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The Encoding of TM

The Encoding of TM. Motivation for encoding of TM Languages defined by TM Recursive and recursively enumerable languages ALAN and MATHISON UTM --Universal Turing Machine. Why Encoding of TM?.

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The Encoding of TM

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  1. The Encoding of TM Motivation for encoding of TM Languages defined by TM Recursive and recursively enumerable languages ALAN and MATHISON UTM --Universal Turing Machine

  2. Why Encoding of TM? • It will help us to show that some languages are not accepted by any TM, and other limitations of TM. • One of main purposes of encoding of TMs is to construct languages ALAN and MATHISON. • CWL, Code Word Language, defined by RE: (a+b a+b(a+b)5)*

  3. Languages Defined by TM • For every TM, T, which runs on strings from the alphabet S, it will divide the set of all finite strings over S into three disjoint sets: accept (T), loop(T), reject(T). • Recursively enumerable language L = accept(T), and L’ = reject (T) + loop(T) • Recursive language L = accept (T), loop(T)= empty, and L’ = reject (T)

  4. ALAN and MATHISON • ALAN -- an example of non-recursively enumerable (r.e.)language, constructed by using CWL. The significance of ALAN is to show that not every language can be recognized by TM. • MATHISON -- an example of r.e.L, that can be recognized by UTM.

  5. Universal Turing Machine • A TM is a special purpose computer. Once its transition function is defined, the machine is restricted to carrying out one particular type of computation -- not general purpose or reprogrammable. • A UTM Mw is an automaton that, given as input the description of any TM M and a string w, can simulate the computation of M on w.

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