# What is language Decidability?

## What is language Decidability?

(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.

## Is regular language decidable?

1. (a) True, since every regular language is context-free, every context-free language is decidable, and every decidable language is Turing-recognizable.

Is every finite language 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.

### What is Decidability in automata theory?

In terms of finite automata (FA), decidable refers to the problem of testing whether a deterministic finite automata (DFA) accepts an input string. A decidable language corresponds to algorithmically solvable decision problems.

### Why do we study Decidability?

If a programming language is decidable, then it will always be possible to decide whether a program is a valid program for that language or not. But even if a program is a valid program for that language, it remains undecidable whether that program may incur a buffer overflow or a deadlock.

What is Turing Decidability?

A Language is called Turing Decidable if some Turing Machine decides it. 3. If there exists a Turing Machine such that when encountering a string in that language, the machine terminates and accepts that string then we can say that type of language is a Turing recognizable.

## Why are all 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.

## Are all finite languages regular?

All finite languages are regular; in particular the empty string language {ε} = Ø* is regular. Other typical examples include the language consisting of all strings over the alphabet {a, b} which contain an even number of as, or the language consisting of all strings of the form: several as followed by several bs.

What is a finite language?

Finite languages, those containing only a finite number of words. These are regular languages, as one can create a regular expression that is the union of every word in the language.

### Can a Turing machine decide an infinite language?

Yes, a Turing machine can decide that langauge: it just looks at the first character and accepts or rejects without even needing to look at the rest of the string.

### How do you prove Decidability?

By definition, a language is decidable if there exists a Turing machine that accepts it, that is, halts on all inputs, and answers “Yes” on words in the language, “No” on words not in the language. Therefore one way of showing that a language is decidable is by describing a Turing machine that accepts it.

What is the difference between completeness and Decidability?

Completeness means that either a proof or disproof exists. Decidability means that there’s an algorithm for finding a proof or disproof. In nice cases, they are equivalent, since in a complete theory, you can just iterate over every possible proof until you find one that either proves or disproves the statement.

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