Questions tagged [decidability]

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Deciding whether a turning machine guaranteed to halt solves sat [closed]

Suppose I give as input a Turing machine M guaranteed to halt in time n^c on inputs of length n for a universal constant c. Is there a Turing machine that given any such M can decide whether M solves ...
-2
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1answer
668 views

Intersection between context-free and context-sensitive language decidability [closed]

I'm trying to find a formal proof of the following fact: Given a context-free language, say $L_1$, and a context-sensitive language, say $L_2$, it is NOT decidable if their intersection is empty ($...
0
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1answer
149 views

Is refuting candidate deciders of the halting problem computable? [closed]

No Turing machine can decide whether any given Turing machine will halt for a given input. That is: If you give me a Turing machine which you claim can take a Turing machine and an input for that ...
98
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15answers
10k views

A simple decision problem whose decidability is not known

I am preparing for a talk aimed at undergraduate math majors, and as part of it, I am considering discussing the concept of decidability. I want to give an example of a problem that we do not ...
2
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1answer
112 views

Is it decidable whether the langauge accepted by a reversal-bounded counter machine is deterministic?

I'm wondering if anyone can point me to either an algorithm or an undecidability proof for the following question: Given a non-deterministic reversal-bounded multicounter machine $M$, is there some ...
9
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2answers
437 views

Is meta-undecidability possible?

There are problems that are decidable, there are some that are undecidable, there is semidecidability, etc. In this case I wonder whether a problem can be meta-undecidable. This means (at least in my ...
9
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0answers
343 views

Deciding if a language induced by a Presburger formula is context-free

Is the following problem decidable? Given $n$ and a Presburger arithmetic formula $\phi(x_1,x_2,\dots,x_n)$, determine whether the language $\{a_1^{i_1} \dots a_n^{i_n}:\phi(i_1,i_2,\dots,i_n)\}$ ...
19
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4answers
918 views

Checking if all products of a set of matrices eventually equal zero

I am interested in the following problem: given integer matrices $A_1,A_2, \ldots, A_k$ decide if every infinite product of these matrices eventually equals the zero matrix. This means exactly what ...
8
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1answer
989 views

Do natural generalizations of P versus NP exist?

Accepted Answer Scott Aaronson's answer has been "accepted" (mainly because it's the only answer!) One-sentence summary of answer  Plausibly natural generalizations of the P versus NP question ...
2
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0answers
264 views

Non-uniform CFG ambiguity decidability

The uniform version (the version which we normally see) of deciding whether a CFG (Context Free Grammar) is ambiguous is undecidable. But here I'd like to know something about the non-uniform version ...
9
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1answer
1k views

Does every Turing-recognizable undecidable language have a NP-complete subset?

Does every Turing-recognizable undecidable language have a NP-complete subset? The question could be seen as a stronger version of the fact that every infinite Turing-recognizable language has an ...
18
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2answers
650 views

Is it possible to decide $\beta$-equivalence within System F (or another normalizing typed λ-calculus)?

I know that's impossible to decide $\beta$-equivalence for untyped lambda calculus. Quoting Barendregt, H. P. The Lambda Calculus: Its Syntax and Semantics. North Holland, Amsterdam (1984).: If A ...
9
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3answers
849 views

Is it possible to compute whether two functions are extensional equal?

If you have two functions implementing a different sorting algorithm, is it then possible to infer by source code that they both have the same external properties? Meaning that they both will have a ...
5
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1answer
253 views

Random walk returning probability

Consider a two-dimensional random walk, but this time the probabilities are not $1/4$, but some values $p_1, p_2, p_3, p_4$ with $\sum_{i=1}^4 p_i=1$. For example, from $(0,0)$, it goes to $(1,0)$ ...
11
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3answers
1k views

Does P contain incomprehensible languages? (TCS community wiki)

Answer: not known Many thanks to all who helped refine this question and the definitions associated to it. The definitions of this wiki provided the starting point for the more recent TCS wiki "...

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