Efficient solution of systems of Boolean equations

Woods, S.; Casinovi, G.

doi:10.1109/iccad.1996.569908

Cited by 4 publications

(4 citation statements)

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“…However, such an application must handle the incompatibility between the lattice structure of 'big' Boolean algebras, which are only partially ordered, and multi-valued logics, which are totally ordered [34]. Some of the ideas expressed herein can also be incorporated in the automated solution of large systems of Boolean equations [33], Boolean equations with many unknowns [14] and Boolean relations [3]. They can also be extended to handle quadratic Boolean equations [17], Boolean ring equations [15,16,18] and Boolean differential equations [28].…”

Section: Discussionmentioning

confidence: 97%

Using variable-entered Karnaugh maps to produce compact parametric general solutions of Boolean equations

Rushdi

Amashah

2011

International Journal of Computer Mathematics

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The variable-entered Karnaugh map (VEKM) is shown to be the natural map for representing and manipulating general 'big' Boolean functions that are not restricted to the switching or two-valued case. The VEKM is utilized herein in producing a compact general solution of a system of Boolean equations. It serves as a powerful manual tool for function inversion, implementation of the solution procedure, handling don't-care conditions and minimization of the final expressions. The rules of using the VEKM are semi-algebraic and collective in nature, and hence are much easier to state, remember and implement than are the tabular and per-cell rules of classical maps. As a result, the maps used are significantly smaller than those required by classical methods. As an offshoot, the paper contributes some pictorial insight into the representation of 'big' Boolean algebras and functions. It also predicts the correct number of particular solutions of a Boolean equation, and produces an exhaustive list of particular solutions. Details of the method are carefully explained and further demonstrated via an illustrative example.

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Section: Discussionmentioning

confidence: 97%

Using variable-entered Karnaugh maps to produce compact parametric general solutions of Boolean equations

Rushdi

Amashah

2011

International Journal of Computer Mathematics

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“…For higher order functions, convergence rates become a serious issue. However, the shannon's decomposition, laid out in [13] and the equation below, could be effectively used to exploit some parallelism.…”

Section: Future Workmentioning

confidence: 99%

A genetic approach to gateless custom VLSI design flow

Shoaib

Kamakoti

2007

2007 Internatonal Conference on Microelectronics

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In this work, we propose a novel technique for evolving transistor netlists from truth table descriptions of arbitrary digital circuits. The proposed methods incorporate the effective use of Genetic Algorithms (GAs). In typical semi-custom and custom design flows, logic optimization is done at the gate level after Boolean translation of the input truth table. The final transistor netlist is then deduced from the simplified gate logic to be laid out on a chip. However transistor level optimizations after the boolean simplification step would still not lead to the minimum number of transistors. This final optimization level is non-existent in present custom design flows. This work aims to address this need. A salient feature of the proposed technique is the bypassing of gate level representation and optimization in the VLSI design flow. We provide genetic methods to directly optimize truth table inputs using transistor level simplification. This eliminates the intermediate gate level optimization step and provides optimized transistor netlists which could be used for dynamic library cell generation for custom and semi-custom designs on the fly.

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“…This method utilizes ''don't care" and ''can't happen" conditions to aid in obtaining the solution. Another efficient algorithm for variable elimination is through function decomposition of Boolean functions represented by the so-called binary decision diagrams (BDD's) [17]. In [10], a pure algebraic method is presented.…”

Section: Introductionmentioning

confidence: 99%