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Questions tagged [promise-problems]

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Complexity of enumerating over promise problems and circuits?

Given an enumeration over all Turing Machine which run with increasing length, is there a ``complexity class'' which describes the complexity of determining whether a given TM satisfies the promise ...
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How hard is gapped satisfiability?

It is well known that general satisfiability (of polynomially many clauses) is NP-hard, and in fact, it is conjectured that an algorithm deciding instances of SAT takes time nearly $2^n$ on $n$ ...
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PromiseBQP and expectation values of operators

This question is regarding The Equivalence of Searching and Sampling by Aaronson. In page 4 he makes the following statement, ... a difficult and unsolved meta-question is whether PromiseBPP = ...
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Sparse-cut approximation for well connected graphs

Theorem: For any graph $G=(V,E)$, there is a polynomial time algorithm that finds a cut $S \subseteq V$ with conductance at most $\sqrt{2\big(1 − \lambda(G)\big)}$. If I understand UGC correctly, ...
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UnambiguousSAT reductions

Let $\Pi$ be an $\mathsf{NP}$-complete problem. It is standard that $3SAT$ and $\Pi$ are reducible from each other. Let UnambiguousSAT, or USAT for short, denote the promise problem which is 3SAT but ...
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NP-Complete problems that admit an efficient algorithm under the promise of a unique solution

I was recently reading a very nice paper by Valiant and Vazirani which shows that if $\mathbf{NP \neq RP}$, then there can not be an efficient algorithm to solve SAT even under the promise that it is ...
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complexity of a constraint satisfaction promise problem

(This is the "upper end" of my question from over 10 months ago on cs.stackexchange. That question and the "lower end" I asked here over 8 months ago, which I also have a bounty on, are both ...
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Density of multiples

I have an infinite collection of positive integers $n_1,n_2,n_3,\ldots$ and I would like to find the density of the numbers divisible by one or more of these.* If the density does not exist, the ...