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

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2
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3answers
53 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 ...
0
votes
0answers
19 views

Is this algorithm an approximation algorithm?

Let us say that we have a maximization problem $P(n)$ that is NP-hard, where $n$ is the input size. We have found a polytime algorithm that finds a solution $SOL$ to $P(n)$ that is bounded as follows: ...
1
vote
2answers
63 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 $B$ ...
3
votes
1answer
44 views

What does the $\leq_{\mathrm{P}}$ symbol mean?

What does $\leq_{\mathrm{P}}$ mean? Is it supposed to mean less than or equal polynomial time?
0
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1answer
31 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- ...
3
votes
2answers
116 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....
1
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1answer
35 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 ...
0
votes
1answer
47 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. <...
1
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1answer
54 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 ...
1
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1answer
42 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 ...
3
votes
2answers
61 views

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 ...
1
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1answer
29 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 ...
1
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2answers
88 views

How do I interpret this divide and conquer algorithm for removing duplicates in a list?

Consider the following divide and conquer algorithm to remove duplicates in a list. The text is in French. What is the meaning of the variables $c1, c2, d1, d2$? Why are only the variables $c1, d1$ ...
4
votes
1answer
167 views

What does ⊢ mean in operational semantics?

I have been reading a couple of texts on operational semantics. In [1], the evaluation of expressions is done as in this rule: $\frac{<e_1,s>\;\Rightarrow \;n_1\;\;\;<e_2,s>\;\Rightarrow ...
1
vote
2answers
63 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?
2
votes
0answers
31 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 ...
0
votes
1answer
36 views

Question on interpreting logical notation, relating to alphabets, theoretical comp sci

$\exists x \in \Sigma^* (t=sx)$ Have I interpreted the above into words correctly?: "There exists a symbol 'x', which is a member of the set which contains all possible strings of alphabet sigma, ...
3
votes
1answer
45 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
106 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
68 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
142 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
66 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
213 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 1993,...
44
votes
2answers
6k views

Order of growth definition from Reynolds & Tymann

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
30 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
41 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
60 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
56 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
28 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
30 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
31 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 ...
1
vote
1answer
58 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
26 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 $...
-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: http://...
1
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1answer
49 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
97 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
24 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 ...
10
votes
3answers
1k 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
97 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 $\Theta\...
3
votes
2answers
268 views

Expressing that a function converges to 1 with linear rate using Landau notation

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
85 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 $\epsilon=\omega\left(\...
0
votes
2answers
448 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
71 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
32 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
124 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, ...
4
votes
1answer
113 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
63 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) ...