Tree-Shellability of Restricted DNFs

Authors:
Yasuhiko Takenaga;Nao Katougi
Affiliations:
-;-
Venue:
IEICE - Transactions on Information and Systems
Year:
2008

Citing 6
Cited 0

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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.