All Questions
Tagged with discrete-mathematics computer-science
716
questions
-1
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Fixed quantities in Big O notation
Consider the following description of a random graph generation algorithm with parameters $n$ (number of vertices) and $m$ (number of edges).
All iterations add an edge except those where a ...
- 3,468
-5
votes
1
answer
49
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Question about concrete mathematics double summation derivation [closed]
How did the author in the image convert the summation into a double summation? I can see how the double summation turns into the sum of squared integers but how would you go about converting the sum ...
- 181k
0
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1
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49
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Proof that if a graph has edge connectivity 3, then the girth is bounded by the number of nodes divided by two + 1, g(G) <= |V(G)| / 2 + 1
I've not been able to solve this problem for a week now. My idea was that I start with a circle with n nodes and because the edge connectivity is 3, every node must have at least 3 neighbours, so to ...
0
votes
1
answer
49
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A proof for the statement: The 3-Dimensional matching problem is NP-Complete
The 3-Dimensional Matching Problem is relatively well known in the fields of discrete mathematics and computer science. The problem consists of determining whether a tripartite
$3$-hypergraph with ...
- 47.4k
5
votes
2
answers
144
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"Encode" all $n$-permutations with the fewest number of swaps
The goal is to find $m$ swaps $s_1, s_2, \dots, s_m$ such that any $n$-permutation can be encoded as a binary sequence of length $m$, $x_1, x_2, \dots, x_m$, where $x_i$ indicates whether to perform ...
2
votes
2
answers
224
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What does it mean when the transition function of a NFA returns an empty set?
Given a NFA, $N = (Q, \Sigma, q_0, \partial, F_Q)$, where $\partial$ is the transition function $Q \times (\Sigma \cup \{ \varepsilon \} ) \to \mathcal{P}(Q) $. So $\partial(q, a)$ returns a set, ...
0
votes
1
answer
87
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What's the behaviour of $\partial(q, a)=\emptyset$ on NFA?
Given an NFA say $N=(Q,\Sigma, q_0, \partial, F_Q)$, where $\partial: Q\times(\Sigma\cup\{\varepsilon\})\to\mathcal{P}(Q)$. It's confusing about the behavior of say $\partial(q, a)=\emptyset$ for any ...
- 322
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2
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57
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Why $d^*(q, \epsilon)$ has definition when $d(q, \varepsilon)$ does not in DFA?
I'm reading an online book about DFA and NFA but it confuses me.
Given a DFA say $D=(Q,\Sigma, q_0, \delta, F_Q)$, its transition function is a total function defined on every symbol from a given ...
1
vote
2
answers
64
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XOR sum of array
When you are given an array of even number of elements:
[$a_1$ $a_2$ $a_3$ ….. $a_n$] ($n$ is even)
Assume the $a_i$ are not all zero
Let $S$ = the XOR sum of all these original elements
You will ...
- 318
3
votes
1
answer
88
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Why would solving #MATCHING(bipartite) problem efficiently solve #MATCHING efficiently?
Im gathering information about the matching counting problem for a graph $G$ (#MATCHING($G$)). I found that for the specific case of $G$ being a bipartite graph then the problem has a simple (not ...
- 47.4k
2
votes
0
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76
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the Ackermann function must be total and unique based on one specific list of rules
This is one following question based on one question I asked before.
In mcs.pdf, it has Problem 7.25 in p251(#259).
One version of the the Ackermann function $A:\mathbb{N}^2 \to \mathbb{N}$ is ...
- 416
0
votes
1
answer
84
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partial function version of the Ackermann function must be total
In mcs.pdf, it has Problem 7.25. (I only solve somewhat important problems referred to in the chapter contents because I have learnt one Discrete Mathematics book before and read mcs to ensure no ...
- 353
0
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0
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25
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Computing transitive closure for relation via other relation
The closure of a relation $R$ over a set $S$ is denoted $R[S]$ and calculated via $\bigcup_{i\in\mathbb{N}}Y_i$ where $Y_0=S$ and $Y_{n+1}=Y_n\cup R(Y_n)$. ($R(Y_n)$ is the image of $Y_n$ under $R$).
...
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1
vote
1
answer
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Constructing Truth Tables for Formulas with Variable Valuations
I was solving a problem from old exams and got stuck here. I'd appreciate the help.
We have the three variables p, q, and r. There are 8 valuations of the variables. If F is a propositional logic ...
- 5,057
-1
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1
answer
59
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Hoare Logic: If-statement
Can someone explain the first assignment and implied? We prove bottom to up and I don't follor after the $(1=x+1)$ if-Statement. This is what my book says about the assignment rule:
, if we wish to ...
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