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In computational complexity, NP is the complexity class consisting of problems whose yes instances can be verified in polynomial time. NP stands for 'nondeterministic polynomial time '.

5 votes
1 answer
2k views

BPP being equal to #P under Oracle

Luca Trevisan here gives a randomized polynomial-time approximation algorithm for #3-coloring given an NP oracle. In a similar vein, I was wondering if there were any results on $BPP^{NP}\stackrel{?} … If there are no such results, then is $BPP^{NP}$ generally believed to be equal to #P? …
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2 votes

Minimal Backtracking Proof Tree

I found a reference which proves that minimum propositional proof length is NP-hard to linearly approximate for a variety of systems from resolution proofs to Frege proofs. … Minimal Propositional Proof Length is NP-hard to Linearly Approximate …
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  • 601
5 votes
1 answer
539 views

Minimal Backtracking Proof Tree

When trying to prove that a particular instance of a problem like graph coloring or SAT is unsatisfiable, generally one explores the search tree using an algorithm like DPLL and the proof of unsatisfi …
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