Is the language of a Turing machine decidable?
A language is called Decidable or Recursive if there is a Turing machine which accepts and halts on every input string w. Every decidable language is Turing-Acceptable. A decision problem P is decidable if the language L of all yes instances to P is decidable.
How do you know if a Turing machine is decidable?
Decidable Language A Turing machine M decides language L if L = L(M) and M halts on all inputs. We say L is decidable if there is a TM M that decides L.
How do you prove a language is Turing decidable?
To show that a language is decidable, we need to create a Turing machine which will halt on any input string from the language’s alphabet. Since M is a dfa, we already have the Turing Machine and just need to show that the dfa halts on every input.
What does it mean if a language is decidable?
(definition) Definition: A language for which membership can be decided by an algorithm that halts on all inputs in a finite number of steps — equivalently, can be recognized by a Turing machine that halts for all inputs. Also known as recursive language, totally decidable language.
What is the language recognized by this Turing machine?
Explanation: The language accepted by Turing machines are called recursively ennumerable (RE), and the subset of RE languages that are accepted by a turing machine that always halts are called recursive.
Is the universal Turing machine decidable?
Otherwise, Accept.” Since we just proved in Stage 1 that D is not even semi-decidable (let alone decidable), it must be the case that our assumption that ATM is decidable is false. So, ATM is undecidable. Thus, we know that there are problems that are semi-decidable but not decidable (e.g., ATM is such a problem).
Are all decidable languages regular?
Regular languages are all TM-decidable. (B) If L and ¯ L are TM-decidable, then L is TM-recognizable. For each suffix language, there is at least one state corresponding to it. (E) If L is regular and L′ is TM-decidable, then L ∩ L′ is TM-decidable.
Is a decidable language regular?
Regular Languages are Decidable Because a regular language in any form (regular expression, DFA, and NFA) can be freely converted to any other form, these operations on automata are fully general.
How can we check whether a problem is decidable or undecidable with example?
A language L is called decidable if there is a decider M such that L( M) = L.
- Given a decider M, you can learn whether or not a string w ∈ L(M). Run M on w. Although it might take a long time, M will accept or reject w.
- The set R is the set of all decidable languages. L ∈ R if L is decidable.
How many tuples are there in Turing machine?
A Turing machine (TM) is a 7-tuple, , where Q is a finite set of states, S is a finite input alphabet, G (which contains S and has B, the blank tape symbol, as an element) is a finite tape alphabet, q0 in Q is the distinguished start state and F contained in Q is the set of accepting (final) states.
Which of the following is decidable?
Which of the following are decidable? Explanation: (A) Intersection of two regular languages is regular and checking if a regular language is infinite is decidable.
Are there any undecidable problems with a Turing machine?
Some more Undecidable Problems related to Turing machine: 1 Membership problem of a Turing Machine? 2 Finiteness of a Turing Machine? 3 Emptiness of a Turing Machine? 4 Whether the language accepted by Turing Machine is regular or CFL?
What makes a language a Turing decidable language?
A language is Turing-decidable(or decidable) if some Turing machine decidesit Aka RecursiveLanguage Review: Turing Recognizable Language A language is Turing-recognizableif some Turing machine recognizesit Aka Recursively EnumerableLanguage
When does a Turing machine recognize a language?
Now a language is recognizable if and only if a Turing machine accepts the string, when the provided input lies in the language. Also, a language can be recognizable if the TM either terminates and rejects the string or doesn’t terminate at all. This means that the TM continues with the computing when the provided input doesn’t lie in the language.
How is a language said to be decidable?
A language is said to be Decidable if there is a Machine that will accept strings in the language and reject strings not in the language. A Language is called Turing Recognizable if some Turing Machine recognizes it. A Language is called Turing Decidable if some Turing Machine decides it.