Overview
NFA simulation advances a set of active states over each input symbol, including epsilon transitions where needed.
CoreSource checked
NFA Simulation
Matches input by tracking all possible nondeterministic automaton states.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Parsing
- Difficulty
- Intermediate
- Family
- Automata Simulation
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
active state setepsilon closurenondeterminismtransition relation
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(input_length * states)
Worst
O(input_length * states)
Space
O(states)
When to Use
- Use when language parsing needs active state set.
- Use when the input matches the assumptions behind automata Simulation.
When Not to Use
- Avoid when the grammar class does not match the parser's assumptions.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Matches input by tracking all possible nondeterministic automaton states
- Uses active state set and epsilon closure to guide the work.
- Produces parse tree.
Use Cases
- Language parsing
- Compiler front ends
- Structured text processing
Inputs
- Tokens or grammar
- Parser state
Outputs
- Parse tree
- Automaton
- Grammar table or parse result
Key Formulas (1)
Active-state update
Snext = εclosure(move(S, char))
S_next = epsilon_closure(move(S, char))Computes all states reachable after consuming one symbol.
Pseudocode
- 1.Prepare tokens, grammar rules, tables, or automaton states
- 2.Advance through tokens or grammar items according to the parsing rule
- 3.Create parse nodes, state transitions, or table entries when a rule applies
- 4.Report an error or return the completed structure
Canonical Example
- Input
- tokens = ['id', '+', 'id', '*', 'id'] with a tiny grammar or precedence table
- Output
- Parse tree
- Explanation
- NFA Simulation applies active state set to produce parse tree.
Implementation Notes
- Report errors with token position and expected grammar symbols.
- Keep the active state set step separate enough to test independently.
- Keep lexical analysis separate from parsing unless the method explicitly combines them.
Common Pitfalls
- Ambiguity and left recursion must be handled according to the parser type.
- Test edge cases, not only clean examples.
- Mixing token positions, character offsets, and grammar states can produce misleading parse errors.
Interactive Mechanism Walkthrough
Sequence Window & Automaton AlignmentShow grammar items, parser states, and consumed input as parsing progresses.
Input:ABABABCABAB
Window:ABAB
Step 1 of 4: Prepare tokens, grammar rules, tables, or automaton states
parsing-mechanismNotes
NFA Simulation should be used with the assumptions and tradeoffs of automata Simulation in mind.
Sources (1)
What each reference supports for this entry.
Introduction to Automata Theory, Languages, and Computation
BookAutomata textbook support for NFA Simulation's state-machine construction, language recognition, and correctness model.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toDFA Construction
NFA simulation and DFA construction are alternative execution strategies for regular expressions.
Related Algorithms
Tags
ParsingAutomatonRegular ExpressionTokenization