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Questions tagged [computability]

83 questions
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Are there any Recursively Enumerable problems that are not RE-hard?

The computability class that I'm taking explains several languages that are in RE - REC (recursively enumerable but not recursive, i.e. solvable by a non-halting turing machine). It first shows how one of them (L_d, language of turing machines…
bmzhao
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Can a Turing machine perform Quicksort?

As far as I know, a Turing machine can be made to execute loops or iterations of instructions encoded on a Tape. This can be done by identifying Line separators and making the Turing machine go back until a specific count of Line separators is…
learner
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Is it possible to create an algorithm which generates an autogram?

An autogram is a sentence which describes the characters it contains, usually enumerating each letter of the alphabet, but possibly also the punctuation it contains. Here is the example given in the wiki page. This sentence employs two a’s, two…
Lou
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Security of Exclusive-OR (XOR) encryption

XOR encryption is known to be quite weak. But how weak is it if I have a key that is made up of multiple keys of different (ideally prime) lengths which are combined to make a longer key. eg I have a text keys of length 5, 9 and 11. If I just apply…
El Ronnoco
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To prove something is NP-hard, why do you need to reduce to it from an NP-complete?

From wikipedia: A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H (i.e., L ≤ TH). Why does the problem(call it W) being reduced from need to be NP-complete? Why can't it just…
UnknownGuy
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HaltingProblem in Agda?

I am working through a paper trying to implement their Haskell code in Agda. They want to formulate the halting problem by saying let bot be a program such that for any data type a: bot :: a bot = bot They go on to define data S = T so the…
user2154420
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Template Metaprogramming: Primitive Recursive?

In this article, the writer asserts: ...the program did show that the template instantiation mechanism is a primitive recursive language that can perform nontrivial computations at compile time. I found this rather interesting, as I help to teach…
Dan M. Katz
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Make the assumption that P = NP

Suppose P = NP, would that mean that Hamiltonian-Cycle is no longer NP-Hard? Hamiltonian-Cycle is a language where a given graph G contains a Ham-Cycle.
user7821248
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Why is chess, checkers, Go, etc. in EXP but conjectured to be in NP?

If I tell you the moves for a game of chess and declare who wins, why can't it be checked in polynomial time if the winner does really win? This would make it an NP problem from my understanding.
rb612
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Can rebol parse function be able to create rules for parsing css2 / css3 fully?

Are there limitation to rebol parse function power ? Would it be capable of parsing the whole css2 / css 3 spec or will it encounter theorical impossibility to form some rules ? Update after HostileFork answer: I mean in regexp I think it would be…
Rebol Tutorial
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Does there exist an algorithm that can solve Vim Golf problems

Is it possible to create an algorithm to solve Vim-golf problems? For those not familiar with what that is, you are given two different blocks of text, and must transform the first block into the second using the lowest possible number of keystrokes…
Andrew
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NFA Acceptance Confusion

I'm on a senior level theory course, majoring in Computer Science, and was tasked with designing an NFA. If I'm not mistaken, an NFA accepts an input if any path within the NFA can take the string and get to an accepting state. I understand and can…
pcd13
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Complex behavior generated by simple computation

Stephen Wolfram gave a fascinating talk at TED about his work with Mathematica and Wolfram Alpha. Amongst other things, he pointed out how very simple computations can yield extremely complex behaviors. (He goes on to discuss his ambition for…
Yuval Adam
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program to reproduce itself and be useful -- not a quine

I have a program which performs a useful task. Now I want to produce the plain-text source code when the compiled executable runs, in addition to performing the original task. This is not a quine, but is probably related. This capability would be…
Ben
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Can we assure a strictly decreasing function is computable?

I've been assigned to solve an exercise that questions the following: Suppose a function f: N->N that is strictly decreasing. Can we assure f is computable? So far I've found that all non-increasing functions are computable but this isn't an valid…
Pol
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