Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An NP search problem is the problem of finding a witness to a given NP predicate, and TFNP is the class of total NP search problems. TFNP contains a number of subclasses containing natural problems; for example, PLS is the class of efficient local search heuristics. These classes are characterized by the combinatorial principle that guarantees the existence of a solution; for example, PLS is the class of such problems whose totality is assured by the principle "every dag with at least one edge has a sink".  show many strong connections beten these search classes and the computational por - in particular the proof complexity - of their underlying principles. These connections, along with lor bounds in the propositional proof systems Nullstellensatz and bounded-depth LK, allow us to prove several new relative separations among PLS, and Papadimitriou's classes PPP, PPA, PPAD, and PPADS.
['Joshua Buresh-Oppenheim', 'Tsuyoshi Morioka']
I am writing a research paper on a idea Relativized NP search problems and propositional proof systems
[{"from": "human", "value": "I am writing a research paper on a idea Relativized NP search problems and propositional proof systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An NP search problem is the problem of finding a witness to a given NP predicate, and TFNP is the class of total NP search problems. TFNP contains a number of subclasses containing natural problems; for example, PLS is the class of efficient local search heuristics. These classes are characterized by the combinatorial principle that guarantees the existence of a solution; for example, PLS is the class of such problems whose totality is assured by the principle \"every dag with at least one edge has a sink\".  show many strong connections beten these search classes and the computational por - in particular the proof complexity - of their underlying principles. These connections, along with lor bounds in the propositional proof systems Nullstellensatz and bounded-depth LK, allow us to prove several new relative separations among PLS, and Papadimitriou's classes PPP, PPA, PPAD, and PPADS."}]