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Che Cheng

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4 papers

2 author rows

AAAI Conference 2026 Conference Paper

Model Counting for Dependency Quantified Boolean Formulas

Long-Hin Fung
Che Cheng
Jie-Hong Roland Jiang
Friedrich Slivovsky
Tony Tan

Dependency Quantified Boolean Formulas (DQBF) generalize QBF by explicitly specifying which universal variables each existential variable depends on, instead of relying on a linear quantifier order. The satisfiability problem of DQBF is NEXP-complete, and many hard problems can be succinctly encoded as DQBF. Recent work has revealed a strong analogy between DQBF and SAT: k-DQBF (with k existential variables) is a succinct form of k-SAT, and satisfiability is NEXP-complete for 3-DQBF but PSPACE-complete for 2-DQBF, mirroring the complexity gap between 3-SAT (NP-complete) and 2-SAT (NL-complete). Motivated by this analogy, we study the model counting problem for DQBF, denoted #DQBF. Our main theoretical result is that #2-DQBF is #EXP-complete, where #EXP is the exponential-time analogue of #P. This parallels Valiant's classical theorem stating that #2-SAT is #P-complete. As a direct application, we show that first-order model counting (FOMC) remains #EXP-complete even when restricted to a PSPACE-decidable fragment of first-order logic and domain size two. Building on recent successes in reducing 2-DQBF satisfiability to symbolic model checking, we develop a dedicated 2-DQBF model counter. Using a diverse set of crafted instances, we experimentally evaluated it against a baseline that expands 2-DQBF formulas into propositional formulas and applies propositional model counting. While the baseline worked well when each existential variable depends on few variables, our implementation scaled significantly better to larger dependency sets.

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SAT Conference 2025 Conference Paper

Fine-Grained Complexity Analysis of Dependency Quantified Boolean Formulas

Che Cheng
Long-Hin Fung
Jie-Hong Roland Jiang
Friedrich Slivovsky
Tony Tan

Dependency Quantified Boolean Formulas (DQBF) extend Quantified Boolean Formulas by allowing each existential variable to depend on an explicitly specified subset of the universal variables. The satisfiability problem for DQBF is NEXP-complete in general, with only a few tractable fragments known to date. We investigate the complexity of DQBF with k existential variables (k-DQBF) under structural restrictions on the matrix - specifically, when it is in Conjunctive Normal Form (CNF) or Disjunctive Normal Form (DNF) - as well as under constraints on the dependency sets. For DNF matrices, we obtain a clear classification: 2-DQBF is PSPACE-complete, while 3-DQBF is NEXP-hard, even with disjoint dependencies. For CNF matrices, the picture is more nuanced: we show that the complexity of k-DQBF ranges from NL-complete for 2-DQBF with disjoint dependencies to NEXP-complete for 6-DQBF with arbitrary dependencies.

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IJCAI Conference 2024 Conference Paper

Knowledge Compilation for Incremental and Checkable Stochastic Boolean Satisfiability

Che Cheng
Yun-Rong Luo
Jie-Hong R. Jiang

Knowledge compilation has proven effective in (weighted) model counting, uniquely supporting incrementality and checkability. For incrementality, compiling an input formula once suffices to answer multiple queries, thus reducing the total solving effort. For checkability, the compiled formula is amenable to producing machine-checkable proofs for verification, thus strengthening the solver’s reliability. In this work, we extend knowledge compilation from model counting to stochastic Boolean satisfiability (SSAT) solving by generalizing the dec-DNNF representation to accommodate the SSAT quantifier structure and integrate it into SharpSSAT, a state-of-the-art SSAT solver. We further study proof generation from the compiled representation and extend CPOG, a certified model-counting toolchain, to generate proofs for certifying the results of SharpSSAT. Experimental results show the benefits of the proposed knowledge compilation approach for SSAT in sharing computation efforts for multiple queries and producing checkable dec-DNNF logs with negligible overhead.

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AAAI Conference 2023 Conference Paper

Lifting (D)QBF Preprocessing and Solving Techniques to (D)SSAT

Che Cheng
Jie-Hong R. Jiang

Dependency stochastic Boolean satisfiability (DSSAT) generalizes stochastic Boolean satisfiability (SSAT) in existential variables being Henkinized allowing their dependencies on randomized variables to be explicitly specified. It allows NEXPTIME problems of reasoning under uncertainty and partial information to be compactly encoded. To date, no decision procedure has been implemented for solving DSSAT formulas. This work provides the first such tool by converting DSSAT into SSAT with dependency elimination, similar to converting dependency quantified Boolean formula (DQBF) to quantified Boolean formula (QBF). Moreover, we extend (D)QBF preprocessing techniques and implement the first standalone (D)SSAT preprocessor. Experimental results show that solving DSSAT via dependency elimination is highly applicable and that existing SSAT solvers may benefit from preprocessing.

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