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Syntactic approximations to computational complexity classes

Summary: Syntactic approximations to computational
complexity classes
Argimiro Arratia1
and Carlos E. Ortiz2
Dpto. de Matem´atica Aplicada, Facultad de Ciencias, Universidad de Valladolid,
Valladolid 47005, Spain, arratia@mac.cie.uva.es,
Department of Mathematics and Computer Science, Arcadia University, 450 S.
Easton Road, Glenside, PA 19038-3295, U.S.A. ortiz@arcadia.edu
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 built­in (linear) order, SOLP can describe NP­complete 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


Source: Arratia, Argimiro A. - Departamento de Matemática Aplicada, Universidad de Valladolid


Collections: Mathematics