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

Lexical Analysis:
Lexical analysis is the first phase of the compiler where the source code is divided into a sequence of lexemes (tokens). A lexeme is the smallest meaningful unit of the programming language. The lexical analyzer reads the source code character by character and groups them into lexemes based on predefined patterns called regular expressions. These lexemes are then passed to the parser for further processing.

Finite State Automaton (FSA):
Finite State Automaton, also known as Finite State Machine (FSM), is a mathematical model used to represent systems that can be in different states and transition between states based on inputs. In the context of lexical analysis, FSA is used to recognize and classify lexemes based on their patterns.

How FSA is used in Lexical Analysis:
1. Tokenization: FSA is used to define regular expressions that describe the patterns of different tokens in the programming language. Each regular expression is converted into a corresponding FSA.

2. Deterministic Finite Automaton (DFA): The FSA is converted into a DFA, which is a more efficient representation of the FSA. DFA has a fixed number of states and transitions, making it easier to implement.

3. Lexical Analyzer Generator: The DFA is used by the lexical analyzer generator tool, such as Lex or Flex, to generate the lexical analyzer code. The lexical analyzer code is responsible for scanning the source code, recognizing lexemes based on the DFA, and generating tokens.

4. Token Recognition: The lexical analyzer uses the DFA to recognize lexemes by traversing through the states of the DFA based on the current input character. When a final state is reached, the lexical analyzer generates a token corresponding to the recognized lexeme.

5. Error Handling: FSA also helps in handling lexical errors. If the lexical analyzer encounters an input that does not match any of the defined patterns, it can transition to an error state and report a lexical error.

Conclusion:
In summary, the concept of Finite State Automaton (FSA) is used in the lexical analysis phase of the compiler. FSA is used to define regular expressions, convert them into DFA, generate lexical analyzer code, recognize tokens, and handle lexical errors. It plays a crucial role in breaking down the source code into meaningful units for further processing by the parser and other compiler phases.