# Questions tagged [notation]

Use this tag whenever you have a question about what some particular symbol/notation means.

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### Meaning of double colon $::$

I've came across this expression regarding function composition in some notes by people from computer science, and I don't know what the notation "$::$" means. \begin{equation} g \circ f : A \...
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64 views

### What Does The Notation of Union Over K represent?

I am currently studying about polynomial time in Comp Theory. The definition for polynomial time given in my textbook as follows: $$P= \bigcup_{k}TIME(n^k)$$ I have not seen the Union over k notation ...
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### Are there color conventions in CS? [closed]

I don't remember seeing any color conventions in Computer Science used to represent some abstract information or to simplify diagrams. For instance, chemists have the CPK coloring which associates ...
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178 views

### What does $CS - CF$ means?

What does $L_1 \in CS - CF$ means? I think the meaning is $L_1$ can be generated by context-sensitive grammars, but cannot be generated by context-free grammars. Am I understanding this correctly? ...
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### What does this mean $[X]_1^T$?

I found this in information theory paper, P.3883* the authors states the following Most existing theoretic studies of network coding focus on DAGs due to its simpler structure and dure to the fact ...
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### Determining asymptotic notation of a complex function

$$5n^4\log{n} - \frac{100n^2}{\log_4(n^2)} + 40$$ I am currently studying algorithm analysis and i need to express this function in terms of big O, theta and omega, so I should find C, and N0 for ...
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1k views

### Meaning of L* if L is a language

I can't find anywhere the meaning of $L^*$, given that $L$ is a language. I know $^*$ means repetition, for example $0^*$ = $\{ \epsilon, 0, 00, 000, \dots \}$. Or if $A$ is an alphabet $A^*$ are all ...
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33 views

### What is the equivalent of the integers symbol Z for n bit only integers?

We refer to the set of all integers as $\mathbb{Z}$. Now suppose we have a set of integers that can be held within a computer variable of $n$ bits width. Clearly they can only be of $2^{n}$ range, ...
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55 views

### Constructing a new graph. G'. What does it mean v ∈ S_{i+1}?

John lives in a city whose streets has the same length. His apartment is located at a specified node H. John need to do his errands where he visits each of k different shop in order. However, each ...
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205 views

### How the language $\{a^nb^mc^nd^m | n \geq1, \ m\geq1\}$ is used to check whether formal and actual parameters are equal?

How does the language $L=\{a^nb^mc^nd^m \mid n \geq1, m\geq1\}$ abstract the problem of checking that the number of formal parameters in the declaration of a procedure agrees with the number of actual ...
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173 views

### $\tilde \Omega$ for division by logarithmic factor

Is $\Omega \left(\frac{n}{\log{n}} \right)\subset \tilde\Omega(n)$?
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131 views

### On asymptotic complexity class notation?

Is the class of problems with complexity $O(n^{n^\epsilon})$ at every $\epsilon>0$ same as class of problems with complexity $O(n^{f(n)})$ at every $f(n)\in\omega(1)$ and hence both classes are ...
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476 views

### How to read 'max min' and 'min max'?

Here is an exercise I came across while studying MaxFlow / MinCut and I'm rather stumped: Designate $G = (V, E)$ as an undirected graph that has at least two vertices. Every edge $(e)$ on this graph ...
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198 views

### What is the Haskell-style type signature called (i.e., who is it named after)?

A type signature in Haskell is written in the following format: functionName :: arg1Type -> arg2Type -> returnType There's a (hyphenated, after a person or ...
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### How to express taking the next bit of an infinite string in small-step semantics?

I have to write a rule as part of a small step operational semantics (https://en.wikipedia.org/wiki/Operational_semantics). Whenever this rule is applied, the next bit belonging to an infinite bit ...
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22 views

### How to understand the mathematical constraint of potentials?

Good evening! I am studying scheduling problems and I have some difficulties understanding constraints of potentials: Let be $t_j$ the time when a task $j$ starts, and $t_i$ the time when a task $i$ ...
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### Maximum Subarray Problem - Analyzing best case, worst case, and average case time complexity big o

New to the board, if this is the wrong section I apologize and I will delete it. Will be helpful to be provided correct exchange to guide me through this process of learning. If you have a given an ...
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24 views

### Notations for dealing with generators in algorithms

This question is about generators, which are functions that return an item from a (usually very large or infinite) set on demand, an example from Python is: ...
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### Can I say ≤ O(f(x)) rather than = O(f(x)) if the bound is not tight?

Suppose I just invented merge sort, but due to my limited ability was only able to prove that the running time is $O(n^2)$. However, I suspect that the running time is actually better (in reality it's ...
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56 views

### Converting sets into regular expressions

In my book: The set {abb, a, b, bba} is said to be converted into regular expression abb + a + b + bba. The set ...
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45 views

### Express semantic duplicates of records formally

I'm working on a paper about record linkage and duplicate detection and want to visualize my definitions of "hard" and "semantic" duplicates. Hard ones are a 100% match; where's only true or false- ...
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### Turing Machine notation

I'm a bit confused on some of the notation being used for turing machines in one of our exercises in class. The question gives us a string $\alpha \in \{0,1\}$* and the function $\mathsf{int}(\alpha)$...
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206 views

### What is meant by the notation $L(…)$?

I am currently studying about formal languages and automata. I am trying to solve a problem but there is a notation whose meaning I'm not sure of. I have a question to find out the relationship ...
2answers
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### Terminology for worst-case N-complexity on $O(1)$ insert after amortisation

Normally, when discussing amortisation and worst-case complexity, amortisation negates the worst-case scenarios, and the BigO describes the average for the operation (the way it's used in interviews ...
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234 views

### Convert for loop into math sigma notation

Have some code (written in C), need the equivalent notation for mathematics. Is it possible using if-statements and sigma notation for this, and if so, how? ...
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### What does $\overline{L}^*$ signify?

Suppose that $L$ is a language. What does $\overline{L}^*$ signify? Is $\overline{L^*}$ the same as $(\overline{L})^*$?
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### How to represent a map data structure mathematically

Wondering how to represent a map object such as the following mathematically: var foo = { a: 10, b: 'bar', c: true } You could say that it was a function ...
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### A commonly-used symbol for the set of all heads of directed edges?

Let $G = (V, E)$ be a digraph, and consider the set $\left\{ v \in V \; \middle| \; \left(\{v\} \times V \right) \cap E \neq \varnothing \right\}$, the set of vertices which form edges with other ...
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421 views

### How do I normalize a push down automaton?

Looking at the above PDA, I am unsure whether or not it is normalized. Specifically, the loop transition from $q_1$ to $q_1$, because I know a transition must either push OR pop from the stack. Does ...
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112 views

### representing set of non-overlaping string in formal notation

I want to represent a set of any substrings which come from an original string with constraint that all substrings should not be overlapped. To be more clear please consider the example below: e.g. <...