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Questions tagged [intuition]

Questions that ask for help building intuition for formal or complex concepts.

45 questions
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Algorithmic intuition for logarithmic complexity

I believe I have a reasonable grasp of complexities like $\mathcal{O}(1)$, $\Theta(n)$ and $\Theta(n^2)$. In terms of a list, $\mathcal{O}(1)$ is a constant lookup, so it's just getting the head of the list. $\Theta(n)$ is where I'd walk the entire…
Khanzor
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Why do we believe that PSPACE ≠ EXPTIME?

I'm having trouble intuitively understanding why PSPACE is generally believed to be different from EXPTIME. If PSPACE is the set of problems solvable in space polynomial in the input size $f(n)$, then how can there be a class of problems that…
user25876
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Is there a more intuitive proof of the halting problem's undecidability than diagonalization?

I understand the proof of the undecidability of the halting problem (given for example in Papadimitriou's textbook), based on diagonalization. While the proof is convincing (I understand each step of it), it is not intuitive to me in the sense that…
user118967
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Rule of thumb to know if a problem could be NP-complete

This question was inspired by a comment on StackOverflow. Apart from knowing NP-complete problems of the Garey Johnson book, and many others; is there a rule of thumb to know if a problem looks like an NP-complete one? I am not looking for something…
Vitaly Olegovitch
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Strategies for becoming unstuck in understanding TCS

I am a graduate student taking a course in theory of computation and I have serious trouble producing content once I'm asked to. I'm able to follow the textbook (Introduction to the Theory of Computation by Michael Sipser) and lectures; however when…
trigoman
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19
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7 answers

What are the characteristics of a $\Theta(n \log n)$ time complexity algorithm?

Sometimes it's easy to identify the time complexity of an algorithm my examining it carefully. Algorithms with two nested loops of $N$ are obviously $N^2$. Algorithms that explore all the possible combinations of $N$ groups of two values are…
Barry Fruitman
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Why larger input sizes imply harder instances?

Below, assume we're working with an infinite-tape Turing machine. When explaining the notion of time complexity to someone, and why it is measured relative to the input size of an instance, I stumbled across the following claim: [..] For example,…
user20
12
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2 answers

What do we gain by having "dependent types"?

I thought I understood dependent typing (DT) properly, but the answer to this question: https://cstheory.stackexchange.com/questions/30651/why-was-there-a-need-for-martin-l%C3%B6f-to-create-intuitionistic-type-theory has had me thinking…
PhD
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11
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3 answers

How to feel intuitively that a language is regular

Given a language $ L= \{a^n b^n c^n\}$, how can I say directly, without looking at production rules, that this language is not regular? I could use pumping lemma but some guys are saying just looking at the grammar that this is not regular one. How…
doniyor
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Turing Recognisable => enumerable

I get the proof of going from an enumerator to a Turing Machine (keep running enumerator and see if it matches input) but I don't see how the other way works. According to my notes and the book (Intro to the Theory of Computation - Sipser), to get…
T. Kiley
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10
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Intuition for convolution in image processing

I have read many documents about convolution in image processing, and most of them say about its formula, some additional parameters. No one explains the intuition and real meaning behind doing convolution on an image. For example, intuition of…
hqt
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How to tell if a language is recognizable, co-recognizable or decidable?

If you have a language L, without doing any proofs, is there a way to tell if it's recognizable or co-recognizable or decidable? Basically any hints or tricks that can be used to tell. Or maybe the common patterns to search for to tell which kind it…
omega
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Elimination rule for the equality type aka J axiom

I'm implementing a interpreter for lambda calculus, and now I want to add the equality type. The introduction rule for it is easy, but the elimination rule is rather obscure for me. I found this stackoverflow thread, but it explains the J axiom only…
盛安安
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Is it intuitive to see that finding a Hamiltonian path is not in P while finding Euler path is?

I am not sure I see it. From what I understand, edges and vertices are complements for each other and it is quite surprising that this difference exists. Is there a good / quick / easy way to see that in fact finding a Hamiltonian path should be…
Lazer
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Visualization of Lamport's three-dimensional "space-time diagram" with introduced "tick lines"

In the third page (the third paragraph in the right column) of the paper "Time, Clocks, and the Ordering of Events in a Distributed System" by Leslie Lamport, it says that The reader may find it helpful to visualize a two-dimensional spatial…
hengxin
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