Complete problems for dynamic complexity classes

W. Hesse1, N. Immerman1
1Computer Science Department, UMass, Amherst, USA

Tóm tắt

We present the first complete problems for dynamic complexity classes including the classes Dyn-FO and Dyn-ThC/sup 0/, the dynamic classes corresponding to relational calculus and (polynomially bounded) SQL, respectively. The first problem we show complete for Dyn-FO is a single-step version of the circuit value problem (SSCV). Of independent interest, our construction also produces a first-order formula, /spl zeta/, that is in a sense universal for all first-order formulas. Since first-order formulas are stratified by quantifier depth, the first-order formula /spl zeta/ emulates formulas of greater depth by iterated application. As a corollary we obtain a fixed quantifier block, QBC, that is complete for all first-order quantifier blocks.

Từ khóa

#Polynomials #Computer science #Complexity theory #Databases #Heuristic algorithms #Data structures #Logic #Calculus #Circuits #Application software

Tài liệu tham khảo

hesse, 2001, The dynamic complexity of transitive closure is in TC0, Intl Conf on Database Theory, 234 10.1006/inco.1995.1102 barrington, 1990, On uniformity within NC1, JCSS, 41, 274 10.1016/0304-3975(94)90159-7 libkin, 1999, On the Power of Incremental Evaluation in SQL-Like Languages jagadish, 1998, View maintenance issues for the chronicle data model, Materialized Views Techniques Implementations and Applications, 241 10.1007/978-1-4612-0539-5 10.1145/800061.808733 10.1006/jcss.1997.1520