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Questions tagged [decision-problem]

A question in some formal system with a yes-or-no answer.

537 questions
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Does every computational problem have a decision version?

Is the following claim correct?: Every computational problem has a decision version of roughly equal computational difficulty. If the above claim is correct, please give a reference for it. (I find this pdf from Prof. E. Demaine, but he doesn't…
H.H
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how to prove a language is decidable

Hopefully this is not a duplicate How do I prove a Language L={a,b,c} is decidable or not I read somewhere that if a turing machine accepts a language and halts on every input string then the language is decidable. Having said that how do i design /…
Swathi
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Show why the following post's correspondence problem is unsolvable

We have the following pairs of strings. $$\begin{bmatrix} aa\\b \end{bmatrix} \begin{bmatrix} ba\\baa \end{bmatrix} \begin{bmatrix} aba\\a \end{bmatrix}$$ The problem is now, to find a concatenation of those pairs, such that the resulting string of…
Kinyx
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Paths between tuples, MSV, decision trees

I'm reading about Multiset Size Verification Problem and in the following paper - http://www.skynet.ie/~sos/mapviewer/docs/Voronoi_Diagram_Notes_2.pdf - I got stuck just on the first lemma. However, since my concrete problem is rather specific, I'll…
socumbersome
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"Multi-consequent" Decision graph/tree?

As I understand, Decision graph is a directed graph where each vertex is a "Question" (decision to make), and each edge is an "Answer" (decision made for the vertex this edge is coming from). The terminal nodes of that graph is a solution. Problem:…
Philipp Munin
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How many decision problems do exist?

Are there countable infinte decision problems or uncountable infinite? Thank you
Kevin Meier
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Can all decision problems reduce to undecidable?

If one could build a machine that for any input will never accept, but always loop forever, then will all problems reduce to this? Or did I just misunderstood the idea of reduction?
revisingcomplexity
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Decision Tree and rank?

Consider all strictly decreasing functions from {1,2,3,4} to {1,2,3,4,5,6}, or in other words, all functions defined on {1,2,3,4} such that f(1)>f(2)>f(3)>f(4). Draw a decision tree so that the leaves are in lexicographical order when read from left…
Michael Johnson
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Is polynomial over x with real roots decidable?

Today while I'm looking at definition of Algorithm from Sipser's textbook, he defined the following language: $$D_1 = \{ p \mid\ p\text{ is polynomial over }x\text{ with integral roots}\}$$. This language is decidable since we can bound the integral…
user777
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Decision Making using Multiple Variables

What should I learn if I want to make a decision based on multiple variables? Followings are the example of a problem. I have a farm. My variables are weather, humidity of air, humidity of soil, size of my fruits, etc.. Every hour, I will capture…
dude
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Given a solution for the post correspondence problem, is it co-semidecidable if the solution is a palindrom?

This was an old exam question. I think, though, that it is some sort of trick question. Isn't this simply decidable and therefore also trivially co-semidecidable? Because I wouldn't know how to prove that it is co-semidecidable for itself. Being…
Julian
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Turing machine that accepts language with more a's than b's

I am doing an assignment for my 1st year langauges and automata class. I have been having trouble with the last question which is this: Create a Turing machine that acccepts more a's than b's. I think I am supposed to pair the a's and b's together…
Matt
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Integer factorization: Why can't we use the test algorhitm to create an algorhitm to decide the factoring decision problem in polynomial time?

I'm reading Nielsen and Chuang. On page 142 the integer factoring decision problem is introduced: The integer factorization problem can be reduced to a decision problem: Given a composite integer m and l < m, does m have a non-trivial factor less…
Opinel
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Traveling salesman problem

Could someone tell me how many stopping points are needed for the traveling salesman to be impractical to be solved by current computing?
Octupos
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Is necessarily the following language not decideable

For A,B that are not decidable, does AB U BA not necessarily decidable? I think that the answer is NO. Not necessarily. I thought about the following example, but it does not refute exactly: If we take A and A complement, and without losing…
Ella
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