Document Type : Original Article

**Authors**

Department of Mathematics, University of Payame Noor, Tehran, Iran

**Abstract**

In computer science, a binary decision diagram is a data structure that is used to represent a Boolean function and to consider a compressed representation of relations. This paper considers the notation of T.B.T (total binary truth table), and introduces a novel concept of binary decision (hyper)tree and binary decision (hyper)diagram, directly and in as little time as possible, unlike previous methods. This study proves that every T.B.T corresponds to a binary decision (hyper)tree via minimum Boolean expression and presents some conditions on any given T.B.T for isomorphic binary decision (hyper)trees. Finally, for faster calculations and more complex functions, we offer an algorithm and so Python programming codes such that for any given T.B.T, it introduces a binary decision (hyper)tree.

**Keywords**

**Main Subjects**

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April 2024

Pages 117-130