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Erik Jonsson School of Engineering and Computer Science. CS 4384 – 001. Automata Theory. http://www.utdallas.edu/~pervin. Thurs day : Section 2.9 Look at Ullman’s Lecture 7. Tuesday 2-04-14. FEARLESS Engineering. FINAL EXAMINATION. 6 May 2014 2:00pm – 4:45pm S2.312. Rui Li
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Erik Jonsson School of Engineering and Computer Science CS 4384– 001 Automata Theory http://www.utdallas.edu/~pervin Thursday: Section 2.9 Look at Ullman’s Lecture 7 Tuesday2-04-14 FEARLESS Engineering
FINAL EXAMINATION 6 May 2014 2:00pm – 4:45pm S2.312
Rui Li • rxl122350@utdallas.edu • ECSS4.215 • MW 9-11 Teaching Assistant
Decision Problems Martin, P. 148 (1st Ed.)
PUMPING LEMMA M&S P. 68 Theorem 2.9.1
Proof: If A is regular it has a DFA with a finite number, n, of states. Let p = n. Then for any string s in A of length at least p, suppose the decomposition s = xyz satisfies the conditions.
Examples 1-5 from M&S: Classic Examples
The intersection with a*b* is necessary because the complement contains all strings with a and b out of order!
If the problem was n > m, then choose s = a^{p+1}b^p which is just at the edge of being in L. Then pump DOWN (i=0) since y must consist of a’s.
Extended Pumping Lemma Essentially the same proof!
Theorem: Let M be a DFA with p states. L(M) is not empty iff M accepts a string z with |z| < p. (ii) L(M) has an infinite number of members iff M accepts a string z with p <= |z| < 2p.
