Reducing NEXP-complete problems to DQBF

08/11/2022

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by   Fa-Hsun Chen, et al.

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We present an alternative proof of the NEXP-hardness of the satisfiability of 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-Schönfinkel-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.