Generating Models of a Matched Formula With a Polynomial Delay

Authors: Petr Savický, Petr Kučera

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Reproducibility Variable Result LLM Response
Research Type Theoretical We prove that the problem of counting the number of the models (satisfying assignments) of a matched formula is #P-complete. On the other hand, we define a class of formulas generalizing the matched formulas and prove that for a formula in this class one can choose in polynomial time a variable suitable for splitting the tree for the search of the models of the formula. As a consequence, the models of a formula from this class, in particular of any matched formula, can be generated sequentially with a delay polynomial in the size of the input. The main result of the paper is an algorithm which generates models of a matched formula with a polynomial delay.
Researcher Affiliation Academia Petr Savick y EMAIL Institute of Computer Science, The Czech Academy of Sciences Pod Vod arenskou Vˇeˇz ı 2, 182 07 Praha 8, Czech Republic. Petr Kuˇcera EMAIL Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and Physics, Charles University in Prague, Malostransk e n am. 25, 118 00 Praha 1, Czech Republic.
Pseudocode Yes Algorithm 1 Constructing pure literal sequence Require: A CNF formula ϕ. Ensure: A maximal strict pure literal sequence L for ϕ and the corresponding reduced formula.
Open Source Code No The paper does not provide any specific links or statements regarding the availability of open-source code for the methodology described. It discusses algorithms and theoretical complexity.
Open Datasets No This paper is theoretical and focuses on algorithms and proofs for boolean formulas. It does not conduct experiments using specific datasets, thus no information on publicly available datasets is provided.
Dataset Splits No The paper is theoretical and does not perform experiments on datasets. Therefore, it does not specify any training/test/validation dataset splits.
Hardware Specification No The complexity bounds are derived for the RAM model with the unit cost measure and the word size O(log ϕ ), where ϕ is the input formula. No specific hardware used for experiments is mentioned as the paper is theoretical.
Software Dependencies No The paper is theoretical and does not describe an implementation of its algorithms or present experimental results. Therefore, no specific software dependencies with version numbers are provided.
Experiment Setup No The paper describes theoretical algorithms and proofs, without presenting any experimental results. Consequently, there is no experimental setup, hyperparameters, or training configurations described.