functions. Other types of integrals are defined similarly.

Prandtl's boundary layer theory may be considered one of the origins of systematic scale analysis and asymptotics in fluid mechanics. Due to the vast scale differences in atmospheric flows such analyses have a particularly strong tradition in theoretical meteorology. Simplified asymptotic limit equations, derived through scale analysis, yield a dee...

Double-struck B sign2 is the Boole algebra with two elements. The paper defines the Riemann integrals and the derivatives of the f : double-struck R sign → double-struck B sign2 functions. Other types of integrals are defined similarly.

In the paper we take profit on the possibility of defining an integral-differential calculus for the R →{0,1}x...x{0,1} functions in order to construct the elements of a distributions theory over such test functions.

The R→B 2 functions may be interpreted to represent: subsets of R, models of the electrical signals, propositions having a logical value that depends on time. Our purpose is to define and characterize the R→B 2 differentiable functions.

We write the relations that characterize the simpliest timed automaton, the inertial delay buffer, in two versions: the non-deterministic and the deterministic one, by making use of the derivatives of the } 1 , 0 { → R functions.

We note with 2 B the Boole algebra with two elements. In the paper we take profit on the possibility of defining an integral-differential calculus for the 2 B R → n functions in order to construct the elements of a distributions theory over such test functions. AMS Classification: primary:46F99, secondary:26B05.

Our purpose is to characterize the solution for the equations of the asynchronous automata (real time, discrete space systems) in the special case that the stability under the technical condition of good running is satisfied.