Questions tagged [notation]

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

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1answer
47 views

What does x sign mean in functions

I came across this cross sign when reading a book. Does anyone know what does this mean in the context of a function?
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1answer
439 views

What is the meaning of this symbol that looks like an inverted uppercase A?

I found this symbol in a book I'm reading. Does anyone know what this symbol means? Does it mean for all js?
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1answer
55 views

What is the origin of the Bottom Type notation? Why does it look like... a bottom?

I couldn't help but notice the opening summary in Wikipedia's article on Bottom Types: In type theory, a theory within mathematical logic, the bottom type is the type that has no values. It is also ...
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0answers
34 views

How to write a job shop problem with these constraints in alpha|beta|gamma notation?

I have a job shop scheduling problem with the following characteristics. How would I write that in alpha|beta|gamma notation (see 1,2)? I know some of the parts, but not all. I add my suggestions in <...
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1answer
26 views

What does n with an index 0 mean in defenition of Theta/Big Omega/ Big-oh notation?

We define theta notation as follows: $\Theta(g(n))$ = {f(n): there are exist $c_1, c_2$ > 0 and $n_0$ such that 0 $\leq$ $c_1$g(n) $\leq$ f(n) $\leq$ $c_2$g(n) for all n > $n_0$}. I found an ...
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1answer
13 views

Set notation for ACL matrix

This might not be a computer science specific question and apologies if that is the case but it does come from material related to working out access control lists and I cannot understand the notation ...
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1answer
30 views

On lambda calculus notation: FGa

If we've got this expression: FGa where F and G are functions (as well as a, of course; but let's treat a as a constant). It must be understood that: first apply F taking G as input; then apply the ...
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2answers
41 views

Why are binary numbers sometimes written with one or more leading zeros that don't change the number (quantity) represented?

Binary numbers like '0110', or '00100101' are seen very often in all contexts. What are the leading (left hand side) zeroes for? Why did the writer not write '110' and '100101', respectively?
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1answer
31 views

Raising to the T in machine learning

What does it mean when in a machine learning paper there is $(arg)^{T}$, what does the T does to an arg in this 3b1b video on neural networks he puts the: $(w^{l-1})^{T}$
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1answer
40 views

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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4answers
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Arrow notation?

can someone explain what the following notation is? For j <- 1 to n Legal <- True I've seen these in various places, including wikipedia articles. It ...
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1answer
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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0answers
34 views

Infix to reverse polish notation (RPN)

I have an example: m = n = p = (-1) ^ (m + n + p) * (m + n + p); I don't know what to do with multiple "=". Should I treat them as a sign with the lowest priority or just put them in end of ...
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0answers
73 views

Cheat sheet for notation

I'm reading a paper which has quite a few formulas. I'm getting quite confused with some of the notation. For example I am able to pick-up on the BNF Notation (::= -> "is defined as") ...
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3answers
6k views

Is there any reason why the modulo operator is denoted as %?

I would like to know if there is any reason why many programming languages use the notation % for the modulo operator? It is used in the most "famous" ...
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3answers
88 views

Meaning of $\log^{O(1)}(a+b)$

What's the meaning of $\log^{O(1)}(a+b)$ ? Is it simply $(\log_2(a+b))^k$ where k is calculated in constant time ? That is the base 2 logarithm usually in computer science when no other base is set, ...
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0answers
29 views

Function notation/mapping for this type of functions?

In short, what is the proper function notation/mapping for this type of functions? From Wikipedia regarding maps: In the communities surrounding programming languages that treat functions as first-...
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1answer
28 views

Notation within gaussian function

On our lecture slides we have two different notations of the gaussian function. First it gets introduced as follows: $$p(x_n|\theta) = \frac{1}{\sqrt{2\pi}\sigma}exp\{-\frac{(x_n-\mu)^2}{2\sigma^2}\} \...
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1answer
366 views

Does there exist standardized language-agnostic data structure notation?

I wonder if there exists language-agnostic data structure notation. Preferably a standard, allowing to describe data structures and basic data types. e.g. something like a subset of ...
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1answer
492 views

Convention of a += operator in pseudocode

I have to write some algorithm in pseudocode for a paper. For this I have the "$\leftarrow$" to assign a value. $x \leftarrow y^2$ now I want to write a method which adds to the variable. In ...
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1answer
162 views

What does the notation $ [ i \neq k ] $ mean?

I can't figure out what the notation $[x \neq k ]$ means. Here's a bit of context: The formula is: $Pr[A_i^k = 1] = \frac{[i\neq k]}{|k-i| + 1} = \begin{cases} \frac{1}{k-i+1} \text{ if } i \lt k \\ 0 ...
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2answers
223 views

Same notation/terminology for union of sets and concatenation (Kleene star)?

For the union of sets we use the union operator $\cup$ (or $\bigcup$). And for a concatenation (Kleene star) we also use the union operator. The operations are different, but why the same terminology ...
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1answer
152 views

Is grammar that describes an equation in prefix (Polish) notation always unambiguous?

I recently completed a problem in which I was asked to generate a parse tree for the expression $+ \, 5 \, * \, 4 \, 3$ using the following grammar and rightmost derivation: $$Expr \rightarrow + \, ...
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2answers
55 views

Parentheses after Typing Environment

I've been reading about System F Omega lately, and I keep stumbling across a construct in typing rules that I cannot find an explanation of: Γ(x) = k. For example, ...
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1answer
100 views

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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1answer
35 views

Transformation Function: Gonzalez and Woods

I have been reading Image Processing from Gonzalez and Woods and in the chapter Image Transformation I have come across this equation $$ T \left(u, v\right) = \sum_{x=0}^{M-1} { \sum_{y=0}^{N-1} ...
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1answer
49 views

Why in the code i ≃ n?

i=2; while(i<n) { write('*'); i=i*i; } Why $n ≃ i$? I mean suppose $n=1000$ and so $i= 2,4,16,32,256,65536$ is in every steps. In the book wrote $2^2 ...
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1answer
74 views

Difference between ⫾ (U+2AFE) and ⫿ (U+2AFF) in the context of Dijkstra's Guarded Command Language?

Continuing https://tex.stackexchange.com/questions/435986/how-to-draw-the-box-of-dijkstras-guarded-command-language, what is the difference in the intended usage of ⫾ (Dijkstra choice, U+2AFE) and ⫿ (...
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2answers
138 views

Typesetting LTL in Unicode?

Unicode has an abundance of open circles, diamonds and boxes. Using these, we can typeset linear-time temporal logic formulas such as $$ (\mathop{⬦}ψ)\ \,\land\ \,\mathop{⬦}(θ\ \mathsf{U}\ \mathop{◻}\...
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1answer
89 views

Exact meaning of $2^{\mathcal{O}(f(n))}$

In Sipser's Introduction to the Theory of Computation he uses the notation $2^{\mathcal{O}(f(n))}$ to denote some asymptotic running time. For example he says that the running time of a single-tape ...
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2answers
944 views

Weight functions in graph algorithms

In text books, for instance in the 3rd edition of Introduction to Algorithms, Cormen, on page 625, the weights of the edge set $E$ is defined with a weight function $w:E\rightarrow \mathbb{R}$. Why ...
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1answer
38 views

Asymptotic notation and random variables

I have two random variables $X$ and $Y$ and I want to bound the value of one in terms of the other (for now, I don't care about the actual distribution of their values). Suppose that the two ...
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1answer
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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3answers
64 views

Why is subarray $A[p..k-1]$ empty when $k=p$?

I'm working through a proof of correctness for merge sort. I'm given a loop invariant for a for loop, which makes reference to a subarray $A[p..k-1]$. During the initialization step of the ...
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1answer
31 views

When and what must be present on the left-hand side of the turnstile in metalogics?

Let me show the problem on an example... An actual task from one of the former exams: Consider a simple functional language: $$e::= x|n|e_1e_2|\lambda x.e$$ With typing rules: $$\tau ::= \mathtt{int} ...
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0answers
37 views

Substituting a term for a variable in a context

At this link you can read Nicola Gambino's slides on one way to approach the formal syntax of Martin-Löf dependent type theory. (They are concise and very readable.) On slide 10, he gives a standard ...
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0answers
261 views

What's the difference between Acfg and ALLcfg

In computational theory, and talking about CFGs, Turing Machines, and so forth I haven't a satisfactory explanation or definition for what ATM means versus ALLTM or the same or similar uses with ...
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0answers
62 views

What is this weird gate?

This came from a picture of something that I'm supposed to make, and I can't find it in the program I'm supposed to use (LogicWorks). It looks like it 'not's only one of its inputs, but that doesn't ...
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1answer
38 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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1answer
171 views

Can the notation for polynomial reduction, A ≤p B be reversed in computability theory?

I don't know this is a proper question on this forum but I was reading about computability theory and I saw the reduction concept and its notation like this: $A \le_pB$. I just wanted to know is this ...
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2answers
2k views

Why do ¬, ∀ and ∃ have the same precedence?

I thought the order of precedence of operators and quantifiers was arbitrary, but I don't really understand why those three have the same "strength" in relation to other operators (e.g., ¬ will have ...
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0answers
35 views

Did Menezes et al. switch the letters $\mu$ and $\lambda$ in Floyd's cycle detection note 3.8?

The letters $\mu$ and $\lambda$ are usually used to represent, respectively, the length of the tail of the graph and length of the cycle in the graph. But Menezes on note 3.8, page 91 (or PDF-page 6),...
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1answer
790 views

How I can find all equivalence classes by Myhill-Nerode?

first of all I'm sorry for my bad English and second I'm sorry for my mistakes of understanding the following topic, I still going to school and learning this for interest. The topic is Myhill-Nerode ...
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1answer
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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2answers
67 views

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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10answers
11k views

O(·) is not a function, so how can a function be equal to it?

I totally understand what big $O$ notation means. My issue is when we say $T(n)=O(f(n))$ , where $T(n)$ is running time of an algorithm on input of size $n$. I understand semantics of it. But $T(n)$ ...
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1answer
350 views

What is the meaning of max() in intro. to algorithms?

I'm reading chapter 3(growth functions) of CLRS and in giving an example of proving theta for a standard quadratic function the book gives the following value for $n_0 = 2 \cdot max(|b|/a, \sqrt{|c|/a}...
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2answers
274 views

Clarify the steps: what happened in this mathematical modelling of TSP?

Source: http://examples.gurobi.com/traveling-salesman-problem I don't get this part: (look at the source) $$\sum_{i,j\in\{1,2,3\},i\neq j} x_{ij}=3>2=|\{1,2,3\}|-1$$ I get that $x_{ij}$ is ...
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1answer
232 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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13 views

How to denote a graph class which allows only $k$ instances of a certain induced subgraph?

Suppose that a graph class $\mathcal{C}$ is defined as follows: A graph $G$ belongs to $\mathcal{C}$ if, and only if $G$ is chordal, but has at most $k$ $5$-cycles. I am aware that the ...