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13 July, 14:38

A marker automaton (MA) is a deterministic 1-tape 1-head machine with input alphabet {0, 1}. The head can move left or right but is constrained to the input portion of the tape. The machine has the ability to write only one new character to a cell, namely #. (a) Give an example of language D that is accepted by an MA but is not context-free. Justify your answer. (b) Show that Kma = { hM, wi : M is an MA accepting w } is recursive.

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  1. 13 July, 16:20
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    See explaination

    Explanation:

    In our grammar for arithmetic expression, the start symbol is, so our initial string is:

    Using rule 5 we can choose to replace the nonterminal, producing the string:

    *

    We now have two nonterminals, to replace, we can apply rule three to the first nonterminal, producing the string:

    +*

    We can apply rule two to the remaining nonterminal, we get:

    (number) + number*number

    This is a valid arithmetic expression as generated by grammar.

    Given a grammar G with start symbol S, if there is some sequence of production that when applied to the initial string S, result in the string s, then s is in L (G). the language of the grammar.
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