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(2) S -> aSa S -> bsb S-> a S-> b €, a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa and L is regular €, a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa and L not regular a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa, abbba and L is regular O a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa, abbba and L is not regular

(2) S -> aSa S -> bsb S-> a S-> b €, a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa and L is regular €, a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa and L not regular a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa, abbba and L is regular O a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa, abbba and L is not regular

Database System Concepts
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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Let Σ = {a, b}. For the language L defined by each of the following grammars, list the first ten elements of L in lexicographic order (shortest first, then alphabetically if same length), and then indicate whether or not L is regular.
Transcribed Image Text:Let Σ = {a, b}. For the language L defined by each of the following grammars, list the first ten elements of L in lexicographic order (shortest first, then alphabetically if same length), and then indicate whether or not L is regular.
The image presents a context-free grammar and multiple-choice options regarding the nature of the language it generates. Grammar Rules: 1. \( S \rightarrow aSa \) 2. \( S \rightarrow bSb \) 3. \( S \rightarrow a \) 4. \( S \rightarrow b \) Options: 1. \( \varepsilon, a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa \) and \( L \) is regular 2. \( \varepsilon, a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa \) and \( L \) not regular 3. \( a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa, abbba \) and \( L \) is regular 4. \( a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa, abbba \) and \( L \) not regular Explanation: - The given grammar generates palindromes made up of the characters 'a' and 'b'. - The options list several examples of strings and question whether the language \( L \) is regular or not. Note: In formal language theory, regular languages are typically described by regular expressions or finite automata, whereas context-free languages are often more complex and require context-free grammars or pushdown automata. The options are evaluating the regularity of the language generated by the given grammar.
Transcribed Image Text:The image presents a context-free grammar and multiple-choice options regarding the nature of the language it generates. Grammar Rules: 1. \( S \rightarrow aSa \) 2. \( S \rightarrow bSb \) 3. \( S \rightarrow a \) 4. \( S \rightarrow b \) Options: 1. \( \varepsilon, a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa \) and \( L \) is regular 2. \( \varepsilon, a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa \) and \( L \) not regular 3. \( a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa, abbba \) and \( L \) is regular 4. \( a, b, aaa, aba, bab, bbb, aaaaa, aabaa, ababa, abbba \) and \( L \) not regular Explanation: - The given grammar generates palindromes made up of the characters 'a' and 'b'. - The options list several examples of strings and question whether the language \( L \) is regular or not. Note: In formal language theory, regular languages are typically described by regular expressions or finite automata, whereas context-free languages are often more complex and require context-free grammars or pushdown automata. The options are evaluating the regularity of the language generated by the given grammar.
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Step 1: Introduction

A regular language is a language that can be expressed with a regular expression or a deterministic or non-deterministic finite automata or state machine. 


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