Reducing NEXP-complete problems to DQBF

TL;DR

This paper provides a simple proof that satisfiability of Dependency Quantified Boolean Formulas (DQBF) is NEXP-hard and introduces a general method to reduce various NEXP-complete problems to DQBF, highlighting its broad applicability.

Contribution

It offers a new, straightforward proof of NEXP-hardness for DQBF satisfiability and a general reduction technique for NEXP-complete problems to DQBF.

Findings

Explicit reductions from NEXP-complete problems to DQBF

Demonstrates DQBF's applicability to various NEXP-complete problems

Highlights the potential of DQBF solvers in research

Abstract

We present an alternative proof of the NEXP-hardness of the satisfiability of {\em Dependency Quantified Boolean Formulas} (DQBF). Besides being simple, our proof also gives us a general method to reduce NEXP-complete problems to DQBF. We demonstrate its utility by presenting explicit reductions from a wide variety of NEXP-complete problems to DQBF such as (succinctly represented) 3-colorability, Hamiltonian cycle, set packing and subset-sum as well as NEXP-complete logics such as the Bernays-Sch\"onfinkel-Ramsey class, the two-variable logic and the monadic class. Our results show the vast applications of DQBF solvers which recently have gathered a lot of attention among researchers.