empty string) and xy is their concatenation. Show that if x, y and xy are all in PALINDROME, then there is a word z such that x= z' and y=z" for some integers n and m. 3. (1 pt) Let S={ab, bb} and T={ab, bb, bbb}. Show that S*#T* but that S*cT*. 4. (1 pt) Write the regular expression for the language of all strings, over alphabet {a, b}, that end in a double letter, i.e. ending in aa or bb but not ab or ba 5. (1 pt) Draw Deterministic Finite Automata to accept the following sets of strings, over the alphabet {0,1}, that contain exactly four Os (not necessarily consecutive zeros) Extra Credit: (1 pt) Write the regular expression for the language of all strings, over alphabet {0, 1}, the set of all strings in which every pair of adjacent zeros appears before noont onog Luotifiu

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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2. (1 pt) Let x and y be two words (both different than the
empty string) and xy is their concatenation. Show that if x,
y and xy are all in PALINDROME, then there is a word z
such that x= z' and y=z" for some integers n and m.
3. (1 pt) Let S={ab, bb} and T={ab, bb, bbb}. Show that
S*#T* but that S*cT*.
4. (1 pt) Write the regular expression for the language of all
strings, over alphabet {a, b}, that end in a double letter, i.e.
ending in aa or bb but not ab or ba
5. (1 pt) Draw Deterministic Finite Automata to accept the
following sets of strings, over the alphabet {0,1}, that
contain exactly four Os (not necessarily consecutive zeros)
Extra Credit: (1 pt) Write the regular expression for the
language of all strings, over alphabet {0, 1}, the set of all
strings in which every pair of adjacent zeros appears before
any pair of adjacent ones. Justify.
Transcribed Image Text:2. (1 pt) Let x and y be two words (both different than the empty string) and xy is their concatenation. Show that if x, y and xy are all in PALINDROME, then there is a word z such that x= z' and y=z" for some integers n and m. 3. (1 pt) Let S={ab, bb} and T={ab, bb, bbb}. Show that S*#T* but that S*cT*. 4. (1 pt) Write the regular expression for the language of all strings, over alphabet {a, b}, that end in a double letter, i.e. ending in aa or bb but not ab or ba 5. (1 pt) Draw Deterministic Finite Automata to accept the following sets of strings, over the alphabet {0,1}, that contain exactly four Os (not necessarily consecutive zeros) Extra Credit: (1 pt) Write the regular expression for the language of all strings, over alphabet {0, 1}, the set of all strings in which every pair of adjacent zeros appears before any pair of adjacent ones. Justify.
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