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 a list of language options to determine whether the language generated by the grammar is regular or not.### Grammar Rules1. \( S \to aS \)2. \( S \to bS \)3. \( S \to \varepsilon \)### Language OptionsChoose the correct set of strings generated by the grammar and its regularity:1. \( \varepsilon, a, b, aa, ab, ba, bb, aaa, aab, aba \) and \( L \) is regular2. \( \varepsilon, a, aa, ab, ba, bb, aaa, aab, aba \) and \( L \) is not regular3. \( a, b, aa, ab, ba, bb, aaa, aab, aba, abb \) and \( L \) is regular4. \( a, b, aa, ab, ba, bb, aaa, aab, aba, abb \) and \( L \) is not regular### Explanation- The grammar describes strings that can be constructed with any combination of 'a' and 'b' and allow transitioning to an empty string (\( \varepsilon \)).- The task is to identify the correct set of strings (language \( L \)) produced by these rules and determine whether \( L \) is a regular language. Regular languages can be expressed by a finite automaton or regular expression.

(3) S-> aS S-> bs S-> € O €, a, b, aa, ab, ba, bb, aaa, aab, aba and L is regular O e, a, b, aa, ab, ba, bb, aaa, aab, aba and L is not regular O a, b, aa, ab, ba, bb, aaa, aab, aba, abb and L is regular O a, b, aa, ab, ba, bb, aaa, aab, aba, abb and L is not regular

(3) S-> aS S-> bs S-> € O €, a, b, aa, ab, ba, bb, aaa, aab, aba and L is regular O e, a, b, aa, ab, ba, bb, aaa, aab, aba and L is not regular O a, b, aa, ab, ba, bb, aaa, aab, aba, abb and L is regular O a, b, aa, ab, ba, bb, aaa, aab, aba, abb and L is not regular

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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Question

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 a list of language options to determine whether the language generated by the grammar is regular or not.

### Grammar Rules
1. \( S \to aS \)
2. \( S \to bS \)
3. \( S \to \varepsilon \)

### Language Options
Choose the correct set of strings generated by the grammar and its regularity:

1. \( \varepsilon, a, b, aa, ab, ba, bb, aaa, aab, aba \) and \( L \) is regular
2. \( \varepsilon, a, aa, ab, ba, bb, aaa, aab, aba \) and \( L \) is not regular
3. \( a, b, aa, ab, ba, bb, aaa, aab, aba, abb \) and \( L \) is regular
4. \( a, b, aa, ab, ba, bb, aaa, aab, aba, abb \) and \( L \) is not regular

### Explanation
- The grammar describes strings that can be constructed with any combination of 'a' and 'b' and allow transitioning to an empty string (\( \varepsilon \)).
- The task is to identify the correct set of strings (language \( L \)) produced by these rules and determine whether \( L \) is a regular language. Regular languages can be expressed by a finite automaton or regular expression.

Expert Solution

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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