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...
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| 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 |
| 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. |
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