Recursive and Recursive Enumerable Languages in Theory of Computation | GATECSE | TOC
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Let us understand the concept of recursive language before learning about the recursively enumerable language in the theory of computation (TOC).
Recursive Language
A language L is recursive (decidable) if L is the set of strings accepted by some Turing Machine (TM) that halts on every input.
Example
When a Turing machine reaches a final state, it halts. We can also say that a Turing machine M halts when M reaches a state q and a current symbol ‘a’ to be scanned so that δ(q, a) is undefined.
There are TMs that never halt on some inputs in any one of these ways, So we make a distinction between the languages accepted by a TM that halts on all input strings and a TM that never halts on some input strings.
Recursive Enumerable Language
A language L is recursively enumerable if L is the set of strings accepted by some TM.
If L is a recursive enumerable language then −
If w ∈ L then a TM halts in a final state,
If w ∉ L then a TM halts in a non-final state or loops forever.
If L is a recursive language then −
If w ∈ L then a TM halts in a final state,
If w ∉ L then TM halts in a non-final state.
Recursive Languages are also recursive enumerable
Proof − If L is a recursive then there is TM which decides a member in language then −
M accepts x if x is in language L.
M rejects on x if x is not in language L.
According to the definition, M can recognize the strings in language that are accepted on those strings.
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What is the difference between recursive and recursive enumerable language?
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Why are recursive languages a proper subset of recursive enumerable languages?
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the class of recursively enumerable language is known as
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Contact Datils (You can follow me at)
Instagram: Instagram: ahmadshoebkhan
LinkedIn: LinkedIn: ahmad-shoeb-957b6364
Facebook: Facebook: ahmadshoebkhan
Watch Complete Playlists:
Data Structures: Introduction to Data Structures || Da...
Theory of Computation: Introduction to Theory of Computation...
Compiler Design: Ambiguous Grammar | Introduction to A...
Design and Analysis of Algorithms: Design and Analysis of Algorithms
Let us understand the concept of recursive language before learning about the recursively enumerable language in the theory of computation (TOC).
Recursive Language
A language L is recursive (decidable) if L is the set of strings accepted by some Turing Machine (TM) that halts on every input.
Example
When a Turing machine reaches a final state, it halts. We can also say that a Turing machine M halts when M reaches a state q and a current symbol ‘a’ to be scanned so that δ(q, a) is undefined.
There are TMs that never halt on some inputs in any one of these ways, So we make a distinction between the languages accepted by a TM that halts on all input strings and a TM that never halts on some input strings.
Recursive Enumerable Language
A language L is recursively enumerable if L is the set of strings accepted by some TM.
If L is a recursive enumerable language then −
If w ∈ L then a TM halts in a final state,
If w ∉ L then a TM halts in a non-final state or loops forever.
If L is a recursive language then −
If w ∈ L then a TM halts in a final state,
If w ∉ L then TM halts in a non-final state.
Recursive Languages are also recursive enumerable
Proof − If L is a recursive then there is TM which decides a member in language then −
M accepts x if x is in language L.
M rejects on x if x is not in language L.
According to the definition, M can recognize the strings in language that are accepted on those strings.
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turing machine languages
Language accepted by turing machine
What is the difference between recursive and recursive enumerable language?
What do you mean by recursive and recursively enumerable languages?
Is every recursive language also recursively enumerable?
Why are recursive languages a proper subset of recursive enumerable languages?
recursive and recursively enumerable languages tutorialspoint
properties of recursive and recursively enumerable languages pdf
recursively enumerable languages are closed under union
recursively enumerable languages are closed under mcq
the class of recursively enumerable language is known as
recursive languages are closed under complementation
a recursively enumerable language l can be recursive if
recursive language example
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