Chomsky Hierarchy
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  • TM is the most general and powerful computational model developed so far.
  • It is interesting to observe that though a large number of variations of TMs exists, all are equivalent to the basic TM model in terms of power or capability i.e. all can accept r.e language only. This implies that it is not possible to increase the power of a TM by putting more features in terms of complex and /or additional structures to the basic model.
  • But by putting some kind of restrictions on the use of the structures of the TM, it is possible to limit the power. For example,
    • If only a finite amount of tape is allowed to use with read-only tape that can move only to right one call at a time, we get a FA accepting regular language.
    • If the tape is restricted to be used as stack, it will work like a nondeterministic pushdown automata.
  • Similarly, we get another interesting type of automata by restricting the number of tape cells that can be used.
  • This new automata, denoted "linear bounded automata" (or LBA), accepts a smaller class of languages than the class of r.e. languages. An LBA is exactly similar to a TM except that on any input wwith |w| = n, it can use only (n+2) numbers of cells of the input tape.The input string is always put between a left-end marker, <, and a right-end marker, >, which are not puts of the input string. The read-write head cannot move to the left of the left-end marker or to the right of the right-end marker. The two end markers cannot be overwritten in any case.
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