If M is a DFA and ɛ e L(M), what simple property must be true of M?

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:**

If \( M \) is a DFA and \( \varepsilon \in L(M) \), what simple property must be true of \( M \)?

**Explanation:**

A DFA (Deterministic Finite Automaton) is a state machine used to recognize patterns represented by a regular language. If the empty string \( \varepsilon \) is a part of the language \( L(M) \) accepted by the DFA, it implies that the start state of the DFA is also an accept state. 

This simple property ensures that the DFA can accept the empty string and immediately satisfy the conditions for acceptance without any input.
Transcribed Image Text:**Question:** If \( M \) is a DFA and \( \varepsilon \in L(M) \), what simple property must be true of \( M \)? **Explanation:** A DFA (Deterministic Finite Automaton) is a state machine used to recognize patterns represented by a regular language. If the empty string \( \varepsilon \) is a part of the language \( L(M) \) accepted by the DFA, it implies that the start state of the DFA is also an accept state. This simple property ensures that the DFA can accept the empty string and immediately satisfy the conditions for acceptance without any input.
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