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Recursive and Recursive Enumerable Languages in Theory of Computation GATECSE TOC
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#recursiveenumerablelanguage, #recursivelanguage, #gatecse, #thegatehub • Contact Datils (You can follow me at) • Instagram: / ahmadshoebkhan • LinkedIn: / ahmad-shoeb-957b6364 • 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. • recursive and recursively enumerable languages in toc • recursively enumerable languages in turing machine • recursively enumerable language in toc • recursive enumerable language • recursive enumerable language in toc • 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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