Constructing a Finite Automaton for a Given Pattern in Java

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Finite Automata (FAs) are fundamental models in computer science, particularly in the fields of formal languages, compilers, and pattern matching. They provide a mathematical framework for recognizing patterns within strings, making them essential for tasks such as lexical analysis, text searching, and input validation. In this article, we will explore how to construct a finite automaton for a given pattern in Java, covering both theoretical foundations and practical implementation.

1. Understanding Finite Automata

A Finite Automaton is a theoretical machine used to recognize patterns within input strings. It consists of:

• States: A finite set of states, including one initial state and one or more accepting (final) states.
• Alphabet: A finite set of symbols that the automaton can read.
• Transition Function: A set of rules that describe how to move from one state to another based on input symbols.
• Start State: The state where the automaton begins processing.
• Accept States: The states that, if reached after processing the input string, indicate that the string is accepted by the automaton.