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Quantum Supremacy Task

I’m trying to understand the task performed by Google’s Sycamore that recently achieved alleged Quantum Supremacy. I’ve read the paper in Nature but the actual task that would have taken 10,000 years to compete is over my head. Is anyone able to…
Yolo_chicken
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Are all Integer Linear Programming problems NP-Hard?

As I understand, the assignment problem is in P as the Hungarian algorithm can solve it in polynomial time - O(n3). I also understand that the assignment problem is an integer linear programming problem, but the Wikipedia page states that this is…
Matt
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Complexity of computing matrix powers

I am interested in calculating the $n$'th power of a $n\times n$ matrix $A$. Suppose we have an algorithm for matrix multiplication which runs in $\mathcal{O}(M(n))$ time. Then, one can easily calculate $A^n$ in $\mathcal{O}(M(n)\log(n))$ time. Is…
Shitikanth
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Is Hidoku NP complete?

A Hidoku is a $n \times n$ grid with some pre-filled integers from 1 to $n^2$. The goal is to find a path of successive integers (from 1 to $n^2$) in the grid. More concrete, each cell of the grid must contain a different integer from 1 to $n^2$ and…
ipsec
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Finding shortest and longest paths between two vertices in a DAG

Given an unweighted DAG (directed acyclic graph) $D = (V,A)$ and two vertices $s$ and $t$, is it possible to find the shortest and longest path from $s$ to $t$ in polynomial time? Path lengths are measured by the number of edges. I am interested in…
robowolverine
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How to devise an algorithm that suggests feasible cooking recipes?

I once had a veteran in my course that created an algorithm that would suggest cooking recipes. At first, all sort of crazy recipes would come out. Then, she would train the cooking algorithm with real recipes and eventually it would suggest very…
Oeufcoque Penteano
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Initial temperature in simulated annealing algorithm

I've done some testing of different initial temperatures in my simulating annealing algorithm and noticed the starting temperature has an affect on the performance of the algorithm. Is there any way of calculating a good initial temperature?
Undefined
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Intuition behind eigenvalues of an adjacency matrix

I am currently working to understand the use of the Cheeger bound and of Cheeger's inequality, and their use for spectral partitioning, conductance, expansion, etc, but I still struggle to have a start of an intuition regarding the second eigenvalue…
m.raynal
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Why is the blank symbol not considered part of the input alphabet of a Turing machine?

Definitions of Turing machines are always explicit about the blank symbol not being part of the input alphabet. I wonder what goes wrong when you would make it part of the input alphabet, because effectively the blank symbol already seems to be part…
Confusion
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Is the SK2 calculus a complete basis, where K2 is the flipped K combinator?

Specifically, if I defined a new $K_2$ as $$K_2 = \lambda x. (\lambda y. y)$$ instead of $$K = \lambda x. (\lambda y. x)$$ would the $\{S, K_2,I\}$-calculus be a compete basis? My guess is "no," just because I can't seem to be able to construct the…
cole
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Can a Turing Machine decide if an NFA accepts a string of prime length?

I want to know if the following problem is decidable: Instance: An NFA A with n states Question: Does there exist some prime number p such that A accepts some string of length p. My belief is that this problem is undecidable, but I can't prove it.…
Chill
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Sampling perfect matching uniformly at random

Suppose I have a graph $G$ with $M(G)$ the (unknown) set of perfect matchings of $G$. Suppose this set is non-empty, then how difficult is it to sample uniformly at random from $M(G)$? What if I am okay with a distribution that is close to uniform,…
Artem Kaznatcheev
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What is a 'Key' in computer science?

I'm a bit confused on what exactly the meaning of a 'key' is in computer science. I understand key-value pairs, primary keys, etc... But I can't find a definition of what the term 'key' means by itself. As far as I can tell it just means a piece of…
TheMax
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Number of words of a given length in a regular language

Is there an algebraic characterization of the number of words of a given length in a regular language? Wikipedia states a result somewhat imprecisely: For any regular language $L$ there exist constants $\lambda_1,\,\ldots,\,\lambda_k$ and…
Gilles 'SO- stop being evil'
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Shannon Entropy of 0.922, 3 Distinct Values

Given a string of values $AAAAAAAABC$, the Shannon Entropy in log base $2$ comes to $0.922$. From what I understand, in base $2$ the Shannon Entropy rounded up is the minimum number of bits in binary to represent a single one of the values. Taken…
Sean C
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