1. For each of the following languages of the form {w € {a,b}* | ...} where the rule ... in each case is described below, construct a deterministic finite automa- ton over {a, b} accepting that language. (a) w has both ab and ba as (not necessarily disjoint) subwords. (b) w has an even number ofa's and an odd number of b's. (c) w has an odd length and exactly two b's. (d) all blocks of consecutive b's in w have length of the form 2n + 3 for n = 0, 1, 2,.... 2. Describe how, for any alphabet Eand any k > 2, you would construct a deterministic finite automaton Ak which accepts the following language: {w € L' | |w| = kn, n = 0, 1,2,...} 3. Convert the following NFA over the alphabet {a, b} to an equivalent DFA: a a 2 e a 9. 3

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
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Question 1
1. For each of the following languages of the form
{w € {a,b}° | ... }
where the rule ...in each case is described below, construct a deterministic finite automa-
ton over {a, b} accepting that language.
(a) w has both ab and ba as (not necessarily disjoint) subwords.
(b) w has an even number of a's and an odd number of b's.
(c) w has an odd length and exactly two b's.
(d) all blocks of consecutive b's in w have length of the form 2n + 3 for n = 0, 1, 2, ...
2. Describe how, for any alphabet Eand any k > 2, you would construct a deterministic finite
automaton Ak which accepts the following language:
{w € £* | |w| = kn, n = 0, 1,2,...}
3. Convert the following NFA over the alphabet {a, b} to an equivalent DFA:
a
a
a
e
9.
3
Transcribed Image Text:Question 1 1. For each of the following languages of the form {w € {a,b}° | ... } where the rule ...in each case is described below, construct a deterministic finite automa- ton over {a, b} accepting that language. (a) w has both ab and ba as (not necessarily disjoint) subwords. (b) w has an even number of a's and an odd number of b's. (c) w has an odd length and exactly two b's. (d) all blocks of consecutive b's in w have length of the form 2n + 3 for n = 0, 1, 2, ... 2. Describe how, for any alphabet Eand any k > 2, you would construct a deterministic finite automaton Ak which accepts the following language: {w € £* | |w| = kn, n = 0, 1,2,...} 3. Convert the following NFA over the alphabet {a, b} to an equivalent DFA: a a a e 9. 3
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