# Questions tagged [proof-complexity]

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### Explicit tautologies requiring lots/few uses of modus ponens in minimal proofs

I am interested in minimal length proofs of tautologies in propositional logic. For concreteness, let's fix a particular Frege system $F$ (i.e., sound and complete set of axioms and deduction rules ...
493 views

### Zero-knowledge proof for $P \ne NP$?

In computational complexity, $P \ne NP$ is a widely believed conjecture. Suppose that someone discovered a proof for it. He wants to publish a proof that he correctly proved the conjecture. I am aware ...
113 views

### Lengths of proofs and quasilinear time

Length of proofs depends not only on the theory but also on its axiomatization. Once an axiomatization is fixed, typical proof systems are equivalent up to a polynomial factor. But what if we care ...
619 views

### Is there good reference for proof complexity?

I am asking if there are some good or standard references for proof complexity theory? I didn't find references when I search in internet. Thanks!
2k views

### Connections between Complexity Theory & Set Theory

Inspired by Joshua Grochow and Iddo Tzameret's answers in a post on http://cstheory.stackexchange.com , I would like to get more references on possible connections between complexity theory and set ...
554 views

256 views

### Is there a program for theory of incompleteness in NP?

Motivated by Suresh's post, Techniques for showing that problem is in hardness limbo, it seems that there might be an underlying theory that explains why some of these problems can not be complete for ...
127 views

### Results where complexity bounds implies finite number of test cases

We have all been there, when a formula works for the first 30 parameters, but it is not sufficient for a proof. My question is where one can actually just check a finite number of cases, to conclude ...
1k views

### Finite versions of Godel' s incompleteness

Assume you have some notion of proof complexity: for instance, at the basic level, the length of a proof, or the number of symbols used, take your pick (there are more involved measures, but for sake ...
559 views

### Measure of progress towards a proof

Can one define some measure of progress towards a proof of a statement? I'm not sure if it's even possible for general first order logic statements so let's restrict ourselves to propositional ...
683 views

### Proof system with same complexity as "informal mathematics"?

The Completeness Theorem in first-order logic states that any mathematical validity is derivable from axioms. Hence, any informal mathematical proof (which is rigorous) can be translated into a formal ...
579 views

### Proof systems and their hierarchy

Why ZFC is placed in top of the proof system hierarchy? How it can p-simulate other systems?