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1500 questions
12
votes
3 answers
Is there an efficient test for if an NFA accepts a subset of another NFA?
So, I know that testing if a regular language $R$ is a subset of regular language $S$ is decidable, since we can convert them both to DFAs, compute $R \cap \bar{S}$, and then test if this language is empty.
However, since this requires converting to…
Joey Eremondi
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12
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7 answers
Is $A$ regular if $A^{2}$ is regular?
If $A^2$ is regular, does it follow that $A$ is regular?
My attempt on a proof:
Yes, for contradiction assume that $A$ is not regular. Then $A^2 = A \cdot A$.
Since concatenation of two non-regular language is not regular $A^2$ cannot be regular. …
akshay
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12
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1 answer
Which non-regular languages are in $AC^0$?
For example, I know that the non-regular language $a^nb^n$ is in $AC^0$. I would like to know more examples like this.
Alex Grilo
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12
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2 answers
Infinite chain of big $O's$
First, let me write the definition of big $O$ just to make things explicit.
$f(n)\in O(g(n))\iff \exists c, n_0\gt 0$ such that $0\le f(n)\le cg(n), \forall n\ge n_0$
Let's say we have a finite number of functions: $f_1,f_2,\dots f_n$…
mrk
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12
votes
3 answers
How often is Prolog/ASP used in non-research areas?
I've just recently found out about KRR (Knowledge representation and Reasoning) and ASP, not hearing a thing about them before (except a bit about prolog). I've read a bit about them and one of their primary usage seems to be AIs.
My question would…
FloriOn
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12
votes
1 answer
Does a subcubic algorithm exist for the following problem?
Given a symmetric real $n \times n$ matrix $A=(a_{ij})$, is there an algorithm which computes the sum $$\sum_{i,j,k}\max(a_{ij},a_{ik},a_{jk})$$ over all $1\leq i
user89217
- 123
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12
votes
1 answer
Explaination for Variation of Boyer-Moore Majority voting algorithm
Boyer-Moore's majority vote algorithms can be used to determine the majority element in a linear time and constant space.
The intuition behind finding the majority element is understandable as it has to be greater than the count of other elements…
thebenman
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12
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2 answers
How to derive dependently typed eliminators?
In dependently-typed programming, there are two main ways of decomposing data and performing recursion:
Dependent pattern matching: function definitions are given as multiple clauses. Unification ensures that all omitted cases are impossible, and…
Joey Eremondi
- 30,277
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- 122
12
votes
0 answers
Covering a complete graph with n copies of an arbitrary graph: NP-complete?
Given a complete graph $G$, an arbitrary graph $H$, and a positive
integer $n$, are there subgraphs $A_1,\dots,A_n$ of $G$ (not necessarily disjoint) such that
their union is $G$, and each of them are isomorphic to $H$?
This is a problem which…
Theemathas Chirananthavat
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12
votes
1 answer
Priority queue with both decrease-key and increase-key operations
A Fibonnaci Heap supports the following operations:
insert(key, data) : adds a new element to the data structure
find-min() : returns a pointer to the element with minimum key
delete-min() : removes the element with minimum key
delete(node) :…
Joe
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12
votes
0 answers
Can you multiply complex 2x2 matrices in fewer than 21 real multiplies?
It is well known that 2x2 matrices can be multiplied using just 7 (instead of the obvious 8) multiplications in the ground field (Strassen-Winograd, etc.). It is also well known that complex numbers can be multiplied using just 3 real…
Steve Linton
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12
votes
2 answers
Reducing products in HoTT to church/scott encodings
So I am currently going though the HoTT book with some people. I made the claim that most inductive types we will see can be reduced to types containing only dependent function types and universes by taking the type of the recuror as inspiration for…
Jake
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12
votes
2 answers
Is the equality of two DFAs a decidable problem?
So given two DFAs, is the problem of finding if they generate the same language a Decidable problem?
I already know that Equality of two CFL is not Decidable
but what about Equality of two DFAs? considering most of the problems with DFAs are…
Richard Jones
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12
votes
1 answer
Why product type is a dependent SUM?
It might just be a stupid question but I simply see no obvious reason why dependent sum type is a generalized form of product type. Concretely, the sigma type $\Sigma(x:S)T$ degenerates to a product type if $T$ does not depend on $x$ and is…
Jason Hu
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12
votes
1 answer
Why are computable functions continuous?
I am working on writing an easy to read document about denotational semantics of the lambda calculus. For that I introduce CPOs, monotonicity and continuity.
A CPO is a set $M$ with a partial order $\leq$ and a bottom element $\bot$, requiring…
user3389669
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