We consider the following classes of quantified boolean formulas. Fix
a finite set of basic boolean functions. Take conjunctions
of these basic functions applied to variables and constants in
arbitrary way. Finally quantify existentially or universally some of
the variables. We prove the following dichotomy theorem: For
any set of basic boolean functions, the resulting set of formulas is
either polynomially learnable from equivalence queries alone or else it is
not PAC-predictable even with membership queries under
cryptographic assumptions. Furthermore we
identify precisely which sets of basic functions are in which
of the two cases.
CitationDalmau, V. "A Dichotomy theorem for learning quantified Boolean formulas". 1997.
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