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Precise definition of a brute force algorithm

What is the precise definition of a brute force algorithm? Is it one that simply has non-polynomial runtime?
Geremia's user avatar
  • 152
1 vote
1 answer
33 views

Seeking a reference for NP-hardness of optimization problems

Most optimization textbooks do not cover the concept of NP-hardness. Some examples include: "Convex optimization" by Boyd and Vandenberghe "Numerical Optimization" by Nocedal and ...
Fraïssé's user avatar
  • 821
0 votes
0 answers
21 views

Why do the authors use the 'trigraph' to characterize some class of graphs?

I have read the series of papers about "the structure of claw-free graphs" (https://doi.org/10.1016/j.jctb.2008.03.002). Here the authors used the trigraph, that is the adjacency relation ...
Hanchun Yuan's user avatar
1 vote
1 answer
60 views

What is a heuristic in human computer interaction?

I have found multiple definitions of what a heuristic is, and I have found multiple computer science-related definitions. In my university course, the lectures cite the Nielson Norman Group defining a ...
Eris's user avatar
  • 13
0 votes
1 answer
67 views

Definition of the term "small systems" in computer science

What is the definition of the term "small systems" in the context of computer science? My professor didn't really define the term, they just gave examples of some small systems. I'm having a ...
Sega dude's user avatar
  • 101
0 votes
2 answers
89 views

What is the right name for a "map" data structure?

I'm trying to say this in my paper: "$M$ is a key-value store, where 1) all keys are unique, 2) $k \in M$ means that the $k$ key exists in the store, 3) $M + (k, v)$ is a new store equal to $M$ ...
yegor256's user avatar
  • 113
3 votes
1 answer
84 views

Are two regularity properties on hypergraphs equivalent?

Let $H=\left( E_0 ,E_1 ,E_2 , \ldots , E_d \right)$ be a $d$-dimensional full-hyper graph/complex. That is to say, if for some $i\in \left[d \right]$ the hyper-edge $e_j \in E_i$ than for any $i-1$-...
Benicio Agüero's user avatar
2 votes
2 answers
147 views

Alternate definition of recursively enumerable languages

Exercise 9.2.3(c) of the book by Hoffman, Motwani, Ullman states In fact a definition of the RE-but-not-recursive languages is that they can be enumerated but not in numerical order How do we show ...
muser's user avatar
  • 150
0 votes
4 answers
517 views

What is a procedure?

Non-computer scientist here, trying to understand what SICP (Structure and Interpretation of Computer Programs) means by a procedure, whether it matches the dictionary definition, and also how a ...
Piovezan's user avatar
  • 113
1 vote
1 answer
122 views

formal definition for "data type with larger range"

Wikipedia defines range of data type: the set of possible values that that variable can hold. Suppose we have two data types A and B. Now, with attention to the ...
hasanghaforian's user avatar
0 votes
1 answer
70 views

What's the difference between computation and symbolic manipulation?

I have lived my academic career thinking these two terms were interchangeable but something arose in me that said they're distinct. Are there any logical, formal definitions distinguishing between the ...
Fomalhaut's user avatar
1 vote
2 answers
152 views

Formal definition of algorithm runtime

In the analysis of algorithms textbooks that I've seen, as far as I could tell, the runtime of an algorithm is defined intuitively. Is there a simple formal definition of this concept? I.e. a ...
user56834's user avatar
  • 3,892
0 votes
0 answers
166 views

Definition of the term "access efficiency" in the context of computer systems

In a two-level virtual memory, the memory access time for main memory, $t_M=10^{−8}$ sec, and the memory access time for the secondary memory, $t_D=10^{−3}$ sec. What must be the hit ratio, $H$ such ...
Abhishek Ghosh's user avatar
1 vote
1 answer
72 views

Probabilistic Turing Machine Transition Relation vs Transition Function

In wiki, PTM are defined with two transition functions and a fair coin toss which determines which one is used at each step. One can also define them, much like NDTM, using a transition relation where ...
José Duarte de Azevedo e Cunha's user avatar
2 votes
0 answers
50 views

Regarding the definitions of time-constructible functions on Wikipedia

I am reading the Wikipedia article on time-constructible functions and got confused by its definitions, given as follows: There are two different definitions of a time-constructible function. In the ...
3nondatur's user avatar
  • 457
0 votes
1 answer
48 views

Same instances for different problems

According to the formal definition of an instance, it is a set of input data containing the values of the parameters of some problem (What is an instance of NP complete problem?). So, two problems may ...
Stencil's user avatar
  • 103
0 votes
2 answers
49 views

What's the error about the definition of NP?

Many sources (including Wolfram's MathWorld) say that NP problem is defined as a decision problem "verifiable in nondeterministic polynomial time" (check Google to see more sources). But ...
porton's user avatar
  • 493
2 votes
2 answers
740 views

What defines how many lookahead a lexer has?

if a lexical grammar has multiple token which start with the same character like > >> ...
noamin's user avatar
  • 21
0 votes
1 answer
74 views

Having trouble understanding blatantly non-private definition because of Little-o notation

I was pretty confident that I understand asymptotic notation until now. However, I am having a hard time understanding some basic definition that use asymptotic notation, specially little-o. ...
Henry's user avatar
  • 3
1 vote
0 answers
49 views

Language of all words of the form $ww$ is in $\mathsf{NTIME}(n)$

Show that the language $\{ ww \mid w \in \{0,1\}^* \}$ is in $\mathsf{NTIME}(n)$. I have a doubt first of all how can I prove that. Secondly, what does NTIME mean? Can we use a $k$-Tape Turing ...
Aman Shaikh's user avatar
1 vote
1 answer
108 views

Can inputs in the decision tree model be computed?

The Wikipedia definition of the decision tree model says that it allows the sign functions of certain classes to be computed in constant time (and presumably also memory). My questions, still ...
ByteEater's user avatar
  • 115
2 votes
1 answer
55 views

On the definition of Error-Correcting Codes

Let us start with the following well-known definition: Definition 1. Let $C\subseteq A^n$ be a code over $A$ and let $t\in \Bbb Z^+$ be a positive integer. We say that the code $C$ is $\boldsymbol t$...
Chris's user avatar
  • 123
0 votes
1 answer
40 views

Isn't an improper subset of edges of a cyclic graph, cyclic and thus not a minimum spanning tree?

This is the formal definition of a minimum spanning tree taken from Algorithms by Dasgupta, Papadimitrious and U. Vazirani. Input: An undirected graph $G = (V,E)$; edge weights $w_e$. Output: A tree $...
heretoinfinity's user avatar
0 votes
2 answers
86 views

PRECISE DPLL algorithm definition

I am confused about the precise definition of the DPLL algorithm. Various sources tend to define DPLL differently: In pages 110-114 of the book Handbook of Satisfiability(Editors: Biere, A., Heule, M....
Nice_weather's user avatar
1 vote
1 answer
41 views

Equivalene of big O definitions (Limit Definition $\Longleftrightarrow$ Quantifier Definition)

I need to proof, that both definitions of the Big 0 notation are equiavlent, but I am not sure if my proof works both ways of the equivalence. Definitions: Let f,g be functions. $f(n)\in \mathcal{O}(...
Florian Bauer's user avatar
2 votes
1 answer
206 views

What is the difference between Hamming Distance and Manhattan Distance for non-binary data?

What is the difference between Hamming Distance and Manhattan Distance for non-binary data (specifically I am comparing points in $\mathbb{R}^2$)? I understand Manhattan sums the absolute difference ...
John D's user avatar
  • 123
0 votes
0 answers
30 views

How isolate the last bit work on teory Binary Indexed Trees

I'm learning about the Binary Indexed Trees, and I understand how it works, but I'm interested in the theory that there is behind! In particular, I don't understand what is meant the following ...
macros's user avatar
  • 45
2 votes
1 answer
149 views

Why are $L$-reductions defined the way they are?

I was reading about $L$-reductions and there was one part in the definition that I thought was interesting. I wanted to know what motivated people who came up with it to have it included in the ...
mursalin's user avatar
  • 413
1 vote
0 answers
43 views

A genral Turing model with one tape to define sublinear space (L,NL,..)

A genral Turing model with one tape to define sublinear space (L,NL,..) Normally to define sub-linear space complexity we need special Turing models with many tapes, at least two: a read-only tape and ...
rl1's user avatar
  • 243
4 votes
0 answers
93 views

Understanding the Transition points of a BST

I'm trying to understand the definition of Transition point of a BST, as given in Demaine, Erik D., et al. "Dynamic optimality-almost." SIAM Journal on Computing 37.1 (2007): 240-251 ...
Margaret Bloom's user avatar
2 votes
2 answers
591 views

Definition of NP-hardness for non-decision problems

As I understand, the term "NP-hardness" is applicable when we also talk about optimization or search problems (i.e. return the satisfying assignment for 3-SAT). How do we formally define NP-...
user avatar
1 vote
1 answer
304 views

Nondeterministic polynomial time algorithm versus certificate/verifier for showing membership in NP

In this paper (https://arxiv.org/pdf/1706.06708.pdf) the authors prove that optimally solving the $n\times n\times n$ Rubik's Cube is an NP-complete problem. In the process, they must show that the ...
Atsina's user avatar
  • 113
1 vote
1 answer
137 views

A question regarding definition of Deterministic Subexponential Time (SUBEXP)

First Look at the definition of SUBEXP from Complexity Zoo: SUBEXP: (Deterministic Subexponential-Time) The intersection of DTIME($2^{n^\epsilon}$) over all $\epsilon$>0. (Note that the algorithm ...
user777's user avatar
  • 729
0 votes
1 answer
247 views

Sets in Mathematics are immutable but in Computer Science sets are mutable and called "Dynamic Sets" - truth of the statement

While reading the classic text Introduction to Algorithms by Cormen et. al. I came across the following claim: Sets are as fundamental to computer science as they are to mathematics. Whereas ...
Abhishek Ghosh's user avatar
0 votes
1 answer
198 views

Clarifying statements involving asymptotic notations in soln of $T(n) = 3T(\lfloor n/4 \rfloor) + \Theta(n^2)$ using recursion tree and substitution

Below is a problem worked out in the Introduction to Algorithms by Cormen et. al. (I am not having problem with the proof but only I want to clarify the meaning conveyed by few statements in the text ...
Abhishek Ghosh's user avatar
1 vote
1 answer
77 views

When does a Monte Carlo algorithm solve a problem?

When can we say that a Monte Carlo algorithm solves a problem? To quote from Wikipedia on Monte Carlo algorithms For instance, the Solovay–Strassen primality test is used to determine whether a ...
3nondatur's user avatar
  • 457
18 votes
11 answers
5k views

Why do logic gates behave the way they do?

I am a Software Developer but I came from a non-CS background so maybe it is a wrong question to ask, but I do not get why logic gates/boolean logic behave the way they do. Why for example: ...
aldokkani's user avatar
  • 317
0 votes
1 answer
245 views

Formal definition of hash function

I was reading through the classic CLRS with the intention of reviewing the hash tables theory, more specifically the hash function definition I just wanted a reference to quote. I cannot find a ...
user8469759's user avatar
1 vote
1 answer
906 views

Difference between task and process

I'd like to know which is the difference between a task and a process in computer science. I'm studying a course on real-time systems and there are some definitions that I don't know. Thank you in ...
Gennaro Arguzzi's user avatar
3 votes
0 answers
51 views

What is the name of visiting an array starting at first element, then last element, then second, then last but one, then third, etc

For example if I have an array [0, 1, 2, 3, 4, ..., n] and I want to iterate over it in an order like ...
Azat Ibrakov's user avatar
1 vote
0 answers
45 views

Randomized version of the class $APX$?

Is there a class which is to APX what BPP is to P? I'm looking for a definition that is like the following: "For $r > 0$, an $r$-RPCA (randomized polynomial-time constant-factor approximation) ...
Elle Najt's user avatar
  • 374
7 votes
3 answers
2k views

Simple cycles of length two in an undirected graph

Pedagogical question. Background A cycle in a graph can be defined as a sequence of vertices $v_1,\dots,v_n$ with $v_1=v_n$ such that, for each $i \in \{1,\dots,n-1\}$, the graph has an edge $(v_i,...
usul's user avatar
  • 4,129