The hardness of the Expected Decision Depth problem

Dana Ron*, Amir Rosenfeld, Salil Vadhan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a function f over n binary variables, and an ordering of the n variables, we consider the Expected Decision Depth problem. Namely, what is the expected number of bits that need to be observed until the value of the function is determined, when bits of the input are observed according to the given order. Our main finding is that this problem is (essentially) #P-complete. Moreover, the hardness holds even when the function f is represented as a decision tree.

Original languageEnglish
Pages (from-to)112-118
Number of pages7
JournalInformation Processing Letters
Issue number3
StatePublished - 14 Feb 2007


  • Computational complexity
  • Decision trees


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