Read-Once Functions Revisited and the Readability Number of a Boolean Function

Martin Charles Golumbic, Aviad Mintz, Udi Rotics

Research output: Contribution to journalArticlepeer-review


In this paper, we present the first polynomial time algorithm for recognizing and factoring read-once functions. The algorithm is based on algorithms for cograph recognition and a new efficient method for checking normality. Its correctness is based on a classical characterization theorem of Gurvich which states that a positive Boolean function is read-once if and only if it is normal and its co-occurrance graph is P4-free. We also investigate the problem of factoring certain non-read-once functions. In particular, we show that if the co-occurrence graph of a positive Boolean function f is a tree, then the function is read-twice. We then extend this further proving that if f is normal and its corresponding graph is a partial k-tree, then f is a read 2k function and a read 2k formula for F for f can be obtained in polynomial time.

Original languageEnglish
Pages (from-to)357-361
Number of pages5
JournalElectronic Notes in Discrete Mathematics
StatePublished - 15 Oct 2005


  • boolean functions
  • cographs
  • k-trees
  • normal functions
  • read-once functions

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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