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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\...
Sebastian Ben Daniel's user avatar
16 votes
0 answers
541 views

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 ...
Daniel Apon's user avatar
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13 votes
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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 $\...
András Salamon's user avatar
12 votes
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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} \...
sdcvvc's user avatar
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10 votes
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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?
eof's user avatar
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10 votes
0 answers
174 views

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|^{...
Dominik Peters's user avatar
10 votes
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363 views

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 ...
Arthur MILCHIOR's user avatar
9 votes
0 answers
536 views

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 ...
Mohammad Al-Turkistany's user avatar
9 votes
0 answers
564 views

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 ...
v s's user avatar
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7 votes
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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 ...
Anonymous's user avatar
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3 votes
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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\}^...
Izaak Meckler's user avatar
2 votes
0 answers
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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 ...
Chill2Macht's user avatar
2 votes
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111 views

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 $\...
echuly's user avatar
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