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# Questions tagged [proof-complexity]

propositional proof systems and corresponding bounded arithmetic theories

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0answers
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### 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 ...
0answers
106 views

### Transforming a DAG-like resolution proof to a tree like resolution proof

How can a DAG-like resolution proof be transformed to a tree-like resolution proof? Is such a transformation possible in polynomial time?
0answers
125 views

### Proof of Correctness of Bottleneck Dijkstra Algorithm [closed]

I am working on a bottleneck multicast tree for which I am using bottleneck Dijkstra algorithm. My question is 1) bottleneck Dijkstra has the same correctness as that of (simple) Dijkstra or not ? 2)...
0answers
105 views

### Techniques for showing intermediate status between $\mathsf{NP \cap coNP}$ and coNP-completeness

Inspired by Suresh's post, for a new problem in $\mathsf{coNP}$, whose true proof complexity is intermediate between $\mathsf{NP \cap coNP}$ and being coNP-complete, I am interested in methods which ...
0answers
136 views

### Do problems have to be statable in $\Pi_1$ to use Levin's universal search to find short proofs if P=NP

In If P=NP, could we obtain proofs of Goldbach's Conjecture etc.? it talks about the hypothetical world where P=NP and using the proof of it to prove a problem/theorem assuming that it has a short ...
1answer
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 ...
1answer
236 views

### In regards to the tautologies of a polynomially-bounded propositional proof system

In the book 'Logical Foundations of Proof Complexity', co-authored by Stephen Cook, the following definition is given: A proof-system $F$ is said to be polynomially-bounded if there is a polynomial p(...
1answer
58 views

### Understanding the definition of a “restriction of a resolution derivation”

I am reading the paper An Introduction to Lower Bounds on Resolution Proof Systems. In its subsection 2.3 the author gives an inductive definition of the restriction of a resolution refutation $\pi$. ...
1answer
105 views

### On the difference between propositional proof system and polynomially-bounded proof system

For the definition of a propositional proof system we have: An abstract proof system is a polynomial time function f whose range is equal to the set of tautologies. If τ is a tautology, then an f-...
1answer
81 views

### On the (Cook) definition of a propositional proof system [closed]

Def: An abstract proof system is a polynomial time function f whose range is equal to the set of tautologies. If T is a tautology, then an f-proof of T is any value w such that f(w)= T I'm a bit ...
1answer
271 views

### NP-completeness of one generalized subset sum problem (target sum belongs to interval) [closed]

I need to prove that decision problem: for a given set of positive integers $a_1, ..., a_n$, does it exist a subset that sums up to a value within interval \$[\frac{1}{2}\sum a_i; \frac{1}{2}\sum a_i+...
1answer
120 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 ...