Functions Of K-valued Logic Research Articles

Tunable multifunction logic modules based on parametric representation of functions of k-valued logic over quasifields

We propose a new class of tunable logic modules that realize functions of k-valued logic. These modules are characterized by homogeneous structure and linear dependence of the number of tunable inputs on the number of input variables.

Completeness of systems of functions of k-valued logic associated with transformation groups of variables

The lattice of closed classes is introduced and the completeness of k-valued logic is examined for the case of identification of functions that are transformed into one another by semigroups (and groups) of transformations of variables.

Functional completeness in P2×Pk

Two-sorted invariant relations are used to describe all maximum subalgebras of the iterative algebra P2×P k —the arity-calibrated product of the algebras of Boolean functions and of functions of k-valued logic with k≥3. Functional completeness criteria are obtained for P2×P k and also for the system P2×...×P2×P k .

On α-closed classes and α-complete Systems of k-valued logic functions

On α-closed classes and α-complete Systems of k-valued logic functions

The completeness problem in the algebra of partial functions of finite-valued logic

All maximal subalgebras of the algebra of partial functions of k-valued logic (k≥4) are described using invariant relations. The problem of functional completeness in the system of partial functions of finite-valued logic is solved.

The complexity of dynamic tests for functions of k-valued logic

The complexity of dynamic tests for functions of k-valued logic

An algebraical system for polynomial representation of k-valued logical functions

An algebraical system < A k ;+;⊗ >, in which ‘almost each’ k-valued logical function (k-composite integer) had representation in the form of polynomial in modulo k, is presented.

Polynomial forms of partial functions of k-valued logic

Polynomial forms of partial functions of k-valued logic

The search for the maximum upper zero for a class of monotonic functions of finite-valued logic

THE PROBLEM of finding the maximum upper zero of a monotonic function of finite-valued logic is solved in the Shannon formulation. It is proved that in the finite-valued case the solution has a form similar to well-known solutions for Boolean functions and functions of k-valued logic.

Search for a maximum upper zero for a class of monotonic functions in k-valued logic

MONOTONIC functions of k-valued logic, which take the values 0 or 1 are considered. The problem of finding a maximum upper zero is solved for them in Shannon's formulation.

Combinatorial approach to the classification of k-valued logical functions

Combinatorial approach to the classification of k-valued logical functions

A Local algorithm of index 1 for constructing the sum of dead-end disjunctive normal forms for functions of k-valued logic

An algorithm of index 1 is constructed, deciding the question of the occurrence of an elementary conjunction in the disjunctive normal form, which is the sum of dead-end disjunctive normal forms of a given function of k-valued logic, and its majorantness is proved.

Number of maximal closed, under superposition, classes of function over a finite family of finite sets

Due to their applications in cybernetics, computers, and mathematical logic, great attention has been devoted during the last decades to the study of systems of functions, in particular, of the class of functions of k-valued logic (k = 2, 3, 4 . . . . ) that are closed under superposition. For the analysis and synthesis of contact networks it is important to possess a complete system of basic functional elements, i.e., a system of functions that generate all other functions.

A certain method of synthesizing functions of k-valued logic

A certain method of synthesizing functions of k-valued logic

Representatives of functions of k-valued logic by polynomials mod k

Representatives of functions of k-valued logic by polynomials mod k

On the realization of functions of K-valued logic

On the realization of functions of K-valued logic