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Questions tagged [decidable]

Decidable languages are languages such that the problem of whether a given word belongs to it or not is decidable. A decision problem, i.e., a question with a yes/no answer, is called decidable if there exists an algorithm (a Turing machine) that can and will return a Boolean true or false value (instead of looping indefinitely).

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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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Is This Language Regular or not?

I have the language {4^(w⋅g)34^(g)|w,g∈NAT} over the alphabet {0,1}. I need to find out if this language is recognizable, decidable, context free, regular or none of these. How would i go about doing that or knowing? Thanks
user3706271
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How to prove that the following language is not decidable?

L = { | M is a Turing machine over {0, 1}, and || (not in) L(M)} How do I prove that L is not recognizable? Any ideas? I've proven the L compliment is recognizable: Set Turing machine to J 1. Run J on input || 2. TM J accepts then…
johny59
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EPR formulas with equality and inequality

I am encoding sets as relations and operations over sets as universally quantified implications. I have a selection operator over sets that produces new sets by selecting elements satisfying a unary predicate p (eg: v<4, v>4, ..). Due to this…
Gowtham Kaki
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How to construct two-tape Turing Machine that decides a language with specific number of inputs

I am supposed to write a two-tape Turing machine (low level, all states, complete 7-tuple) to decide the following language: L = {w : w has exactly i a’s, exactly j b’s, and exactly k c’s, and k > i + j}, Σ = {a, b, c}. I then have to define a…
jamesvs642
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Applying Reflexivity of String Equivalence in Agda Proofs

In my Agda program, I have a small function that checks for string equality (simplified for example): open import Data.String.Base using (String) open import Date.String.Properties using (_≈?_) open import Relation.Nullary.Decidable using…
PaulProgrammerNoob
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Are linear problems on rational numbers decidable in Z3?

I'm working with linear problems on rationals in Z3. To use Z3 I take SBV. An example of a problem I pose is: import Data.SBV solution1 = do x <- sRational "x" w <- sRational "w" constrain $ x.< w constrain $ x + 2*w .>=0 .|| x .== 1 My…
Shenkok Kotoro
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Prove that we can decide whether a Turing machine takes at least 100 steps on some input

We know that the problem “Does this Turing machine take at least this finite number of steps on that input?” is decidable, because it will always answer yes or no, where it will say yes if the machine reaches the given number of steps and no if it…
Ananya Nayak
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Recognizabilty of a set in regards to their size bounds

Trying to teach myself Computational Theory, and stumbled upon this question: Suppose we have two sets: {T | T is a turing machine and L(T) contains at least 1001 string} {T | T is a turing machine and L(T) contains at most 1001 string} One of…
DazedAndConfused
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Recursive vs recursively enumerable language in Turing Machines?

We say language L is recursive if it is decided by a TM. L is recursively enumerable (r.e.) if it's recognized by a TM. Suppose, enumerator (en-r) is a deterministic Turing Machine with a printer that starts with a blank tape and can print strings…
lee2020
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Undecidable if TM overwrites its input?

I came across a statement postulating that it's undecidable whether a TM overwrites any of its own input. What would be intuition as well as an actual proof for that?
InfiniteLoop
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Looking for the Agda module that contains decidable equality for lists

Given two lists xs and ys, I would like to obtain a value of Dec(xs ≡ ys). Does any one know the name of the standard library module which contains such an operator?
user1023733
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reduction from ALLtm to Etm

I am trying to understand why this "proof" of Etm undecidability is wrong. ALLtm={ < M >|M is a TM, L(M)=∑*} ETM={< M >|M is a TM, L(M)=∅} We know that ALLTM is undecidable, lets assume ETM is decidable (T is a TM that decides ETM) and get a…
Dan
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Turing-decidable language and Turing-decidable machine. difference?

I have a Turing-Machine M and i have proven that M is not a decider. I have then proven A=L(M) or that the language A that M recognizes. I have now been asked "Is the language (A) Turing-decidable". my question is, if i have already proven that M is…
skerr4311
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Determining whether the following language is decidable

{⟨M,N⟩ | All strings in L(M)∩L(N) begin with 110.} I think that this language is decidable. We can make a Turing Machine TM, which takes as input . For every string that is in L(M)∩L(N), if the string starts with 110, after the first 3 digits, we…
jPrime
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