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

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3
votes
1answer
39 views

What is the origin of using Q to denote a set of states in an automaton?

When talking about DFAs and NFAs as 5-tuples, it's common to use the letter $Q$ to denote the set of states in the automaton and to denote individual states with names like $q_0$, $q_1$, etc. Is ...
1
vote
1answer
103 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 ...
0
votes
0answers
54 views

What does an = sign with an x beneath it mean?

I am studying for a test in Logic right now, and saw the symbol $\underset{x}{=}$, which is used like this: $I \underset{x}{=} I'$. I've seen it in the solutions of questions like this one: Prove ...
3
votes
5answers
115 views

What is the difference between $\log^2(n)$, $\log(n)^2$, $(\log n)^2$, $\log (n^2)$ and $\log \log n$?

In research articles (e.g. this one's abstract), I often see the complexity of an algorithm expressed using a somewhat ambiguous notation: $\log^2(n) = ?$ $\log(n)^2 = ?$ $(\log n)^2 = (\log(n)) ...
1
vote
1answer
53 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 ...
8
votes
1answer
168 views

What does up arrow ($\uparrow$) mean in pseudocode?

I'm learning vantage point trees, and I met this while reading the paper Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces by Peter Yianilos (Proceedings of SODA ...
38
votes
3answers
6k views

Not sure if there is a mistake in a computer science book or if I am misunderstanding something

I am reading a book called Principles of Computer Science (2008), by Carl Reynolds and Paul Tymann (published by Schaum's Outlines). The second chapter introduces algorithms with an example of a ...
0
votes
1answer
22 views

There is any notation for a language that is empty infinite?

Assume that $L$ is a language, is there any established notation that means that $L$ is infinite or empty?
1
vote
1answer
28 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 ...
0
votes
3answers
36 views

Difference in having * inside vs outside of brackets for NFA

If you have a question saying "draw the NFA for the following language" what difference does it makes if the language is $(0^* \cup1^*)$ vs $(0 \cup1)^*$ in otherwords what difference does it make for ...
2
votes
1answer
56 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?
1
vote
1answer
55 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 ...
0
votes
1answer
26 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 ...
1
vote
1answer
17 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 $i$ ...
2
votes
1answer
24 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 ...
1
vote
1answer
20 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 ...
-1
votes
1answer
25 views

Clarification notation in CLRS runtime analysis

I am learning algorithms from the clrs book. I am having trouble understanding the notation the book has placed. The book wrote the following: $t_j$ denote the number of times the ...
0
votes
1answer
54 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? ...
2
votes
1answer
25 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 ...
-1
votes
1answer
43 views

Notation: $L_R = \{w\#y\space|\space R(w,y)\}$?

What is the set $$L_R = \{w\#y\space|\space R(w,y)\}$$ Specifically what kind of conditional is $R(w,y)$? Also what's the purpose of $\#$? This comes from page 2 of the Clay paper on P vs NP: ...
0
votes
1answer
48 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 ...
2
votes
1answer
91 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
votes
0answers
19 views

Properties of Reverse Polish Notation expressions that are algebraically invariant

The RPN expressions a b + c * and f d e + * are algebraically equivalent, though the names of the variables are different ...
9
votes
3answers
848 views

What is the purpose of using NIL for representing null nodes?

In my Algorithms and Data Structures course, professors, slides and the book (Introduction to Algorithms, 3rd edition) have been using the word NIL to denote for ...
3
votes
2answers
93 views

Combining these two results into one asymptotic notation

Assume you have two parameters, $N \gg 1$ and $\epsilon < 1$. I have an algorithm (and matching lower bounds) that runs in $\Theta(\epsilon^{-1}+\log N)$ for $\epsilon > N^{-1}$, and ...
3
votes
2answers
261 views

Landau notation for functions whose limit is 1 (should big-Oh or big-Omega be used?)

I am working on an algorithm which approximates a certain optimal quantity. The approximation becomes better when the size of the problem ($n$) becomes larger: the difference from the optimum is ...
2
votes
3answers
83 views

Notation for asymptotic bounds on both sides

I am writing my first paper, and one of the results can be written as follows: For any $W,\epsilon$ such that $\epsilon = o\left(\frac{\log^4 W}{W\log\log W}\right)$ and ...
0
votes
2answers
176 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 ...
2
votes
1answer
70 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: ...
3
votes
1answer
31 views

How to state that a complexity bound does not depend on a given parameter size?

I am often ill at ease with Landau (Big O) notation, because it seems often to be abusing mathematical notation. The best example is the use of the equal sign to express a set membership. And this can ...
5
votes
4answers
112 views

Can I use ellipses in first order logic

I ask, because I have to come up with a first-order logic sentence that shows that there are exactly N objects in the universe. What I've been able to come up with is: $$ \forall x \; \exists y_1, ...
3
votes
1answer
89 views

type theory notation troubles

I'm working through "Types and Programming Languages" by Benjamin Pierce and I don't quite understand the notation. Particularly on Page 106, (chapter 9 Simply Typed Lambda-Calculus) there is a lemma ...
1
vote
2answers
62 views

Is there a generally agreed short notation for “a points to b”

Is there a conventional symbol for "points to" or "is a pointer to". I've been using a short right arrow; for example "a is a pointer to b" would be (approximately) ...
3
votes
1answer
43 views

What does does $O$ mean in this context?

I understand big O notation in computational complexity theory, but I don't see how it applies in the equation below. From Pattern Recognition and Machine Learning: If we weren't familiar with ...
3
votes
2answers
78 views

Differences in Postfix Syntax

A question about postfix/RPN came up in my class due to the current ACSL competition. Is it a rule or convention that 4 + (5 * 6) in infix is written 4 5 6 * + in postfix, as opposed to 5 6 * 4 + in ...
0
votes
1answer
86 views

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 ...
0
votes
1answer
117 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 ...
2
votes
2answers
244 views

What is a conventional format for presenting algorithms?

I'm writing a technical paper and the review committee wants my methodology to be represented in a conventional algorithm format. I've been searching all over the web for the conventional structure ...
3
votes
1answer
71 views

Hierarchy of complexity classes $\bigcup_{c > 0} \mathrm{Time}(2^{c \log^k n})$, w.r.t. $k$

This is a true/false question: For each integer $k > 1$, define the complexity class $\sf QP_k := \bigcup_{c > 0} Time(2^{c \log^k n})$. Then for all integers $k > 1$, $\sf QP_k ...
0
votes
1answer
15 views
4
votes
1answer
89 views

Determining Number of States in a Turing Machine

I am looking at an example Turing machine in my textbook, Automata and Computability by Dexter C. Kozen, and I'm confused as to how they determine the number of states this particular machine has. ...
0
votes
1answer
123 views

Principles of Programming Languages: Understanding Judgements

I am taking a principles of programming languages class right now and am trying to understand the following judgement form. ...
6
votes
1answer
94 views

Use of Big O Notation in a recent paper by Khot et al

I'm reading a paper about Constraint Satisfaction Problems, specifically "A Characterization of Strong Approximation Resistance", Subhash Khot, Madhur Tulsiani, Pratik Worah (ECCC TR13-075). The ...
4
votes
1answer
246 views

Can a Big-Oh time complexity contain more than one variable?

Let us say for instance I am doing string processing that requires some analysis of two strings. I have no given information about what their lengths might end up being, so they come from two distinct ...
3
votes
2answers
69 views

Origins of misconception about using equality signs with Landau notation

From "Misconception 1" from Søren S. Pedersen's blog, and as many have seen before, a major misconception in Big-O (and others) notation is to say a function is "equal" to Big-O of some other ...
1
vote
1answer
56 views

What does superscript + mean in relational algebra?

What does superscript + mean in relational algebra? Suppose $A$ is a subset of attributes of all attributes in a relation $R$. What does $A^+$ mean?
4
votes
1answer
62 views

In type systems, is there a name for SQL's way of cutting and combining record types into new types?

I'd like to have this feature in my application programming language (which these days, is Scala), but when I went to learn more about it on the internets, I realized I don't know the name of it. I'm ...
3
votes
1answer
126 views

Notation for average case complexity of an algorithm

I'm just wondering what the correct notation is when referring to an average case complexity of an algorithm that was calculated by doing empirical analysis. For example, I have tested my algorithm ...
0
votes
0answers
31 views

What are these notations O(1)/O(n)/O(log n)? [duplicate]

I am a newbie here I recently read tutorials on java about collection framework. The time complexity of various objects in reading/writing data What does it mean? ...
1
vote
0answers
86 views

Correct mapping “update” notation for computer science papers

A nice easy one. I'm interested to know the most standard and accepted way to denote the update of a mapping in the context of a theoretical computer science paper. By example, suppose we have a ...