What makes a language decidable?

A language is called Decidable or Recursive if there is a Turing machine which accepts and halts on every input string w. A decision problem P is decidable if the language L of all yes instances to P is decidable.

How do you prove a language is 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.

Why all finite languages are decidable?

If A is finite, it is decidable because all finite languages are decidable (just hardwire each of the strings into the TM). If A is infinite, a TM M that decides A operates as follows. As a result, we end up showing that the language is decidable without using the enumerator for the language to construct a decider.

Is a language recognizable if it is decidable?

Note: Decidable languages are closed under complementation, but recognizable languages are not. – Write-only means (a) symbol on output tape does not affect transitions, and (b) tape head only moves right.

Is Sigma * decidable?

But Sigma* is a regular, decidable and context free language.

Are regular languages decidable?

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 do you prove something is not decidable?

For a correct proof, need a convincing argument that the TM always eventually accepts or rejects any input. How can you prove a language is undecidable? To prove a language is undecidable, need to show there is no Turing Machine that can decide the language. This is hard: requires reasoning about all possible TMs.

What is a decidable language?

(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.

Are all languages decidable?

All finite languages are regular. Some infinite languages are regular. Only infinite languages can be undecidable. To be undecidable, there must be individual strings in the language that cause the TM to fail.

Are decidable languages regular?

Solution: True. Regular languages are all TM-decidable. (B) If L and ¯ L are TM-decidable, then L is TM-recognizable.

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.

Is all DFA decidable?

E(dfa) is a decidable language. Proof: A DFA accepts some string iff reaching an accept state from the start state by >traveling along the arrows of the DFA is possible.