NFA Simulator
Non-deterministic Finite Automaton Interactive Tool
Non-deterministic Finite Automaton (NFA)
A mathematical model of computation that can be in multiple states simultaneously
Theory & Concepts
Definition:
An NFA is a 5-tuple (Q, Σ, δ, q₀, F) where Q is finite set of states, Σ is input alphabet, δ is transition function mapping a state and input symbol to a set of states, q₀ is start state, and F is set of final states.
Key Points:
- May have multiple possible transitions for a state-symbol pair
- Can have ε-transitions (transitions without consuming input)
- Non-deterministic - can follow multiple paths simultaneously
- Recognizes regular languages only
- Equivalent in power to DFAs, but can be more concise
Applications:
- Pattern matching in text processing
- Lexical analysis in compilers
- Regular expression implementation
- Protocol verification
- Natural language processing
University Guidelines
Exam Weightage
15-20 MarksSyllabus Coverage:
- NFA Definition and Components
- ε-NFA and its significance
- State Transition Diagrams
- Subset Construction (NFA to DFA conversion)
- Relationship with Regular Languages
- Kleene's Theorem
Common Questions:
- Design NFA for given language specifications
- Convert NFA to DFA using subset construction
- Prove equivalence of NFA and DFA
- Construct NFA for regular expressions
Exam Tips:
Show multiple transitions clearly for same symbol
Mark ε-transitions distinctly
Use set notation for transition function
Verify by tracing all possible paths
Be careful with acceptance conditions
Algorithm Details
O(n|Q|²)
Time Complexity
O(|Q|)
Space Complexity
Algorithm Steps:
- 1Initialize current state set to {q₀}
- 2For each input symbol, compute next state set
- 3Follow all possible transitions for current states
- 4Include ε-closure at each step if applicable
- 5Accept if any final state is in the final state set
States Configuration
Input Alphabet (Σ)
0
1
ε
Note: ε represents the empty string (epsilon)
Transition Function (δ)
Test Input
State Diagram
State
Current State
Accept State
Transition Table
| State | 0 | 1 | ε |
|---|---|---|---|
| →q0 | {q0} | {q1} | {q1} |
| q1* | - | {q1} | - |