Solving Parameterised Boolean Equation Systems with Infinite Data Through Quotienting

2018 ◽  
pp. 216-236 ◽  
Author(s):  
Thomas Neele ◽  
Tim A. C. Willemse ◽  
Jan Friso Groote
Keyword(s):  
Boolean Equation

scholarly journals Verification of reactive systems via instantiation of Parameterised Boolean Equation Systems

2011 ◽  
Vol 209 (4) ◽  
pp. 637-663 ◽  
Author(s):  
B. Ploeger ◽  
J.W. Wesselink ◽  
T.A.C. Willemse
Keyword(s):  
Reactive Systems ◽  
Boolean Equation

A Formalisation of Consistent Consequence for Boolean Equation Systems

2017 ◽  
pp. 462-478
Author(s):  
Myrthe van Delft ◽  
Herman Geuvers ◽  
Tim A. C. Willemse
Keyword(s):  
Boolean Equation

scholarly journals Systems of k Boolean inequations and a Boolean equation

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1261-1270
Author(s):  
Ulfeta Marovac ◽  
Dragic Bankovic
Keyword(s):  
Computer Science ◽  
Generalized Systems ◽  
Boolean Equation

In this paper elementary generalized systems of Boolean equations are investigated. The formula for solving systems of k Boolean inequations and a Boolean equation is presented. This systems have many applications in computer science for solving logical problems. Presented formulas can accelerate application of elementary generalized systems of Boolean equations.

scholarly journals Boolean differential equations: A common model for classes, lattices, and arbitrary sets of Boolean functions

2015 ◽  
Vol 28 (1) ◽  
pp. 51-76 ◽  
Author(s):  
Bernd Steinbach ◽  
Christian Posthoff
Keyword(s):  
Differential Equations ◽  
Boolean Functions ◽  
Differential Calculus ◽  
Short Introduction ◽  
The Core ◽  
Boolean Equation ◽  
General Difference ◽  
Derivatives Of

The Boolean Differential Calculus (BDC) significantly extends the Boolean Algebra because not only Boolean values 0 and 1, but also changes of Boolean values or Boolean functions can be described. A Boolean Differential Equation (BDe) is a Boolean equation that includes derivative operations of the Boolean Differential Calculus. This paper aims at the classification of BDEs, the characterization of the respective solutions, algorithms to calculate the solution of a BDe, and selected applications. We will show that not only classes and arbitrary sets of Boolean functions but also lattices of Boolean functions can be expressed by Boolean Differential equations. In order to reach this aim, we give a short introduction into the BDC, emphasize the general difference between the solutions of a Boolean equation and a BDE, explain the core algorithms to solve a BDe that is restricted to all vectorial derivatives of f (x) and optionally contains Boolean variables. We explain formulas for transforming other derivative operations to vectorial derivatives in order to solve more general BDEs. New fields of applications for BDEs are simple and generalized lattices of Boolean functions. We describe the construction, simplification and solution. The basic operations of XBOOLE are sufficient to solve BDEs. We demonstrate how a XBooLe-problem program (PRP) of the freely available XBooLe-Monitor quickly solves some BDes.

scholarly journals Product form parametric representation of the solutions to a quadratic boolean equation

1987 ◽  
Vol 21 (4) ◽  
pp. 287-305 ◽  
Author(s):  
Y. Crama ◽  
P. L. Hammer ◽  
B. Jaumard ◽  
B. Simeone
Keyword(s):  
Parametric Representation ◽  
Product Form ◽  
Boolean Equation
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