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keywords:
cso
solvers and tools
We consider the task of synthesizing or enumerating graphs modulo isomorphisms subject to additional constraints. SAT Modulo Symmetries (SMS) has recently been proposed for this task when the constraints are specifiable in propositional logic (in NP) and has been extended with domain-specific approaches to some constraints beyond, such as enumerating graphs that are not 3-colorable (which is a coNP-complete condition). In this work, we extend the scope of SMS to constraints specified as general quantified Boolean formulas (QBF). We develop a QBF-based static symmetry-breaking method, extend several existing QBF solvers with dynamic SMS-style symmetry breaking, and develop our own symmetry-breaking 2-QBF solver. Our analysis points out tradeoffs: domain-specific approaches can sometimes outperform generic QBF-based ones, while QBF-based approaches are easier to implement and can provide formal proofs.
