# Asynchronous Operators of Sequential Logic: Venjunction & by Vadim Vasyukevich

This publication is devoted to new mathematical tools assigned for logical modeling of the reminiscence of electronic units. The for instance is logic-dynamical operation named venjunction and venjunctive functionality in addition to sequention and sequentional functionality. Venjunction and sequention function in the framework of sequential good judgment. In a sort of the corresponding equations, they organically healthy analytical expressions of Boolean algebra. therefore, a kind of symbiosis is shaped utilizing parts of asynchronous sequential good judgment at the one hand and combinational good judgment nevertheless. So, asynchronous common sense is represented within the type of better Boolean good judgment. The publication includes preliminary techniques, primary definitions, statements, rules and principles wanted for theoretical justification of the mathematical equipment and its validity for asynchronous common sense. Asynchronous operators named venjunctor and sequentor are designed for functional implementation. those uncomplicated components are assigned for understanding of reminiscence services in sequential circuits. current study paintings is the ultimate level of generalization and systematization of all these rules and investigations, author’s curiosity to which alternately flashed up and pale over decades and for numerous purposes until eventually shaped “critical mass”, and all findings have been prepared definitively as a mathematical foundation of a conception thoroughly linked less than a typical topic – asynchronous sequential good judgment, primarily categorized as switching good judgment, which falls into class of algebraic logics.

This publication is devoted to new mathematical tools assigned for logical modeling of the reminiscence of electronic units. The for instance is logic-dynamical operation named venjunction and venjunctive functionality in addition to sequention and sequentional functionality. Venjunction and sequention function in the framework of sequential good judgment. In a sort of the corresponding equations, they organically healthy analytical expressions of Boolean algebra. therefore, a kind of symbiosis is shaped utilizing parts of asynchronous sequential good judgment at the one hand and combinational good judgment nevertheless. So, asynchronous common sense is represented within the type of better Boolean good judgment. The publication includes preliminary techniques, primary definitions, statements, rules and principles wanted for theoretical justification of the mathematical equipment and its validity for asynchronous common sense. Asynchronous operators named venjunctor and sequentor are designed for functional implementation. those uncomplicated components are assigned for understanding of reminiscence services in sequential circuits. current study paintings is the ultimate level of generalization and systematization of all these rules and investigations, author’s curiosity to which alternately flashed up and pale over decades and for numerous purposes until eventually shaped “critical mass”, and all findings have been prepared definitively as a mathematical foundation of a conception thoroughly linked less than a typical topic – asynchronous sequential good judgment, primarily categorized as switching good judgment, which falls into class of algebraic logics.

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Extra info for Asynchronous Operators of Sequential Logic: Venjunction & Sequention: Digital Circuit Analysis and Design (1st Edition)

Example text

X ) = 1 . 3) i =1 The equation represents a necessary condition for sequention to be set at logic 1. However, it is not sufficient to have unity values of all variables for obtaining 〈x〉 = 1. Corresponding binary set needs to be ordered in time taking into account priorities of elements in a sequence 〈x1 x2 … xn〉. Concretely, logical unity setting x1 = 1 needs to be ahead in time of all other settings: x2 = 1, x3 = 1, x4 = 1, … xn = 1. In turn, x2 = 1 value needs to be ahead of x3 = 1, x4 = 1 … xn = 1; x3 = 1 – ahead of x4 = 1 … xn = 1, and so on.

7) includes 5 layers. 3 Simple and Complicated Sequentions 49 Layer 0 Zeroes layer is the layer assigned for function. It is occupied by entire sequention with all its embeddings. Layer 1 On the first layer, the following components are embedded into initial sequention: complicated sequention 〈x 〈y z〉〉; complicated sequention 〈〈u〉 〈〈v〉 〈p 〈r〉〉 s〉〉. – – Layer 2 On the second layer, the following components are embedded into complicated sequentions of the first layer: – initial elements x1 , x2 ...

1) 1∠ x ≠ x . 1 Logical Indeterminacy If a logic function after and as a result of setting of known values of the variables does not certainly reduce either to zero or unity, such a function is considered to be not determined, that is indeterminate function. Indeterminacy generates ambiguousness in the form of not uniquely defined value J ∈ {0, 1}. This uncertain situation can be equally decided in favor of J = 1 as well as in favor of J = 0. Indeterminacy of venjunction z = x ∠ y is caused by the factor of switching of variables.