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Citació: Arratia, A.; Ortiz, C. Syntactic approximations to computational complexity classes. A: Conference on Computability in Europe. "Computation and Logic in the Real World, Third Conference on Computability in Europe (CiE 2007)". Siena: 2007, p. 1-15.
Títol: Syntactic approximations to computational complexity classes
Autor: Arratia Quesada, Argimiro Alejandro Veure Producció científica UPC; Ortiz Gómez, Carlos
Data: 2007
Tipus de document: Conference report
Resum: We present a formal syntax of approximate formulas suited for the logic with counting quantifiers SOLP. This logic was studied by us in [1] where, among other properties, we showed: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and fragments of it capture classes like P and NL; (ii) weakening the ordering relation to an almost order we can separate meaningful fragments, using a combinatorial tool adapted to these languages. The purpose of the approximate formulas presented here, is to provide a syntactic approximation to logics contained in SOLP with built-in order, that should be complementary of the semantic approximation based on almost orders, by producing approximating logics where problems are described within a small counting error. We state and prove a Bridge Theorem that links expressibility in fragments of SOLP over almostordered structures to expressibility with respect to approximate formulas for the corresponding fragments over ordered structures. A consequence of these results is that proving inexpressibility results over fragments of SOLP with built-in order could be done by proving inexpressibility over the corresponding fragments with built-in almost order, where separation proofs are allegedly easier.
URI: http://hdl.handle.net/2117/9306
Versió de l'editor: http://www.lsi.upc.edu/~argimiro/mypapers/Journals/aacoCiE07.pdf
Apareix a les col·leccions:LARCA - Laboratori d´Algorísmia Relacional, Complexitat i Aprenentatge. Ponències/Comunicacions de congressos
Departament de Llenguatges i Sistemes Informàtics. Ponències/Comunicacions de congressos
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