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Questions tagged [computability]

83 questions
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Computability: SAT Formula with Bounded Number of Clauses

Define SAT2016 = {\phi | \phi is a CNF formula with at most 2016 clauses}. Assuming P \neq NP, is SAT2016 NP-complete? Since the number of literals in each clause isn't bounded, it's not immediately clear whether there exists a polynomial time…
Spitzi Spitzi
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What is the simplest cellular automaton that simulates simple particle physics?

Mind the following particle physics animation: var atoms = [{pos:10, vel:1.2913513}, {pos:20,vel:0}, {pos:24, vel:-2}, {pos:60,vel:0}, {pos: 60, vel:0}]; setInterval(function(){ var has_atom = {}; for (var i=0, l=atoms.length; i
MaiaVictor
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Can a program decide whether an arbitrary program halts for SOME input?

Is there a program (may-halt? p) that can tell whether there exists an input so that (p input) halts? I tried simple diagonalization, but it only tells me that (may-halt? diag-may-halt) must be true. It doesn't help proving whether the program…
Larry
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Ways to measure bit sequence complexity

I'm looking for a simple way to estimate the complexity of a sequence of bits of a fixed size (probably a maximum of length 10). For example, I imagine 0000000 and 111111 aren't very complex at all, but 101010 and 101101 sit elsewhere on the…
Psyche
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Java Programming Method Overloading

First time posting here sorry about the format. public static void main(String args[]) { float x, y, z; System.out.println("Enter two integers to calculate their sum "); Scanner in = new Scanner(System.in); x =…
user28894
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Recursively enumerable (computably enumerable) languages closed under permutation?

If L is any language. The language perms(L) is the language of all permutations of words from L. True or False: If L is recursively enumerable (computably enumerable), then perms(L) is also recursively enumerable. This was on a previous final along…
user3688391
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Turing Machines and Lambda Calculus equivalence

I am wondering can anyone explain to me in general terms, some proofs of the equivalence of Lambda calculus and turing machines and the general method of the proof. In as plain terms as possible.
Greg Peckory
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Does there exist a TM for all countable languages?

I know that if a Turing machine exists for a language, that language is recursively enumerable and therefor there exists a enumeration procedure for it. However, if a language is countable, does that mean that there must be a TM for it? Thanks!
Þorvaldur Rúnarsson
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Prove that all non-recursive languages are infinite

I am wondering this statement above [the title] is true or not. Here is what I've already had : non-recursive means undecidable. I've read this Are all infinite languages undecidable? which says: If a Language is undecidable(non-recursive), there…
geasssos
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Deciding inhabitation?

Consider the basic system of simple types usually known as TAλ. One can prove that (as a consequence of the so called Subject Reduction Property and the fact that any typable term is strongly β-normalising) If τ has an inhabitant, then it has one in…
user35549
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Understanding Σ* and Σ in formal languages

If I have Σ={a} , what words does Σ* has ? Σ*= {a,aa,aaa,aaaa.....} ? Thanks
JAN
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Sticky footer not working in IE

I have created a Sticky footer for my website which you can view in this fiddle: http://jsfiddle.net/Aw6vn/ #main_Ticker{ position: fixed; bottom: 0; right: 12%; z-index: 6000 !important; } It works for all browsers in jsfiddle,…
devmonster
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How to prove set of all two argument functions cannot be countable

We can prove that set of all one argument functions cannot be countable using the cantor's diagonal. for example 1 2 3 4 5 6 7 ...... f1 10 12 23 1 3 12 3 ...... f2 15 6 7 8 9 11 4…
Aruna Karunarathna
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NP optimization problems (definition)

I'm trying to understand the definition of NPO. I read the definition here : http://www.nada.kth.se/~viggo/wwwcompendium/node2.html If we consider trying to find a minimal vertice cover, what is I,sol(x) and m ? (goal is min)
Belgi
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Prove that the following problem is undecidable by a reduction from the halting problem:

Prove that the following problem is undecidable by a reduction from the halting problem: “Does a given Turing Machine M accept any string of form a^2k for k ≥ 1?” I'm having trouble understanding the intuition behind the Halting problem reduction,…
Suleyman Kiani
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