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 auton ton over {a, b} accepting that language.

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
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Question 1
1. For each of the following languages of the form
{we {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 Σ and any k ≥ 2, you would construct a deterministic finite
automaton A, 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
b
a
3
b
a
2
P
a
a
b
9
Transcribed Image Text:Question 1 1. For each of the following languages of the form {we {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 Σ and any k ≥ 2, you would construct a deterministic finite automaton A, 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 b a 3 b a 2 P a a b 9
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