# Questions tagged [definitions]

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### 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. ...
17 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 ...
16 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 ...
31 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 $\boldsymbol t$...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
445 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-...
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### Informal definition of a safety property

Could someone kindly explain why safety properties are commonly informally described as "something bad never happens"? This doesn't seem accurate at all. Rather, it seems that one should say ...
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### 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 ...
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### 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 ...