Questions tagged [notation]

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

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Meaning of , and ; in relation to defining context

I have seen use of , and somewhere use of ; when defining context : $$\dfrac{\phi \ , \ \Gamma \ \vdash } {} $$ somewhere else i have seen : $$\dfrac{\phi \ ; \ \Gamma \ \vdash ...
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1answer
641 views

What does > mean in this TAOCP solution?

For our assignment we have to implement a solution given to one of the problems in The Art of Computer Programming by D.E. Knuth (Ex24; Chapter 5: Sorting; TAOCP, Vol3, 2nd). However, I fail to ...
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1answer
115 views

Equivalent expression in English: Set Notation $\{0,1\}^K$

I am overviewing this expression given in set notation. Could someone translate what M "Element of" $\{{0,1}\}^k$ stands for? Im looking for an explanation in English like what I did below. $K_e = \...
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1answer
60 views

What does $\mathbf{Q}^+$ mean in approximation texts?

Often, in a lot of texts concerning approximation algorithms I see the following notation (for example, here in page 19 of the PDF or the first page of the introduction): ... and a cost function on ...
2
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1answer
8k views

What's the difference between the concatenation and union of symbols within a language

I feel like I'm confusing myself perhaps but I'm having a bit of trouble figuring out how exactly this language works. I'm given the following regular expression (a + b)* (abba* + (ab)*ba) Can ...
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1answer
74 views

Meaning of $\stackrel{*}{\rightarrow}$ production rule?

I've seen the production rule $\stackrel{*}{\rightarrow}$ in some papers concerning regular languages. What's the meaning of $\stackrel{*}{\rightarrow}$ production rule?
2
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1answer
75 views

Is this a standard representation of a 'space' character?

I recently came across a handwritten note with directions to push a string of text into a database. There was a strange character in the string I've never seen before, a lower case 'b' with a forward ...
2
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1answer
132 views

What does $|w|$ mean in the statement “ $|w|$ where $w \in L \subset \Sigma^*$”?

In my assignment I find these symbols: $|w|$ where $w \in L \subset \Sigma^*$ I believe it means the lexikografic value of a word, but I am not 100% certain. Let me phrase my question this way: ...
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3answers
99 views

Is there a standard (common) notation for the following operation on binary strings?

Typically, we use the notation $S = \{0, 1\}^n$ to denote the set of all $n$-bit strings. Suppose that I wanted to extract a subset of the strings where certain bits have some fixed values. For ...
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1answer
391 views

Short notation for Turing machine configurations

I'm writing about Turing machines and often need to denote the tape. I'm using exponential tapes, i.e. a repetition count for each symbol. I usually use something similar to $(x_k^{e_k})_{1 \leq k \...
2
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1answer
27 views

Notation for field access in Algorithm

While writing array index in an algorithm $a[i]\gets v$ is conventionally used. Is the notation $a_{i}\gets v$ also used ? If the algorithm uses struct or ...
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1answer
88 views

What is the standard notation for introducing syntactical formalism in a paper

Suppose you want to introduce a format for a language, commands, ... etc. (Specially in the filed of computer science) in a paper for example something like below: ...
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1answer
2k views

What does the R superscript notation mean in regular/formal languages?

What does the capital R superscript notation mean in regular languages? I am working on a homework assignment and don't recall my professor mentioning what the what the R superscript means. For ...
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1answer
60 views

What do the commas separating atomic events in a Relational Calculus formula means?

For instance, take the example of this book here on page 30. About the formula $$ Q(x,x') = R(x), S(x,y), S(x',y), R(x') $$ described there, what do the commas mean? Is it the same as an "and" ...
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2answers
47 views

Help on the notation of the 2-bit operation: $\frac 12{(I+Z_1Z_0)}$

This was adapted from Quantum Mechanichs for Computer Scientists. On this equation, we have $I$ representing the identity operator, with $Z$ being defined for 1 bit as: $$ Z|0⟩ = |0⟩, \quad Z|1⟩ = -|...
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1answer
56 views
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1answer
156 views

How to denote the space complexity in terms of output

Normally the space complexity of an Algorithm $A$ is denoted $\textrm{SPACE}(A)$, which means how much space is needed by the computation itself. I would however like to also describe how much storage ...
2
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1answer
24 views

What does $\alpha_r\supset\beta_r$ mean in the tolerance definition of System Z?

I'm reading up on System Z introduced by Judea Pearl (in System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning). A central definition is that of tolerance of a ...
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1answer
22 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: $$\...
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1answer
189 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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2answers
31 views

Can I notate time complexity depending on the result of an algorithm?

I have a program that calculates the first year some two events happen on the same day. I have not calculated any upper limit for the year. The time complexity of the program would be equivalent to O(...
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1answer
38 views

Meaning of ⟨_⟩ in the context of verifiers

A verifier for a language A is an algorithm V, where $$A = \{w \mid V \text{ accepts $\langle w,c \rangle$ for some string $c$}\}$$ ($c$ is called a certificate or proof) What's the definition of $\...
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0answers
209 views

Why mantissa and exponent are stored differently in a float?

As we know, in IEEE 754 standard, float number's exponent and mantissa are stored differently. While the exponent is stored as an unsigned number, taking advantage of the bias, the mantissa is in sign-...
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0answers
323 views

Explaining TM notation in Lewis/Papadimitriou

I was working on some questions in the book "Elements Of The Theory Of Computation", by Lewis and Papadimitriou, and I need help with one question - question 4.1.8 (chapter 4): Give the full ...
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0answers
38 views

Where, besides Scheme reports (RnRS) has Stoy's notation for auxiliary semantic functions been used?

The denotational semantics of R4RS, R5RS and R7RS Scheme (included in the language report) uses the same notation that was used by J. E. Stoy in his book, "Denotational Semantics: the Scott-Strachey ...
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5answers
274 views

“Smallest set” term in the trees set definition

I often meet such kind of the definition of the set of trees, as: The set of unranked $\Sigma$-trees, denoted by $T$, is the smallest set of strings over $\Sigma$ and the parenthesis symbols ‘)’ and ‘...
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2answers
199 views

Set notation of the set of all strings

How do I present the complement using set notation? I guess it has to be shows with universal set - {aa,bb} but I do not know how to represent the universal set in ...
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2answers
9k views

Operator precedence in propositional logic

there is some kind of priorities for the elements in propositional logic ? for example : p ∧¬q → r , given this ,we there may be two options (p ∧¬q) → r OR p ∧ (¬q → r) , which one is the correct ?...
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1answer
79 views

Does big-Oh notation in optimization follow the same convention as in CS?

I first learned big-Oh (little-Oh, big-Theta.....) complexity for growth of functions using CLRS in a computer science class. Now I am doing a project on optimization. In our optimization class, we ...
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2answers
398 views

How to denote an array in writing paper

How can I represent an array when I am writing to show an algorithm in writing paper. Like Pi is represented by Greek letter. We use that Greek symbol to denote the value of Pi, Kind of like a pointer....
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2answers
456 views

Why are Complexity Notations Called Asymptotic?

Why do we use the term "asymptotic" in complexity. Although I know what an asymptote is, but what is an asymptote doing here?
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1answer
59 views

what is the 'x :=' part mean in a hoare triple?

In Hoare logic, there's a thing called a Hoare triple, e.g.$$ \begin{array}{ccccc} \{x = 2\} & & x := x+1 & & \{x = 3\} \end{array}. $$ What does '$x :=$' mean?
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2answers
86 views

What does $\cdot$ mean as a notation with complexity classes?

In the wikipedia page for Toda's Theorem, the notation $A\cdot B$ is used where $A$ and $B$ are two complexity classes, but without explanation as to its meaning. SO given two classes $A$ and $B$ ...
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1answer
57 views

If c ∈ Σ denotes terminals, then is Y = Σ∖{c} the set of non-terminals?

If $c\in \Sigma$ denotes terminals, then is $Y=\Sigma \setminus \{c\}$ the set of non-terminals? These notations are used here, p. 379. But I cannot find their definitions. So what I'm asking is, is ...
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2answers
61 views

Is $n^3$ an asymtotically tight bound of $(n^{2.99}).(\log_2n)$? How? [duplicate]

Is $n^3$ an asymtotically tight bound of $(n^{2.99}).(\log_2n)$? If so then how?
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1answer
40 views

What does it mean the norm symbol applied to a concept?

I'm reading this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.14 or http://www.jmlr.org/papers/volume10/kontorovich09a/kontorovich09a.pdf On page 1101 are introduced 2 functions ...
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1answer
302 views

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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1answer
51 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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1answer
61 views

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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1answer
121 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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1answer
57 views

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 ...
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1answer
55 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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1answer
28 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
54 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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1answer
110 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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1answer
59 views

$\tilde \Omega$ for division by logarithmic factor

Is $\Omega \left(\frac{n}{\log{n}} \right)\subset \tilde\Omega(n)$?
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1answer
118 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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1answer
288 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 ...
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1answer
153 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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1answer
59 views

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 ...