Generalized satisfiability problems via operator assignments
Schaefer introduced a framework for generalized satisfiability problems on the Boolean domain and characterized the computational complexity of such problems. We investigate an algebraization of Schaefer's framework in which the Fourier transform is used to represent constraints by multilinear...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2019 |
| 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:2117/134848 |
| Acesso em linha: | https://hdl.handle.net/2117/134848 https://dx.doi.org/10.1016/j.jcss.2019.05.003 |
| Access Level: | acceso abierto |
| Palavra-chave: | Logic, Symbolic and mathematical Computational complexity Constraint satisfaction problem Quantum satisfiability Non-local games Dichotomy theorems Linear operators Undecidable problems pp-definitions Lògica matemàtica Complexitat computacional Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Resumo: | Schaefer introduced a framework for generalized satisfiability problems on the Boolean domain and characterized the computational complexity of such problems. We investigate an algebraization of Schaefer's framework in which the Fourier transform is used to represent constraints by multilinear polynomials in a unique way. This representation of constraints gives rise to a relaxation of the notion of satisfiability in which the values to variables are linear operators on some Hilbert space. For constraints given by a system of linear equations over the two-element field, earlier work in the foundations of quantum mechanics has shown that there are systems that have no solutions in the Boolean domain, but have solutions via operator assignments on some finite-dimensional Hilbert space. Our main result is a complete characterization of the classes of Boolean relations for which there is a gap between satisfiability in the Boolean domain and the relaxation of satisfiability via operator assignments. |
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