Lexical analysis is the concept of Finite State Automaton (FSA) used in the compiler.

Introduction to Compiler
A compiler is a software program that transforms source code written in a high-level programming language into a lower-level representation, typically machine code, that can be executed by a computer. The compilation process consists of several phases, including lexical analysis, parsing, semantic analysis, code generation, and code optimization.

Lexical Analysis
Lexical analysis, also known as scanning, is the first phase of the compiler where the source code is divided into a sequence of tokens. It performs a character-by-character analysis of the source code to identify the basic building blocks of the language, such as keywords, identifiers, constants, operators, and punctuation marks.

Finite State Automaton (FSA)
Finite State Automaton (FSA) is a mathematical model used to describe the behavior of a system that can be in a finite number of states and transitions between those states based on input. In the context of lexical analysis, FSA is used to define the lexical rules of a programming language.

Working of FSA in Lexical Analysis
1. Regular Expressions: Lexical rules are often defined using regular expressions, which are patterns that describe a set of strings. Regular expressions provide a concise and flexible way to specify the lexical structure of a language.

2. Tokenization: The FSA uses regular expressions to define the patterns for different tokens in the language. Each token is represented by a unique identifier and associated attributes.

3. Deterministic Finite Automaton (DFA): The FSA can be implemented as a Deterministic Finite Automaton (DFA), which is a type of FSA that has a unique transition for each input symbol and state. The DFA can be represented as a transition table or a state diagram.

4. Lexical Analyzer: The lexical analyzer reads the input source code character by character and generates tokens based on the lexical rules defined by the FSA. It uses the DFA to determine the current state and transitions to the next state based on the input symbol.

5. Error Handling: The FSA also handles error detection and recovery during lexical analysis. If an input does not match any valid token, an error token is generated, and the lexical analyzer continues with the next character.

Conclusion
The concept of Finite State Automaton (FSA) is used in the lexical analysis phase of a compiler to define the lexical rules of a programming language. It provides a systematic and efficient approach to tokenize the source code and generate tokens based on the lexical structure of the language.