A Dichotomy theorem for learning quantified Boolean formulas

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 d...

ver descrição completa

Detalhes bibliográficos
Autor: Dalmau Lloret, Víctor
Formato: informe técnico
Fecha de publicación:1997
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/83484
Acesso em linha:https://hdl.handle.net/2117/83484
Access Level:acceso abierto
Palavra-chave:Dichotomy theorem
Boolean formulas
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
Descrição
Resumo: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.