Consider the language L = {w ∈ {a, b, c} ∗ | n _w (a) = nw(b) = n _w (c)}, where n _w (z) is the number of occurrences of the symbol z in string w. In other words, L contains all strings that have an equal number of a’s, b’s, and c’s. The symbols may be in any order.

(a) Describe a TM T that decides L. You may assume that a t symbol has been placed at the beginning of the tape.

(b) Draw the state diagram of T. You do not need to include the rejecting state.

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