Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the propositional satisfiability problem (SAT) on classes of CNF formulas (formulas in Conjunctive Normal Form) that obey certain structural restrictions in terms of their hypergraph structure, by associating to a CNF formula the hypergraph obtained by ignoring negations and considering clauses as hyperedges on variables.  show that satisfiability of CNF formulas with so-called ``beta-acyclic hypergraphs'' can be decided in polynomial time.#R##N##R##N# also study the parameterized complexity of SAT for ``almost''  beta-acyclic instances, using as parameter the formula's distance   from being beta-acyclic. As distance  use the size of smallest strong backdoor sets and the beta-hypertree width. As a by-product  obtain the W[1]-hardness of SAT parameterized by the (undirected) clique-width of the incidence graph, which disproves a conjecture by Fischer, Makowsky, and Ravve (Discr. Appl. Math. 156, 2008).
['Sebastian Ordyniak', 'Daniël Paulusma', 'Stefan Szeider']
I am writing a research paper on a idea Satisfiability of Acyclic and Almost Acyclic CNF Formulas
[{"from": "human", "value": "I am writing a research paper on a idea Satisfiability of Acyclic and Almost Acyclic CNF Formulas"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the propositional satisfiability problem (SAT) on classes of CNF formulas (formulas in Conjunctive Normal Form) that obey certain structural restrictions in terms of their hypergraph structure, by associating to a CNF formula the hypergraph obtained by ignoring negations and considering clauses as hyperedges on variables.  show that satisfiability of CNF formulas with so-called ``beta-acyclic hypergraphs'' can be decided in polynomial time.#R##N##R##N# also study the parameterized complexity of SAT for ``almost''  beta-acyclic instances, using as parameter the formula's distance   from being beta-acyclic. As distance  use the size of smallest strong backdoor sets and the beta-hypertree width. As a by-product  obtain the W[1]-hardness of SAT parameterized by the (undirected) clique-width of the incidence graph, which disproves a conjecture by Fischer, Makowsky, and Ravve (Discr. Appl. Math. 156, 2008)."}]