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IEICE Transactions on Information and Systems 2008 E91-D(4):996-1002; doi:10.1093/ietisy/e91-d.4.996
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Copyright © 2008 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Papers -- Algorithm Theory

Tree-Shellability of Restricted DNFs

Yasuhiko TAKENAGA1 and Nao KATOUGI1,2

1 The authors are with the Department of Computer Science, the University of Electro-Communications, Chofu-shi, 182–8585 Japan. E-mail: takenaga{at}cs.uec.ac.jp, 2 Presently, the author is with NEC Corporation.


  Abstract

A tree-shellable function is a positive Boolean function which can be represented by a binary decision tree whose number of paths from the root to a leaf labeled 1 equals the number of prime implicants. In this paper, we consider the tree-shellability of DNFs with restrictions. We show that, for read-k DNFs, the number of terms in a tree-shellable function is at most k2. We also show that, for k-DNFs, recognition of ordered tree-shellable functions is NP-complete for k=4 and tree-shellable functions can be recognized in polynomial time for constant k.

Key Words: Boolean function, shellability, prime implicant, binary decision tree

Manuscript received May 31, 2007. Manuscript revised October 24, 2007.


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