# hwsol10 - Theory of Algorithms Spring 2000 Homework 10...

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Theory of Algorithms. Spring 2000. Homework 10 Solutions. Section 9.1 (2) Here is a Turing Machine with only two states which is an acceptor for the language L ( a ( a + b ) * ). Notice that the design of the Turing Machine employs the idea that we don’t have to read the whole string in order to accept it. F = { q f } . δ is given by one clause: δ ( q 0 , a ) = ( q f , a, R ). (3) Regarding the Turing Machine presented in Example 9.7: q 0 aba xq 1 ba q 2 xya xq 0 ya xyq 3 a HALT. Since q 3 is not an accept state, aba is rejected. q 0 aaabbbb xq 1 aabbbb xaq 1 abbbb xaaq 1 bbbb xaq 2 aybbb xq 2 aaybbb q 2 xaaybbb xq 0 aaybbb xxq 1 aybbb xxaq 1 ybbb xxayq 1 bbb xxaq 2 yybb xxq 2 ayybb xq 2 xayybb xxq 0 ayybb xxxq 1 yybb xxxyq 1 ybb xxxyyq 1 bb xxxyq 2 yyb xxxq 2 yyyb xxq 2 xyyyb xxxq 0 yyyb xxxyq 3 yyb xxxyyq 3 yb xxxyyyq 3 b HALT. Since q 3 is not an accpet state, aaabbbb is rejected.

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