Questions tagged [conditional-results]
Add X as a hypothesis, where X is not known to be either true or false.
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Does $EXP\neq ZPP$ imply sub-exponential simulation of BPP or NP?
By simulation I mean in the Impaglazzio-Widgerson [IW98] sense, i.e. sub-exponential deterministic simulation which appears correct i.o to every efficient adversary.
I think this is a proof: if $EXP\...
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Quantum Hardness of Finding Nash Equilibria
This question is inspired by the recent, beautiful work On the Cryptographic Hardness of Finding a Nash Equilibrium by Bitansky, Paneth, and Rosen.
Their main result is that the existence of ...
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Consequences of bipartite perfect matching not in NL?
Are any significant consequences known of $\text{BPM} \not\in \textsf{NL}$?
I'm interested in the status of the following well-studied decision problem, in particular whether it is known to be in $\...
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Is it known that $NEXP = \Sigma_2 \implies NEXP = MA$?
Is it known whether the implication $\mathsf{NEXP} = \Sigma_2 \implies \mathsf{NEXP} = \mathsf{MA}$ holds?
(The question is inspired by well-known $\mathsf{NEXP} \subseteq \mathsf{P/poly} \...
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Does a polynomial-time algorithm for factoring product of two primes imply a polynomial-time algorithm for factoring in general?
Is it known if the existence of a polynomial-time algorithm for the promise problem of factoring of numbers with two prime factors implies that factoring in general has a polynomial-time algorithm?
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Hardness in P: methods to show optimality of $O(m^2n)$-like time?
In recent years, there has been exciting work in proving lower bounds for polynomial-time problems conditional on conjectures like SETH or "All-Pairs-Shortest-Paths (APSP) cannot be solved in $O(|V|^{...
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Collapsing of exptime and alternation bounded turing machine
This question was already asked on math overflow, but I did not find any answer to my question (or let say the answer was that up to the knowledge of those people, no answer were known)
Let C be a ...
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Why do we believe $\mathsf{fewP \ne NP}$?
$\mathsf{fewP}$ ($\mathsf{NP}$ with few witnesses, see the zoo) is one of the important ambiguity-bounded sub-classes of $\mathsf{NP}$. There are interesting natural problems in this class that are ...
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VNP = VP versus complexity classes in Arithmetic Geometry
What is the implication of $VNP = VP$ to cryptography schemes such as Elliptic curve/Abelian Variety/Arithmetic Geometry based cryptography? Are there any papers or books that talk about sophisticated ...
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Does L=P imply any new complexity class separations?
If L=P then P is not equal to PSPACE. This follows from PSPACE properly containing L.
I am wondering if L=P implies any stronger separation between complexity classes? Does it imply P is properly ...
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Pseudodeterministically choosing elements from efficiently samplable distributions (or, the plausibility of a weak choice principle)
Suppose we have a poly-time samplable family of distribution. I.e., a family of distributions $D_n \subseteq \{0, 1\}^{\mathsf{poly}(n)}$ and an algorithm $S$ for which $D_n = (r \leftarrow^\$ \{0,1\}^...
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Is there a complete and finite axiom scheme for conditional independence? (Graphoids)
Note: This is a better-written version of an unanswered question asked before on MathOverflow.
Question: Is there a complete and finite axiom scheme for conditional probability?
If so, is there a ...
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Conditional Results on Bounded Depth Circuit Hierarchy
$\mathsf{AC,ACC,TC}$-hierarchy are basic bounded depth circuit hierarchies.
$AC$-hierarchy is $\bigcup _{i =0}^{\infty} AC^{i} $ , where $AC^{i}$ is the $i$-th level of the hierarchy: a family of $\...
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