The proof-complexity tag has no usage guidance.

**1**

vote

**0**answers

98 views

### Oracle queries asked in parallel

Definition: Assume that $\phi(q)$ is of the form $\exists y \leq 2^{p(n)} \varphi(q,y)$, where $p$ is a polynomial and $n = |q|$ (i.e. $n$ is the length of the binary representation of $q$). Then a ...

**4**

votes

**0**answers

198 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 ...

**3**

votes

**1**answer

108 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 ...

**16**

votes

**3**answers

822 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 ...

**3**

votes

**2**answers

521 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 ...

**3**

votes

**1**answer

586 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 ...

**3**

votes

**1**answer

480 views

### Proof systems and their hierarchy

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

**2**

votes

**0**answers

200 views

### Oracle separating FIP for bounded-depth Frege from FIP for Frege (and hardness conditions on DDH)

Is there an oracle such that in the relativized world, bd-Frege (bounded depth Frege propositional proof system) has FIP (feasible interpolation property) but Frege does not have FIP?
Such an ...

**55**

votes

**29**answers

6k views

### Can infinity shorten proofs a lot?

I've just been asked for a good example of a situation in maths where using infinity can greatly shorten an argument. The person who wants the example wants it as part of a presentation to the general ...