Finite automata (DFA and NFA) in Compiler Design - Step-by-Step Execution

Concept Flow - Finite automata (DFA and NFA)

Start State

↓

Read Input Symbol

↓

Check Transition

↓

Move to Next State

↓

More Input?

No→Accept if Final State

↩Back to Read Input Symbol

The automaton starts at the start state, reads input symbols one by one, follows transitions if available, and accepts if it ends in a final state after all input is read.

Execution Sample

Compiler Design

States = {q0, q1}
Start = q0
Final = {q1}
Transitions:
q0 --a--> q1
q1 --b--> q1

A simple automaton that moves from q0 to q1 on 'a' and stays in q1 on 'b'.

Analysis Table

Step	Current State(s)	Input Symbol	Transition Taken	Next State(s)	Reason
1	q0	a	q0 --a--> q1	q1	Transition exists for 'a' from q0
2	q1	b	q1 --b--> q1	q1	Transition exists for 'b' from q1
3	q1	b	q1 --b--> q1	q1	Transition exists for 'b' from q1
4	q1		-	q1	No more input, q1 is final state, accept input

💡 Input fully read and automaton is in final state q1, so input is accepted.

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
Current State(s)	q0	q1	q1	q1	q1
Input Symbol	a b b	b b	b

Key Insights - 3 Insights

Why does the automaton accept the input even though it stays in the same state multiple times?

Because the state q1 is a final (accepting) state, staying there after reading all input means the input is accepted. See execution_table rows 2-4.

What happens if there is no transition for the current input symbol?

The automaton rejects the input immediately since it cannot move forward. This is shown in the 'No' branch in the concept_flow diagram.

How does an NFA differ in current states compared to a DFA?

An NFA can be in multiple states at once (set of states), while a DFA is always in exactly one state. This affects the 'Current State(s)' column in execution_table.

Visual Quiz - 3 Questions

Look at the execution_table, what is the current state after reading the first input symbol?

A q0

B q1

C q2

D No state

💡 Hint

Check Step 1 in execution_table under 'Next State(s)'

At which step does the automaton finish reading input and decide to accept?

A Step 2

B Step 3

C Step 4

D Step 1

💡 Hint

Look at the 'Reason' column in execution_table for when input ends and acceptance occurs

If the transition q1 --b--> q1 was missing, what would happen at Step 2?

A Automaton would reject input

B Automaton would accept input

C Automaton would stay in q0

D Automaton would move to a new state

💡 Hint

Refer to key_moments about what happens when no transition exists for input

Concept Snapshot

Finite Automata process input symbols one by one.
DFA has exactly one next state per input; NFA can have multiple.
Start at the start state, follow transitions.
Accept if input ends in a final state.
Reject if no valid transition exists.

Full Transcript

Finite automata are simple machines used in computer science to recognize patterns. They start in a special start state and read input symbols one at a time. For each symbol, they move to a next state based on defined transitions. If after reading all input the automaton is in a final (accepting) state, the input is accepted; otherwise, it is rejected. Deterministic Finite Automata (DFA) have exactly one next state for each input symbol, while Nondeterministic Finite Automata (NFA) can have multiple possible next states. This visual trace showed a simple DFA moving through states q0 and q1 on input 'a' and 'b's, accepting the input because it ended in a final state.