open access

https://hdl.handle.net/2115/47467

BEM-II: An Arithmetic Boolean Expression Manipulator Using BDDs (Special Section on VLSI Design and CAD Algorithms)

英語

combinatorial problem

1993-10-25

電子情報通信学会

IEICE transactions on fundamentals of electronics, communications and computer sciences

E76(A10)

1721-1729

Recently, there has been a lot of research on solving combinatorial problems using Binary Decision Diagrams (BDDs), which are very efficient representations of Boolean functions. We have already developed a Boolean Expression Manipulator, which calculates and reduces Boolean expressions quickly based on BDD techniques. This greatly aids our works on developing VLSI CAD systems and solving combinatorial problems. Any combinatorial problem can be described in Boolean expressions; however, arithmetic operations, such as addition, subtraction, multiplication, equality and inequality, are also used for describing many practical problems. Arithmetic operations provide simple descriptions of problems in many cases. In this paper, we present an arithmetic Boolean expression manipulator (BEM-II), based on BDD techniques. BEM-II calculates Boolean expressions containing arithmetic operations and then displays the results in various formats. It can solve problems represented by a set of equalities and inequalities, which are dealt with using 0-1 linear programming. We show the efficient data structure based on BDD representation, algorithms for manipulating Boolean expressions with arithmetic operations, and good formats for displaying the results. Finally we present the specification of BEM-II and an example of application to the 8-Queens problem. BEM-II is customizable to various applications. It has good computation performance in terms of the total time for programming and execution. We expect BEM-II to be a helpful tool in research and development on digital systems.

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