Wataridori is a pencil puzzle that involves drawing paths in a rectangular grid to connect circles into pairs while satisfying several constraints. In this paper, we prove that deciding whether a given Wataridori puzzle has a solution is NP-complete via a reduction from Numberlink, another pencil puzzle that has previously been proved NP-complete.
This short note outlines some of the issues in Czerwinski's paper [Cze23] claiming that NP-hard problems are not in BQP. We outline one major issue and two minor issues, and conclude that their paper does not establish what they claim it does.
We show that one-way functions exist if and only if there exists an efficient distribution relative to which almost-optimal compression is hard on average. The result is obtained by combining a theorem of Ilango, Ren, and Santhanam and one by Bauwens and Zimand.
In this short note, we show that the problem of VEST is $W[2]$-hard for parameter $k$. This strengthens a result of Matoušek, who showed $W[1]$-hardness of that problem. The consequence of this result is that computing the $k$-th homotopy group of a $d$-dimensional space for $d > 3$ is $W[2]$-hard for parameter $k$.
In this document, we collected the most important complexity results of tilings. We also propose a definition of a so-called deterministic set of tile types, in order to capture deterministic classes without the notion of games. We also pinpoint tiling problems complete for respectively LOGSPACE and NLOGSPACE.
We prove an $N^{2-o(1)}$ lower bound on the randomized communication complexity of finding an $ε$-approximate Nash equilibrium (for constant $ε>0$) in a two-player $N\times N$ game.
We consider the Consensus Patterns problem, where, given a set of input strings, one is asked to extract a long-enough pattern which appears (with some errors) in all strings. We prove that this problem is W[1]-hard when parameterized by the maximum length of input strings.
Any monotone Boolean circuit computing the $n$-dimensional Boolean convolution requires at least $n^2$ and-gates. This precisely matches the obvious upper bound.
We present various analytic and number theoretic results concerning the #SAT problem as reflected when reduced into a #PART problem. As an application we propose a heuristic to probabilistically estimate the solution of #SAT problems.
We prove that computing an evolutionary ordering of a family of sets, i.e. an ordering where each set intersects with --but is not included in-- the union earlier sets, is NP-hard.
Given a computable probability measure P over natural numbers or infinite binary sequences, there is no computable, randomized method that can produce an arbitrarily large sample such that none of its members are outliers of P.
J. Palmer West, Dino Sulejmanovic, Shiou‐Jyh Hwu
et al.
AbstractSingle crystals of α‐Cs3KBi2Mn4 (PO4)6Cl (I), β‐Cs3KBi2Mn4 (PO4)6Cl (II), and α‐Cs3KBi2Fe4 (PO4)6Cl (III) are synthesized in reactive CsCl/KCl molten‐salt media from Bi2O3, Mn2O3 (Fe2O3), and P4O10 in a molar ratio of 1:1:1 (I) or 2:1:1 (II) (800 °C, 4 d, 10—30% yield).
Butman, Hermelin, Lewenstein, and Rawitz proved that Clique in t-interval graphs is NP-hard for t >= 3. We strengthen this result to show that Clique in 3-track interval graphs is APX-hard.
We develop a pseudorandom generator that fools degree-$d$ polynomial threshold functions in $n$ variables with respect to the Gaussian distribution and has seed length $O_{c,d}(\log(n) ε^{-c})$.