Overview
Sequitur Compression is a grammar compression method for grammar-based compression. It works by building a context-free grammar by replacing repeated digrams.
ExtendedSource checked
Sequitur Compression
Sequitur Compression addresses grammar-based compression by building a context-free grammar by replacing repeated digrams.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Compression
- Difficulty
- Intermediate
- Family
- Grammar Compression
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
grammar-based compressiongrammar compressionautomata statescompression
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n)
Worst
O(n log n)
Space
O(n)
When to Use
- Use Sequitur Compression when solving grammar-based compression and you want to benefit from building a context-free grammar by replacing repeated digrams.
- Choose it when O(n) average/worst-case time and O(n) memory match your workload profile.
- Prefer it over Context Tree Weighting or Context Mixing when the problem structure favors grammar-based compression.
When Not to Use
- Avoid when speed, random access, or worst-case expansion matters more than compression ratio.
- Avoid when encoder and decoder cannot share the same model assumptions.
What It Does
- Computes grammar-based compression within Grammar Compression workloads (O(n) time, O(n) space).
- Works by building a context-free grammar by replacing repeated digrams.
- Maintains key invariants across grammar-based compression, grammar compression, automata states.
Use Cases
- Production and research workloads requiring grammar-based compression via building a context-free grammar by replacing repeated digrams.
- Grammar Compression pipelines where O(n) time and O(n) space fit system constraints.
- Engineering comparisons against Context Tree Weighting and Context Mixing when tuning grammar-based compression.
Inputs
- Input byte or symbol stream
- Model, dictionary, or coding parameters
Outputs
- Compressed representation
- Updated model or dictionary state
Pseudocode
- 1.Preprocess the input alphabet, pattern/grammar rules, or symbol frequency tables for Sequitur Compression.
- 2.Construct the lookup automaton, suffix/shift index, or coding state (grammar-based compression, grammar compression).
- 3.Scan the input sequence by building a context-free grammar by replacing repeated digrams.
- 4.Emit matches, derivation nodes, or encoded tokens while advancing the state transition table.
- 5.Finalize trailing state and return the completed grammar-based compression output.
Canonical Example
- Input
- Input byte or symbol stream configured for a representative grammar-based compression test case
- Output
- Compressed representation satisfying Sequitur Compression invariants
- Explanation
- Sequitur Compression processes the input by building a context-free grammar by replacing repeated digrams, tracking grammar-based compression and grammar compression to produce the verified grammar-based compression result.
Implementation Notes
- Keep encoder and decoder model updates byte-for-byte consistent.
- Add round-trip tests before measuring compression ratio.
- Document framing, dictionary reset, and end-marker behavior.
Common Pitfalls
- Training or updating the model differently in encoder and decoder.
- Ignoring worst-case expansion on small or already-compressed inputs.
- Forgetting bit-level framing and end-of-stream handling.
Interactive Mechanism Walkthrough
Sequence Window & Automaton AlignmentShow building a context-free grammar by replacing repeated digrams on a small grammar-based compression example.
Input:ABABABCABAB
Window:ABAB
Step 1 of 5: Preprocess the input alphabet, pattern/grammar rules, or symbol frequency tables for Sequitur Compression.
compression-mechanismNotes
Sequitur Compression operates in O(n) time and O(n) space within the Grammar Compression family. Often compared with Context Tree Weighting and Context Mixing.
Sources (1)
What each reference supports for this entry.
Compression and Explanation Using Hierarchical Grammars
PaperReference for Sequitur grammar inference, digram uniqueness, and rule utility.
Open sourceExplore Next
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Alternative toContext Mixing
Compression · Specialized
Sequitur Compression and Context Mixing are practical alternatives within grammar-based compression, with different assumptions and tradeoffs.
Compare with thisRelationships
View full relationship pageAlternative toContext Tree Weighting
Sequitur Compression and Context Tree Weighting are practical alternatives within grammar-based compression, with different assumptions and tradeoffs.
Alternative toContext Mixing
Sequitur Compression and Context Mixing are practical alternatives within grammar-based compression, with different assumptions and tradeoffs.
Alternative toPAQ Compression
Sequitur Compression and PAQ Compression are practical alternatives within grammar-based compression, with different assumptions and tradeoffs.
Tags
Compression