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Serban E. Vlad

Publications and source records attributed to Serban E. Vlad.

31 records · Page 2Linked to original sources
arXiv2004

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↗
arXiv2004

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.

cs.GL↗
arXiv2004

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.

cs.AR↗
arXiv2004

Towards a Mathematical Theory of the Delays 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).

cs.LO↗
arXiv2001

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.

cs.LO↗
arXiv2001

An Asynchronous Automata Approach to the Semantics of Temporal Logic

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 on x and their formulas give the properties of the automaton.

cs.LO↗
arXiv2001

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.

math.GM↗
arXiv2001

Introductory Topics in Binary Set Functions

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 measure theory. We mention the special case of the Riemann integrals.

math.GM↗