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arXiv · 2405.07975

Dynamic Programming for Symbolic Boolean Realizability and Synthesis

Yi Lin·Lucas M. Tabajara·Moshe Y. Vardi
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Abstract

Inspired by recent progress in dynamic programming approaches for weighted model counting, we investigate a dynamic-programming approach in the context of boolean realizability and synthesis, which takes a conjunctive-normal-form boolean formula over input and output variables, and aims at synthesizing witness functions for the output variables in terms of the inputs. We show how graded project-join trees, obtained via tree decomposition, can be used to compute a BDD representing the realizability set for the input formulas in a bottom-up order. We then show how the intermediate BDDs generated during realizability checking phase can be applied to synthesizing the witness functions in a top-down manner. An experimental evaluation of a solver -- DPSynth -- based on these ideas demonstrates that our approach for Boolean realizabilty and synthesis has superior time and space performance over a heuristics-based approach using same symbolic representations. We discuss the advantage on scalability of the new approach, and also investigate our findings on the performance of the DP framework.

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Yi Lin, Lucas M. Tabajara, Moshe Y. Vardi. 2024-06-20. Dynamic Programming for Symbolic Boolean Realizability and Synthesis. https://arxiv.org/abs/2405.07975

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