Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider boolean formulas in conjunctive normal form (CNF). If all clauses are large, it needs many clauses to obtain an unsatisfiable formula; moreover, these clauses have to interleave.  review quantitative results for the amount of interleaving required, many of which rely on the Lovasz Local Lemma, a probabilistic lemma with many applications in combinatorics.#R##N##R##N#In positive terms,  are interested in simple combinatorial conditions which guarantee for a CNF formula to be satisfiable. The criteria obtained are nontrivial in the sense that even though they are easy to check, it is by far not obvious how to compute a satisfying assignment efficiently in case the conditions are fulfilled; until recently, it was not known how to do so. It is also remarkable that while deciding satisfiability is trivial for formulas that satisfy the conditions, a slightest relaxation of the conditions leads us into the territory of NP-completeness.#R##N##R##N#Several open problems remain, some of which  mention in the concluding section.
['Heidi Gebauer', 'Robin A. Moser', 'Dominik Scheder', 'Emo Welzl']
I am writing a research paper on a idea The Lovász Local Lemma and Satisfiability
[{"from": "human", "value": "I am writing a research paper on a idea The Lov\u00e1sz Local Lemma and Satisfiability"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider boolean formulas in conjunctive normal form (CNF). If all clauses are large, it needs many clauses to obtain an unsatisfiable formula; moreover, these clauses have to interleave.  review quantitative results for the amount of interleaving required, many of which rely on the Lovasz Local Lemma, a probabilistic lemma with many applications in combinatorics.#R##N##R##N#In positive terms,  are interested in simple combinatorial conditions which guarantee for a CNF formula to be satisfiable. The criteria obtained are nontrivial in the sense that even though they are easy to check, it is by far not obvious how to compute a satisfying assignment efficiently in case the conditions are fulfilled; until recently, it was not known how to do so. It is also remarkable that while deciding satisfiability is trivial for formulas that satisfy the conditions, a slightest relaxation of the conditions leads us into the territory of NP-completeness.#R##N##R##N#Several open problems remain, some of which  mention in the concluding section."}]