Question

3. For Turing machines: (a). (8 pts) Give the state diagram of a Turing machine that recognizes the following language over ? = {a, b}: L1 = {w : w contains the substring aab} (b). (12 pts) A Turing machine X with Right Tab T is similar to a normal Turing machine except that its transition function is defined as ?: Q × ? ? Q × ? × {L, R, T} where T is an extra tape directive, in addition to Left and Right, that moves the read/write head to the first blank space to the right. Show that X is Turing-complete. Note: Please use the following notation to label your Turing machine transitions: qi ? qj x ? y, z (read symbol x, write symbol y, direction to move is z)

          3. For Turing machines:

(a). (8 pts) Give the state diagram of a Turing machine that recognizes the following language over ? = {a, b}:

L1 = {w : w contains the substring aab}

(b). (12 pts) A Turing machine X with Right Tab T is similar to a normal Turing machine except that its transition function is defined as

?: Q × ? ? Q × ? × {L, R, T}

where T is an extra tape directive, in addition to Left and Right, that moves the read/write head to the first blank space to the right. Show that X is Turing-complete.

Note: Please use the following notation to label your Turing machine transitions:

qi ? qj
x ? y, z

(read symbol x, write symbol y, direction to move is z)

3. For Turing machines:

(a). (8 pts) Give the state diagram of a Turing machine that recognizes the following language over ? = a, b:

L1 = w : w contains the substring aab

(b). (12 pts) A Turing machine X with Right Tab T is similar to a normal Turing machine except that its transition function is defined as

?: Q × ? ? Q × ? × L, R, T

where T is an extra tape directive, in addition to Left and Right, that moves the read/write head to the first blank space to the right. Show that X is Turing-complete.

Note: Please use the following notation to label your Turing machine transitions:

qi ? qj
x ? y, z

(read symbol x, write symbol y, direction to move is z)

Added by Tiffany Y.

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