# Tagged Questions

**5**

votes

**0**answers

106 views

### Are there sampNP-intermediate problems?

This questions is approximately cross-posted from theoretical computer science stackexchange
Ladner's theorem establishes that if $\mathsf{P} \ne \mathsf{NP}$ then $\mathsf{NPI} := \mathsf{NP} ...

**12**

votes

**6**answers

1k views

### SAT and Arithmetic Geometry

This is an agglomeration of several questions, linked by a single observation: SAT is equivalent to determining the existence of roots for a system of polynomial equations over $\mathbb{F}_2$ (note ...

**2**

votes

**1**answer

454 views

### #P version of SUBSET SUM

The decision version of the SUBSET SUM problem asks the following: Given a set of integers $S =$ {$a_1, ..., a_n$}, is there a subset $S'$ of $S$ such that the sum of the elements in $S'$ is equal to ...

**1**

vote

**0**answers

167 views

### Constructing hard inputs for the complement of bounded halting

If there is always a hard input for the complement of bounded halting, can that input be constructed?
More precisely, suppose that
for any $M$ accepting
$$
\text{coBHP}=\{\langle ...

**8**

votes

**3**answers

1k views

### Non-existence of algorithm converting NP algorithm to P algorithm?

[Edit: in the light of Nate Eldredge's answer below I rephrase the question]
P=NP is equivalent to the existence of a map of the following form:
Input: a polynomial-time non-deterministic Turing ...

**18**

votes

**3**answers

2k views

### Satisfiability of general Boolean formulas with at most two occurrences per variable

(If you know basics in theoretical computer science, you may skip immediately to the dark box below. I thought I would try to explain my question very carefully, to maximize the number of people that ...

**6**

votes

**2**answers

1k views

### Best-case Running-time to solve an NP-Complete problem

What is the fastest algorithm that exists to solve a particular NP-Complete problem? For example, a naive implementation of travelling salesman is $O(n!)$, but with dynamic programming it can be done ...

**0**

votes

**3**answers

419 views

### How can one characterize NP^SAT?

Can you help me understand the class of problems solvable by a nondetermimistic Turing machine with an oracle for SAT running in polynomial time?