Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 32.3, Problem 2E
Program Plan Intro
To draw state transition diagram for the pattern ababbabbababbababbabb where ?={a,b}
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Give a DFA over {a,b} that accepts all strings of length exactly 5
For each state in your automaton, give a brief description of the strings associated with that state.
Design a deterministic finite state automaton (DFA) that accepts exactly
the strings over the alphabet {A, B, ...,Z} that contain at least two R, at most one T, and
where every E comes after some S (there may be other letters in between). For instance,
your DFA should accept the strings:
• MYSTICWARRIORS
• MARSMATRIX
• SHOCKTROOPERS
• CONTRAHARDCORPS
STRIDER
but not the strings
• CRAZYTAXI (it does not contain at least two Rs)
LASTRESORT (it contains more than one T)
AFTERBURNER (there are Es without a S somewhere before them)
• BATTLECIRCUIT (all of these at the same time)
Clearly indicate the meaning of each state. One way to do this is to number the states
and have a numbered list of their meanings, but any readable method you use to label
and explain your states is fine.
Hint: there are three separate conditions accepted strings must meet; states will need to
encode whether or not each one is met (or perhaps partially met).
You can label an edge with the word “else" to indicate it…
(a) Build the string-matching automaton for the pattern P = abbab over the alphabetΣ = {a, b}
(b) Illustrate its operation on the text string T = aabbabaabbaababbab
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