Which bases admit non-trivial shrinkage of formulae?

Hana Chockler*, Uri Zwick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that the shrinkage exponent, under random restrictions, of formulae over a finite complete basis B of Boolean functions, is strictly greater than 1 if and only if all the functions in B are unate, i.e., monotone increasing or decreasing in each of their variables. As a consequence, we get non-linear lower bounds on the formula complexity of the parity function over any basis composed only of unate functions.

Original languageEnglish
Pages (from-to)28-40
Number of pages13
JournalComputational Complexity
Issue number1
StatePublished - 2001


  • Boolean functions
  • Formula complexity
  • Lower bounds
  • Random restrictions
  • Shrinkage exponents


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