Rewriting (dependency-)quantified 2-CNF with arbitrary free literals into existential 2-HORN

• Authors: Uwe Bubeck;Hans Kleine Büning
• Venue: SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
• Year: 2010

We extend quantified 2-CNF formulas by also allowing literals over free variables which are exempt from the 2-CNF restriction. That means we consider quantified CNF formulas with clauses that contain at most two bound literals and an arbitrary number of free literals. We show that these ${\it Q2-CNF}^{b}$ formulas can be transformed in polynomial time into purely existentially quantified CNF formulas in which the bound literals are in 2-HORN (∃2−HORNb). Our result still holds if we allow Henkin-style quantifiers with explicit dependencies. In general, dependency quantified Boolean formulas (${\it DQBF}$) are assumed to be more succinct at the price of a higher complexity. This paper shows that ${\it DQ2-CNF}^{b}$ has a similar expressive power and complexity as ∃2−HORNb. In the special case that the 2-CNF restriction is also applied to the free variables (${\it DQ2-CNF}^{*}$), the satisfiability can be decided in linear time.