Boolean Equation Systems Research Articles

Algebraic Fault Analysis for Constrained Combinational Networks

A sequential machine that processes its inputs without changing state can be represented as a constrained combinational network. A system of Boolean equations that represent such a network must include assertions that formalize the required constraints. These constraints can be expressed as assertions about certain gate inputs and certain gate outputs within the network. In such networks, redundant and partially redundant gates are not pathological. The fault analysis method presented provides for the testing of both sides of an irredundant gate and for the detectable side of a partially redundant gate.

On the solvability of infinite systems of Boolean polynomial equations

On the solvability of infinite systems of Boolean polynomial equations

Synthesis of TANT networks using a Boolean analyser

The automated synthesis of TANT combinational networks (Three-level AND-NOT networks with True inputs) is studied using the advantages of Svoboda Boolean Analyzer (SBA) (see Svoboda, 1968). The synthesis procedure consists of (i) calculating the ordinary prime implicants of the given function f using operation Mode I of SBA, (ii) calculation of all generalised prime implicants of f by solving a system of Boolean equations (operation Mode II), (iii) solution of a covering problem using a special Petrick function and operation Mode I of the SBA. The synthesis procedure yields a TANT network containing a minimum number of AND-NOT elements. FORTRAN IV programs have been developed which implement the proposed synthesis method; however, the SBA hardware unit, when available, will prove an efficiency factor in processing time of approximately 104.

Ralph M. Toms. Systems of Boolean equations. The American mathematical monthly, vol. 73 (1966), pp. 29–35.

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Systems of Boolean Equations

(1966). Systems of Boolean Equations. The American Mathematical Monthly: Vol. 73, No. 1, pp. 29-35.

Systems of Boolean Equations

Systems of Boolean Equations

Řešení soustav booleových rovnic

Řešení soustav booleových rovnic

J. A. Postley. A method for the evaluation of a system of Boolean algebraic equations. Mathematical tables and other aids to computation, vol. 9 (1955), pp. 5–8.

J. A. Postley. A method for the evaluation of a system of Boolean algebraic equations. Mathematical tables and other aids to computation, vol. 9 (1955), pp. 5–8.

A method for the evaluation of a system of Boolean algebraic equations

A method for the evaluation of a system of Boolean algebraic equations