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Towards NP−P via Proof Complexity and Search
, 2009
"... This is a survey of work on proof complexity and proof search, as motivated by the P versus NP problem. We discuss propositional proof complexity, Cook’s program, proof automatizability, proof search, algorithms for satisfiability, and the state of the art of our (in)ability to separate P and NP. ..."
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This is a survey of work on proof complexity and proof search, as motivated by the P versus NP problem. We discuss propositional proof complexity, Cook’s program, proof automatizability, proof search, algorithms for satisfiability, and the state of the art of our (in)ability to separate P and NP.
Term Graphs and the NPcompleteness of the ProductFree Lambek Calculus
"... Abstract. We provide a graphical representation of proofs in the productfree Lambek calculus, called term graphs, that is related to several other proof net presentations. The advantage of term graphs is that they are very simple compared to the others. We use this advantage to provide an NPcomple ..."
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Abstract. We provide a graphical representation of proofs in the productfree Lambek calculus, called term graphs, that is related to several other proof net presentations. The advantage of term graphs is that they are very simple compared to the others. We use this advantage to provide an NPcompleteness proof of the productfree Lambek Calculus that uses the reduction of [8]. Our proof is more intuitive due to the fact that term graphs allow arguments that are graphical in nature rather than using the algebraic arguments of [8]. 1