# Questions tagged [proof-complexity]

propositional proof systems and corresponding bounded arithmetic theories

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127 views

### Is mathematical proof itself NP-hard?

At the 8:00 mark of this video, he claims that proving things is itself an NP problem. I'm looking for more insight into this. Could someone help explain this concept to me and also provide a link to ...
112 views

### Proof systems induced by NP-complete problems

Satisfiability is the fundamental NP-complete problem. Cook-Reckhow theorem states that the existence of a propositional proof system that admits polynomial size proofs for all tautologies implies ...
123 views

### Have the proofs in Buss's “On Goedel’s Theorems on Lengths of Proofs” been formalized (mechanically checked)?

The paper On Gödel's theorems on lengths of proofs I: Number of lines and speedup for arithmetics contains quite interesting results on proof length. But some of the details are still, to me, a bit ...
189 views

### Document references describing weaknesses for cutting planes and algebraic proof system?

Here, Fortnow says (section 4.3): Since then complexity theorists have shown similar weaknesses in a number of other proof systems including cutting planes, algebraic proof systems based on ...
106 views

### Eliminating tautological axioms in tree-like $k$-DNF resolution

The propositional proof system $k$-DNF-resolution, a.k.a. $Res(k)$, is a generalization of propositional resolution, where the lines in a proof are $k$-DNF formulas, i.e., disjunctions of $k$-terms of ...
99 views

### Axioms of Minimum Size Resolution Refutations

Let $\phi$ be an unsatisfiable CNF formula and let $\Pi$ be a resolution refutation of $\phi$ of minimum size. Let $\psi$ be the subformula of $\phi$ containing the clauses that actually appear as ...
247 views

1k views

### Automated theorem proving via unsupervised approaches

This question Where and how did computers help prove a theorem? considers some automated theorem proving successes. However they seem to be mostly supervised approaches, such as with the 4 color graph ...
357 views

### Proof Complexity and Circuit Lower bound for coNP

I have two questions (1)Circuit lower bound for coNP TAUT is a set of formulae such that any formula in TAUT is satisfied for all boolean assignments. UnSAT is the complement problem of SAT. It is ...
243 views

### Resolution vs Extended Resolution

Let $R(f)$ and $ER(f)$ be the minimum-size for unsat proofs of $f$ in Resolution and Extended Resolution respectively. What's the best bound we have on $D=\min_f (R(f)-ER(f))$ where $f$ belongs to a ...
557 views

### Graph problems with good characterization but not known to be in $P$

A decision problem has good characterization if it is in $NP \cap coNP$. Many natural graph problems have good characterizations. For instance, Kuratuwski's Theorem gives good characterization of ...
650 views

### Consequences of sub-exponential proofs/algorithms for SAT

Would there be any major consequences if SAT had at most subexponential unsat proofs or even more strongly, SAT had subexponential-time algorithms?
487 views

### Uses of XORification

XORification is the technique to make a Boolean function or formula harder by replacing every variable $x$ by the XOR of $k\geq 2$ distinct variables $x_1 \oplus \ldots \oplus x_k$. I am aware of ...