All mathematical questions about computer science, including theoretical computer science, formal methods, verification, and artificial intelligence. For questions about Turing computability, please use the (computability) tag instead. For numerical analysis, use the (numerical-methods) tag.

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1answer
53 views

Subscript before a function symbol?

Does anyone know what the subscript before the function means? $$ _pf_p $$ It's part of a definition for selfish routing in networks: Let $N = (V,E)$ be the network, which is a directed graph. ...
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1answer
29 views

Natural Decision Problem not in PTIME

Are there any natural decision problems which are guaranteed not to be in $\mathsf{PTIME}$? Preferably natural graph problems like $\mathsf{CLIQUE}, \mathsf{VERTEXCOVER}$ etc. (However, they would be ...
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0answers
14 views

Encoder based on large similar data

Let us say you (Alice) and another agent (Bob) share a large piece of data (say, the Gutenberg project collection of books, or the Linux kernel. You want to send a smaller but still large piece of ...
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1answer
25 views

Range of number systems [closed]

I don't understand how to get the fraction part. This is what I came up with for the integer part. A) For 12 bit unsigned = 0 to 4095 B) For 12 bit signed = -2048 to 2047 C) For 12 bit in 2's ...
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3answers
387 views

Finite Automaton that accepts only the words baa,ab, abb and no other strings longer or shorter

I am trying to understand the answer here for FA that accepts only the words baa, ab, abb and ...
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1answer
68 views

Graph Coloring Question

Given T(n) as a star graph with n edges. (Basically T(n) is a graph that has one vertex u in the center, and from u there is one edge to each vertex v1,...,vn.) It is easily know that star-graphs are ...
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0answers
34 views

Computationnal geometry: vector, basis, point and coordinate system?

I am trying to build a small geometrical library in C++, that is mathematically consistent (not so false). The goal here is to construct two concepts: vectors and points. I am not sure that the ...
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1answer
37 views

Engineering notation algorithm, i.e. 1000 -> 1k, 0.001 -> 1m

I had to come up with a simple algorithm on a low powered embedded system, because dividing numbers by 1000s to get the wanted digits (first three basically) caused a loss in precision in the floating ...
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1answer
45 views

Show that the Turing machine will solve the self-halting problem

Suppose we have Turing machine $M^*$ that: i. halts printing 1 if $M_n$ halts on input 1 ii. halts printing 0 if $M_n$ doesn't halt on input 1 Show that you cannot construct $M^*$. ...
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0answers
33 views

A* vs D* vs Dijkstra [closed]

I understand the basis of A* as being a derivative of Dijkstra, however, I recently found out about D*. From wikipedia, I can understand the algorithm. What I do not understand is why I would use D* ...
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1answer
31 views

Proof that such a Turing machine cannot be constructed…

Prove there can be no Turing machine $M^*$ that takes input $n$ and: i. halts printing 1 if $M_n$ halts on input 1 ii. halts printing 0 if $M_n$ doesn't halt on input 1 Intuitively I can see why ...
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0answers
16 views

Reduction of halting problem

I can show that this reduction !H ≤ H where H is the general halting problem an !H is the complement of it. But what with H ≤ !H ...
2
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3answers
91 views

Exponential Regression: how to get a formula from a given pattern

I'm trying to code a computer script (in Java) that returns an array of numbers that follows a certain pattern. The numbers should be: ...
2
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0answers
50 views

This proof in my textbook involving the pumping lemma appears incorrect - is it?

It states Let $B$ be the language $\{0^n1^n2^n | n \geq 0\}$. We use the pumping lemma to prove that $B$ is not regular. The proof is by contradiction. Assume to the contrary that $B$ is regular. ...
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1answer
26 views

Proving Upper Bound for Two Variable Function?

The question is: Prove (logn)^k = O(n) for every k>=1. I have never encounter a problem for proving an upper bound for two variables, so I am perplexed as to ...
0
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1answer
57 views

How to get 2 percentages to a 100%

First of im new to this site and I've never been the sharpest at math, im a web developer by trade. My question is math related but ill just give you a quick background about my website so that you ...
0
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2answers
27 views

How to compute surface normal pointing out of the object

An object has been approximated by a lot of triangles. Given the vertex positions of these triangles, how can I compute the normal of these vertices which pointing outside of the object. I know the ...
0
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2answers
66 views

Existing Algorithm / Code to calculate exact values of the Riemann Zeta function at even natural numbers?

I wanted to know if there's any existing algorithm to compute exact values of the Riemann Zeta function at even natural numbers? For example, it should compute $\zeta(4)$ as exactly $\frac{\pi^4}{90}$ ...
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0answers
36 views

Iteratively Replacing Substrings

This problem came up while I was helping someone. Informally, we have a string of characters and a "rule" which replaces a specific string with another one, and we repeat this rule until we can no ...
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1answer
68 views

Graph Theory - Introduction Questions [closed]

I have a couple of questions that are probably SUPER easy for anybody that has studied graph theory but are confusing the hell out of me. I know it may be inconvenient to help me but I have a test ...
3
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3answers
62 views

Is $L = \{(x,y,z) | x+y=z\}$ a regular language?

Suppose $x,y,z$ are coded as decimal or their binary representations in an appropriate DFA. Is $L$ regular? My intuition tells me that the answer is no, because there are infinitely many combinations ...
0
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2answers
73 views

Tough Turing machine multiple choice questions

I'm having a tough time deciding whether my answers for these questions are correct. Can anyone help me agree on something? They seem pretty easy, but I've found that they're actually difficult. ...
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0answers
11 views

Echo State Network learning Mackey-Glass function, but how?

I got this example of a minimal Echo State Network (ESN) which I analyse while trying to understand Echo State Networks. Unfortunately I have some problems understanding why this really works. It all ...
4
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1answer
21 views

Is anything nontrivial known about quotients of complexity classes?

This question is just for fun and this is completely outside my area, so it's likely dumb; apologies in advance. By a "quotient" I mean the following: suppose you have two complexity classes, $A ...
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1answer
68 views

Easy Proofs with Functions and Big-O

I have these two questions. I tried answering them, but got them wrong and I don't know how to answer them correctly. This is not homework --- I'd appreciate a solution (at least to one), and an ...
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1answer
54 views

Is there a general formula to represent the cardinality of a Cartesian product of n sets?

For two sets, basically, $|A \times B|=|A| \times |B|$.. Suppose I'm given a random number of sets. Which formula should I use? Or is there a specific method? Using a program It's easy to ...
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2answers
84 views

Which pure mathematical problems could be tackled with an algorithm solving NP-complete problems?

In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for ...
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1answer
64 views

Knuth-Bendix completion algorithm: word problem

Can someone explain me how to set up an algorithm to find the 12 normal forms of the group $A_4$ by making use of the Knuth-Bendix completion algorithm? So we have that $RRR=1, SSS=1$ and $RSRS=1$. ...
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1answer
35 views

Data Representation Question

A computer stores a number of $16$ bits word using floating-point arrangement. Given that the first bit is reserved for the sign and followed by $6$ bits for the exponent using biased form. The ...
3
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1answer
95 views

No of pairs of elements whose XOR satisfies a condition

We are given a set of $n$ non-negative integers. We need to find the number of pairs of integers from this set whose $XOR$ is $ = K$. My approach is to sort the integers which takes $O(NlogN)$. Then ...
3
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1answer
56 views

Recursively deleting every second element in a list

This question got me thinking. If you have a list of length n and recursively delete every other element from the list until only one element remains, is there any ...
0
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0answers
23 views

Recurrence relation by expansion

I'm trying to find a general formula for the following recurrence relation: for n of the form 2^2^k S(n) = (rootn)(S(rootn))+n S(2) = 1 First, I let b = 2^2 just for readability ...
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1answer
40 views

Texture mapping from a camera image (knowing the camera pose)

I'm not sure if I should ask this question here or on stackoverflow, so forgive me if I'm wrong. I want to apply a texture (taken from a camera) on a 3D surface, let me explain my problem: I have ...
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0answers
19 views

Universal hashing proof

So I tried doing this proof but I do not know how to start it properly. I know I have to show that the hash function family has the consistent and random property. The first is rather obvious to ...
0
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1answer
32 views

Derive Time from Sorting Method/Time Complexity

A sorting method with “Big-Oh” complexity O(n log n) spends exactly 1 millisecond to sort 1,000 data items. Assuming that time T(n) of sorting n items is directly proportional to n log n, that ...
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1answer
47 views

Are all constrtuctively describable functions continuous? Do they necessarily come with a topology?

In the paper "An injection from $\mathbb{N}^\mathbb{N}$ to $\mathbb{N}$" by @AndrejBauer, about the question whether there exists an injection $\mathbb{N}^\mathbb{N}\to\mathbb{N}$, we writes ...
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0answers
17 views

looking for hypergraph decompositions

there are many thms for/types of graph decompositions. in contrast, am looking for various types of hypergraph decompositions...? also esp interested in graph analogs that translate somehow eg ...
0
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1answer
24 views

Time complexity of indirect recursion

How to find the complexity of an the given algorithm: Algorithm f(int n) { if(n==1)return(1); else { f(n-1)+g(n-1); } } Algorithm g(int n) { ...
2
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1answer
69 views

Solve the recurrence relation:$T(n)=\sqrt{n}T\left(\sqrt{n}\right)+\sqrt{n}$ [closed]

I have doubt in solving the following questions: $T(n)=2T(\sqrt{n})+n$ $T(n)=\sqrt{n}T(\sqrt{n})+c$ $T(n)=\sqrt{n}T(\sqrt{n})+\sqrt{n}$ T(2)=1 for all the problems Atleast give the final answer.
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2answers
65 views

Avoid dividing by zero with just variables and basic operators

I am working on stats for a sports team, and one of the stats I have the ratio of Shots and Shots on Target (Which I call ...
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3answers
123 views

Prove Upper Bound (Big O) for Fibonacci's Sequence?

NOTE: We are not to use proofs (limits, induction, or otherwise) in this problem. We were to prove the upper bound for the Fibonacci recursion is some exponential. The Fibonacci recurrence relation ...
0
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2answers
134 views

The result of O(f(n)) - O(f(n))

My question is in the field of the big-O-notation and complexity/asymptotic functions: Probably something that I'm missing, but I've couldn't find any well explained solution for the following: What ...
1
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1answer
72 views

Help with Recursive Algorithm

We are to determine a recurrence relation for a recursive algorithm. Let us use the Josephus Problem for this: Given n people standing in a circle, every kth person is killed until one person ...
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0answers
56 views

Related paradigms in Computer Science and Mathematics

I've read in a number of places discussions on whether Mathematics is a branch of Computer Science and vice-versa (see here for example) Having a background in both, I know that the Computer Sciences ...
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1answer
66 views

Context free grammar to pushdown automata…

<expr> −→ <term> | <expr> + <term> <term> −→ <factor> | <term> × <factor> <factor> −→ (<expr>) | b ...
3
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2answers
41 views

$(2^a -1)(2^b -1)=2^{2^c}+1$ has no nonnegative integer solutions

$(2^a -1)(2^b -1)=2^{2^c}+1$ is not possible for a,b,c nonnegative integers. Any solutions using parity Approach: $(2^a -1)(2^b -1)=2^{2^c}+1\Rightarrow$ $2^{a+b}-2^a-2^b=2^{2^c}\Rightarrow$
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1answer
56 views

Let $L_{UIUC}$ = $\{ \langle M \rangle$ : $L(M)$ contains the string $UIUC\}$. Prove that $L_{UIUC}$ is undecidable.

Been stumped as to why the following proof works. Note: I have taken this proof directly from here. Proof by reduction from $A_{TM}$. Suppose that $L_{UIUC}$ were decidable and let $R$ be a Turing ...
3
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1answer
59 views

Is Cartesian Product same as SQL Full Outer Join?

Is Cartesian Product same as Full Outer Join found in Relational Database SQL? I ask because I am taking a Discrete Mathematics course and I just want a better understanding of how what I am studying ...
2
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1answer
40 views

The “computability” of fundamental physical constants

I would like to ask if any of the fundamental physical quantities like the speed of light or plancks constant (all measured according to a common standard of of units) can be classified as computable ...
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1answer
13 views

xyplus recursive language

For {x, y, +}, the language XYPlus is shown recursively as: (1) x and y are in XYPlus . (2) So if a and b are words in XYPlus ...