Stack Overflow
Stack Overflow

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).

92 questions
3
votes
2 answers

Key points and Importance of Decidability

A language is decidable If a TM recognises the language and goes into an Accept or Reject state. As a dev. I think this is important as it would mean we could determine if a program contains buffer overflows or deadlocks. Also, the following…
Robben_Ford_Fan_boy
  • 8,494
  • 11
  • 64
  • 85
3
votes
1 answer

Prove that it is undecidable whether a Deterministic LBA accepts an infinite number of inputs

Deterministic Linear Bounded Automaton (LBA) is a single-tape TM that is not allowed to move its head past the right end of the input (but it can read and write on the portion of the tape that originally contained the input). How can I prove that…
Dan Webster
  • 1,185
  • 1
  • 12
  • 27
2
votes
1 answer

Z3: is Nonlinear integer arithmetic undecidable or semi-decidable

In Z3 (Python), I solved the following: y1,y2,x = Ints('y1 y2 x') univ = ForAll([x], (y1
Theo Deep
  • 666
  • 4
  • 15
2
votes
1 answer

Can a PDA with two stacks accept RE Language?

So, I was having a bit of difficulty figuring what exactly is meant by a String on which Turing Machine does not halt. I read somewhere that a Turing Machine is equivalent to a deterministic automata with 2 stacks. But how will a deterministic…
Q Tw
  • 21
  • 1
  • 3
2
votes
1 answer

Working within agda's decideability framework

I'm having trouble using the string decideability. First, I'm confused why it is so difficult to work with decideability in Agda, when in Coq it seems smooth as butter. When I try to prove this simple theorem about strings, Agda unfolds this mess…
user5775230
2
votes
1 answer

what does regular, Turing-decidable and Turing-recognisable mean?

I know this question has been asked earlier, but I honestly don't understand it clearly. I'm currently undergoing a study about the theory of computation and I'm coming to the terms "Prove that a language is decidable, recognizable or regular". In…
DingDong
  • 367
  • 3
  • 12
  • 22
2
votes
2 answers

Lean complains it can't see that a statement is decidable

I'm trying to define the following quantity partn: variable pi : nat -> Prop variable (Hdecp : ∀ p, decidable (pi p)) definition partn (n : nat) : nat := ∏ p ∈ (prime_factors n), (if pi p then p^(mult p n) else 1) but get the error error: failed…
user3078439
  • 305
  • 1
  • 10
2
votes
1 answer

Proving decidability of subset in Agda

Suppose I have this definition of Subset in Agda Subset : ∀ {α} → Set α → {ℓ : Level} → Set (α ⊔ suc ℓ) Subset A {ℓ} = A → Set ℓ and I have a set data Q : Set where a : Q b : Q Is it possible to prove that all subset of q is decidable and…
Steven Cheung
  • 35
  • 4
2
votes
0 answers

Kolmogorov complexity is uncomputable using reductions

Can anyone please give me a proof of K-Complexity is unsolvable using reductions. eg: PCP(2) <= PCP(3) I can prove that PCP(3) is unsolvable by reducing to PCP(2) (by mapping every instance). I am not sure how to reduce K-Complexity to another…
Krishna Chikkala
  • 91
  • 1
  • 10
2
votes
1 answer

First order logic in practice, how to deal with undecidablity?

I am very new to these things. Hope this is not a very naive question. I tried the following formula in Prolog: A ⇒ B and given that B is true, I evaluate A and it says FALSE. My question is why FALSE? (why not TRUE?) Given the current information…
Daniel
  • 5,839
  • 9
  • 46
  • 85
2
votes
1 answer

Is C++ a recursively enumerable language?

I know that C++ is not decidable. But is it recursively enumerable? Let's define the set of valid C++ programs to be any well defined program under the current C++ standards. Is it possible to construct a compiler that can always identify valid C++…
user2005303
2
votes
1 answer

Decidable Predicates in Agda

I am new to Agda and I need help to understand the Decidable function and Dec type. I am trying to define a first-order-logic predicate, and I want to encode with the proof some sort of boolean value. I found the way to do this is using the Dec…
Yasmine Shaorda
  • 383
  • 1
  • 7
2
votes
1 answer

Is this language decidable, recognizable, or unrecognizable?

The language L that consists of all Turing Machine descriptions M, for which the language accepted by M is finite. I said L is a decidable language because I can just run M on a function D(M) that returns false if there exists a loop somewhere…
3932695
  • 87
  • 1
  • 9
2
votes
0 answers

How to prove that "Total" is not recursive (decidable)

Halt = { f,x | f(x)↓ } is re (semi-decidable) but undecidable Total = { f | ∀x f(x)↓ } is non-re (not even semi-decidable) I need some help in proving that the Total problem is not recursive (decidable). I know the diagonalization proof for the…
Michael Anthony Leber
  • 365
  • 2
  • 10
  • 24
1
vote
1 answer

"Reduction" from the complement of the universal language (L_u) to the language of nonempty-language Turing machines (L_ne)

I have a question from the domain of theoretical computer science. The so-called universal language, L_u, is composed of pairs (M, w) such that w \in L(M). The language L_ne consists of machines M (actually, their descriptions, but let's not be too…
Luka Fürst
  • 71
  • 4
1
2
3 4 5 6 7