Q1Compiler Design
Question
Explain the concept of Finite Automata and its role in lexical analysis.
Answer
Finite Automata (FA) are abstract machines that recognize regular languages. They form the mathematical foundation of lexical analyzers, which are implemented as DFAs to recognize token patterns.
A Finite Automaton (FA) is a mathematical model consisting of a finite set of states, a set of input symbols (alphabet), a transition function, a start state, and a set of final (accepting) states. Two types:
- NFA (Nondeterministic Finite Automaton): Can have multiple transitions from a state on the same input, and ε-transitions (transitions on empty string). Formally: M = (Q, Σ, δ, q0, F) where δ: Q × (Σ ∪ {ε}) → 2^Q.
- DFA (Deterministic Finite Automaton): Exactly one transition from each state on each input symbol. No ε-transitions. Formally: M = (Q, Σ, δ, q0, F) where δ: Q × Σ → Q. DFAs are more efficient to simulate.
The construction pipeline for a lexical analyzer is: Regular Expressions → NFA (Thompson's construction) → DFA (subset construction) → Minimized DFA (state minimization). The minimized DFA is then implemented as the lexer. For each token pattern, the regular expression is converted to an NFA. All NFAs are combined (with ε-transitions from a new start state to each sub-NFA's start state). The combined NFA is converted to a DFA. The DFA recognizes the longest possible token at each step (maximal munch rule) and identifies the token type.