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A Turing Recognizable language can be Enumerated by an Enumerator Consider a Turing Machine M {\displaystyle M} and the language accepted by it be L ( M ) {\displaystyle L(M)} .
In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i.e., if there exists a Turing machine which will enumerate all valid strings of the language.
Turing completeness is the ability for a computational model or a system of instructions to simulate a Turing machine. A programming language that is Turing complete is theoretically capable of expressing all tasks accomplishable by computers; nearly all programming languages are Turing complete if the limitations of finite memory are ignored.
This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine. This set of languages is also known as NLINSPACE or NSPACE(O(n)), because they can be accepted using linear space on a non-deterministic Turing machine. [1]
There are no constraints on the productions rules. They generate exactly all languages that can be recognized by a Turing machine, thus any language that is possible to be generated can be generated by a Type-0 grammar. [8] These languages are also known as the recursively enumerable or Turing-recognizable languages. [8]
A recursive language is a formal language for which there exists a Turing machine that, when presented with any finite input string, halts and accepts if the string is in the language, and halts and rejects otherwise. The Turing machine always halts: it is known as a decider and is said to decide the recursive language.
A language which is accepted by such a Turing machine is called a recursively enumerable language. The Turing machine, it turns out, is an exceedingly powerful model of automata. Attempts to amend the definition of a Turing machine to produce a more powerful machine have surprisingly met with failure.
A universal Turing machine can calculate any recursive function, decide any recursive language, and accept any recursively enumerable language. According to the Church–Turing thesis , the problems solvable by a universal Turing machine are exactly those problems solvable by an algorithm or an effective method of computation , for any ...