Syntactic approximations to computational complexity classes
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hdl:2117/9306
Tipus de documentText en actes de congrés
Data publicació2007
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Abstract
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.
CitacióArratia, 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.
Versió de l'editorhttp://www.lsi.upc.edu/~argimiro/mypapers/Journals/aacoCiE07.pdf
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