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
47 views

prenex equivalence problem

Suppose: $$\forall x\exists y \phi(x,y) \to \neg \exists x\psi(x) $$ which of the following formula are prenex normal equivalence with the above formula? i didn't any idea to explain it. it's a ...
0
votes
0answers
17 views
1
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3answers
87 views

Combination Problem Understanding

How many ways can a Doctor go to the Hospital on $5$ days of January (which has $31$ days) such that no two visits are on consecutive days? I think the solution is: $\displaystyle\binom{27}{5}$ But ...
1
vote
1answer
44 views

Partition Graph Challenging Question

I want to find in which of the following Graph, the edges cannot partitioned to triangles? Km,n,r means 3-Partite Complete Graph with m, n, and r sections. a) K7 b) K12 c) K3,3,3 d) K5,5,5 i ...
0
votes
1answer
18 views

Planner Combination Problem on Graph

I ran into a Graph Problem. Suppose G is A Planner Graph with 100 Vertices such that if connect each two Non-adjacent vertices, the resulting graph would be non-planner. what is the number of edges ...
1
vote
1answer
44 views

Perfect Matching Combination Problem

We know: A perfect matching (a.k.a. 1-factor) is a matching which matches all vertices of the graph. if we remove edges of perfect matching of a 12-Complete Graph. how many triangle remain in this ...
2
votes
2answers
54 views

The value of loop variable at the end of a loop in the insertion sort

I am looking at the algorithm of the insertion sort: Input: $A[1 \dots n]$ ...
0
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0answers
25 views

Space-dependent diffusivity and finite-differences

I want to implement a finite difference code of this simple diffusion equation with space-dependent diffusivity: $$\partial_{t}u =D\partial_{x}^{2}u+\partial_{x}D\cdot\partial_{x}u$$ I go for a ...
0
votes
1answer
22 views

Finding final value of sum from double summation code fragment.

sum = 0; inc = 0 for i from 1 to n for j from 1 to i sum = sum + inc inc = inc + 1 What does it mean when it is asking the "final value of sum" from above code ...
0
votes
1answer
153 views

Proof completion: if $Y$ is a closed term in strong nf, then $Yx$ weakly reduces to a strong nf $Z$

I am self-studying Hindley & Seldin's Lambda-Calculus and Combinators. I would appreciate some help with filling in a final detail for a proof for the following statement regarding combinatory ...
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1answer
55 views

Computable Set & Function

we know that i read this sentence are true? can anyone say an example for following sentence? there are a non computable set A such that
0
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1answer
22 views

Convex hulls for a finite amount of points

I'm trying to understand what a convex hull intuitively is, and say given for a set of points $(x,y)\in\mathbb{R}^2$ how is it generated from these points? I tried reading the wikipedia article and ...
-1
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1answer
82 views

Turing & Computability & Computation

We know if we have: we can show (T=t= Turin Redu.) but i have no idea why this relation be correct? any idea?
0
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0answers
13 views

Must the weight function be nonnegative for the greedy algorithm to be optimal for both a matroid and a greedoid?

Must the weight function be nonnegative for the greedy algorithm to be optimal for both a matroid and a greedoid? For a matroid, the codomain of the weight function is $[0,\infty)$, from Wikipedia ...
2
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0answers
50 views

Big Challenge in TM & R.E Set [closed]

we know that Halting problem {(M.w) | M halts on input w} is r.e but not recursive. i see the following sentence in one book. "the set of {(M.w) | M halts on input w and M is a TM}} is not r.e" ...
-2
votes
1answer
242 views

How to obtain $\operatorname{lcm}(a_1,a_2,a_3,\ldots,a_n)\%1000000007$

The problem is that you have $n$ numbers whose value can be in range $[1,100000]$. The task is to find the LCM of all these numbers. Now the answer can be very large so it should be printed MODULO ...
1
vote
1answer
46 views

Meaning of the characteristic polynomial of a matroid

From wikipedia The characteristic polynomial of a matroid $M$ (which is sometimes called the chromatic polynomial,[29] although it does not count colorings), is defined to be $$ p_M(\lambda) ...
0
votes
1answer
21 views

Linear equation so that the solutions has to be integers.

I have this equation $$-X_5-32X_4-32^2X_3-32^3X_2-32^4X_1=[PARAMETER]$$ I want to get all the solutions to this equation with a given parameter(integer) and all of the solutions has to be integers ...
0
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0answers
62 views

TAUTOLOGIES NP-Complete Condition

The decision problem TAUTOLOGIES is, Given $\forall x_1 \forall x_2 ... \forall x_n$ $\phi(x_1, x_2, ... x_n)$ a set of universally quantified Boolean variables and a Boolean formula ...
0
votes
1answer
36 views

How do you find the probability of a certain state in Markov Chain?

This question appears without answer in an old exam I found (not a homework question) Suppose messages that enter a system need to be processed by two servers. They arrive at the system at a ...
2
votes
2answers
60 views

Equivalent definitions for a coloop?

From wikipedia, in a matroid, An element that belongs to no circuit is called a coloop. Equivalently, an element is a coloop if it belongs to every basis. I wonder why the equivalence? From ...
0
votes
1answer
18 views

How do the dependent sets of a matroid characterize the matroid?

Wikipedia says: The dependent sets of a matroid characterize the matroid completely. The collection of dependent sets has simple properties that may be taken as axioms for a matroid. So I ...
0
votes
0answers
10 views

Maximum amount of positional offset caused by noisy distance measurements in Quadrilateration

Quadrilateration is a range-based localization technique applied to wireless sensor networks. It is the equivalent method of trilateration in 2D. Assume that, there are four beacons (the sensors ...
0
votes
0answers
19 views

to maximize the summation

let F=$∑i=1$ to $N$ $((abs(A[i]-X))^P mod $K$)mod K$ $A[1..N]$ is an array with $N$ elements, the problem is to find $X$ such that the above summation F maximized where $X$ can take any value from ...
5
votes
1answer
55 views

Mathematical definition of Blender's F-Curves

I'm designing software for generating animation curves. I'd like the curves to be based on those found in Blender 3D, which they call "F-Curves." According to the page on the Blender Wiki, they are ...
0
votes
2answers
46 views

How to prove that for all 25 ppl and 4 groups, there is a group of at least 6 ppl from the same group?

As of Jun.17, I predict that Brazil, Germany, Italy, and Argentina will make it to the semi-finals of the FIFA World Cup. Suppose you have a group of 25 footballers from those four countries. Prove ...
3
votes
1answer
45 views

Image Reconstruction:Phase vs. Magnitude

Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. $$ ...
1
vote
1answer
26 views

What kind of set system is defined to have this property?

Let $E$ be a set, and $F \in \mathcal P(E)$ has the following property: For every $x\in E$ and $Y,Z\in F$ with $x\notin Y\cup Z$, there exists $X\in F$ with $(Y\cap Z)\cup\{x\}\subseteq X$. I wonder ...
2
votes
0answers
27 views

Generating interesting random TMs

To get a more intuitive understanding of the halting problem I want to generate some random TMs and see how they behave, what some heuristics can tell about them, etc. The problem is that, if I ...
0
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0answers
35 views

another series problem [duplicate]

I need help in simplification below are the two formulas for AGP series: if $n$ is even $a\cdot r^{(n-1)/2} + d\cdot( 1 + r + r^2 + r^{(n-1)/2})$ if $n$ is odd $a\cdot r^{(n-1)/2} + d\cdot( 1 + ...
0
votes
0answers
42 views

need help in simplification

I need help in simplification below are the two formulas for AGP series: if $n$ is even $a\cdot r^{(n-1)/2} + d\cdot( 1 + r + r^2 + r^{(n-1)/2})$ if $n$ is odd $a\cdot r^{(n-1)/2} + d\cdot( 1 + ...
1
vote
1answer
66 views

another counting problem

There are $k$ warriors that participate in the Wars, which have happened for the past $n$ years. Each year there has been a victor. Further, a particular warrior $W$ has won the Wars an even number of ...
1
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0answers
24 views

A set system generated by a closure operator?

Given a ground set $E$, and a matroid closure operator $\tau$ on $\mathcal P(E)$, we can define a set system $(E,F)$ with $$ F := \{X \in \mathcal P(E): \forall x \in X, x \notin \tau(X-\{x\}) \}$$ ...
1
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0answers
22 views

What does “modular” in “modulr functions” mean?

From Wikipedia If $\Omega$ is a set, a submodular function is a set function $f:2^{\Omega}\rightarrow \mathbb{R}$, where $2^\Omega$ denotes the power set of $\Omega$, which satisfies one of the ...
0
votes
2answers
57 views

minmizing average problem

Given a set containing N numbers, minimize the average where you can take out any string of consecutive numbers in the set. |N|<=100000 Ex. {5, 1, 7, 8, 2} You can take out {1,7}, etc. but the ...
0
votes
0answers
31 views

Two definitions of matroid

From Wikipedia, a finite matroid $M$ is a pair $(E,F)$, where $E$ is a finite set and $F$ is a family of subsets of $E$ either with the following properties: The empty set is in $F$. if $X \in ...
0
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0answers
8 views

Rank feasible subset of a greedoid

From Wikipedia, given a greedoid $(E,F)$, with ground set $E$ and the class $F$ of feasible sets, A subset $X$ of $E$ is rank feasible if the largest intersection of $X$ with any feasible set has ...
0
votes
1answer
56 views

Function Combination on Computer Science

I read some material on Computational Function, every one could describe the result of following combination? suppose $g_1(x)=3x$, $g_2(x)=4x$, $f(x,y)=x+y$, how we compute combination of $f$ with ...
0
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0answers
71 views

Primitive Recursive Predicate Challenge

I'm an Computer scientist, and I recently ran into a challenge. If we have primitive recursive predicate $P(x), Q(x)$, I think that all of following 4 expressions can be primitive recursive. Any hint ...
0
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0answers
46 views

Recursive Set and Complement Problem

if we have $$A=\{x:|W_x\ne\phi\}$$ can we say always my tight listed below is true? $A$ is recursive , $A$ is r.e, complement of $A$ is r.e, complement of $A$ is not recursive?
0
votes
1answer
49 views

Complexity & Computation & Logic Problem [closed]

As i study for prepare to CS Final exam, i have some challenges. can i say all of following statements are true? 1) each infinite recursive set, is union of two disjoint infinite recursive set? 2) ...
1
vote
2answers
47 views

Compressing binary numbers

If I have a arbitrarily long random binary number with the condition that the probability that a given digit is 0 and 1 is 1/4 and 3/4, respectively. What is the best way to compress this into a ...
1
vote
1answer
35 views

Find coordinate $y$ of an elliptic curve point

If I have an elliptic curve over a finite filed $F_p$ ($p$ is prime) defined as $$ y^2 \equiv x^3 + ax + b\pmod p,$$ such that $4a^2 + 27b^2 \neq 0$ and suppose I have only given the coordinate $x$, ...
0
votes
1answer
20 views

Understand the English paragraph on association rule.

I am currently studying Association Rule Pattern Mining. I am reading the explanation on wikipedia about it. Somehow, I feel like I have a problem in understanding the paragraph below. Can somebody ...
0
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0answers
27 views

Using the pumping lemma to prove that a certain language is not regular

I've been trying to understand the pumping lemma since forever, I just don't know what it does, I have no clue what any of it does. My college professor sucks, he thinks writing a bunch of stuff on a ...
11
votes
4answers
166 views

How do you create a nonlinear game that the player can always win?

I thought a lot about this question — and initially, I intended to ask this on gamedev.stackexchange.com — but due to its rather theoretical aspects, I think it might be more appropriate to address a ...
4
votes
3answers
108 views

How is math used in computer graphics? [closed]

I'm doing a research paper on the mathematics of computer graphics and animation (3D) and I do not know where to start. What mathematical equations and concepts are used for computer graphics and ...
0
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0answers
38 views

Check if there's a cycle in an undirected graph

I'm trying to find an algorithms that checks if there's a cycle in a given undirected graph G=(V,E). But I didn't succeed. Can anyone give me such an algorithm?
-2
votes
1answer
34 views

Assume that a text file contains the string “aabbaaccde” . Write Huffman code [closed]

Assume that a text file contains the string "aabbaaccde" . 1-Write Huffman code a, b; c, d and e . 2-What is the size of the compressed file? how can solve this question
2
votes
2answers
70 views

Shortest path between wikipedia articles

I'm trying to figure out whether it is possible (and if so how) to find the shortest path inside a network from one node to another. I know that there are different possible algorithms to do that the ...