A Dichotomy Theorem for Learning Quantified Boolean Formulas

Authors:
Víictor Dalmau
Affiliations:
Departament LSI, Universitat Politècnica de Catalunya, Campus Nord, Mòdul C5, Jordi Girona Salgado, 1-3, Barcelona 08034, Spain. dalmau@lsi.upc.es
Venue:
Machine Learning - Special issue: computational learning theory, COLT '97
Year:
1999

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Abstract

We consider the following classes of quantified boolean formulas. Fixa finite set of basic boolean functions. Take conjunctionsof these basic functions applied to variables and constants inarbitrary ways. Finally quantify existentially or universally some ofthe variables. We prove the following dichotomy theorem: Forany set of basic boolean functions, the resulting set of formulas iseither polynomially learnable from equivalence queries alone or else it isnot PAC-predictable even with membership queries undercryptographic assumptions. Furthermore, weidentify precisely which sets of basic functions are in whichof the two cases.