Complete Problems for Dynamic Complexity Classes

We present the first complete problems for dynamic complexity classes including the classes Dyn-FO and Dyn-ThC ¢ , the dynamic classes corresponding to relational calculus and (polynomially bounded) SQL, respectively. The first problem we show complete for Dyn-FO is a singlestep version of the circuit value problem (SSCV). Of independent interest, our construction also produces a first-order formula, £ , that is in a sense universal for all first-order formulas. Since first-order formulas are stratified by quantifier depth, the first-order formula £ 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.

• Type: Conference
• Year: 2002
• Where: LICS
• Authors: William Hesse, Neil Immerman
• Keywords: Automated Reasoning, Dynamic Complexity Classes, LICS 2002, first Complete Problems, first-order Formula