CS 390 Solutions to Homework 11



pp. 354 - 361

9.2(a): ( q0, ab ) ( q1, b ) ( q1, a ) ( q1, ab ) ( q2, a ) ( q5, a ) ( q6, a b ) ( q7, a b ) ( q7, a bb ) ( q2, bb ) ( q3, bb ) ( q4, a b ) ( q4, ab ) ( q4, u abb ) ( q7, aba ) ( q7, a ba ) ( q7, bba ) ( q7, abba ) ( q2, abba ) ( h, abba )











9.39(b): After reading the last input symbol, this Turing machine sees only blanks. Also since the head always moves right, only the current state determines the next state. Hence after going through all the states at the longest, it gets into an infinite loop.
9.40(a): If the length of every string in the language is at most n, then the language is finite. Hence it is regular. If there are strings longer than n, then this machine does not distinguish strings that differ after the n-th position. Hence the equivalence classes of IL of Corollary 5.1 on p. 171 is finite. Hence the language is regular. (You need to go to pp. 168 - 169 for the definition and explanation of IL).