B1) PCFG
Master PCFG probabilistic grammars for controlled musical generation. Explore how BP3 leverages weights to craft intricate tabla rhythms.
Articles
L20) Grammatical Inference: When the Grammar Itself is Unknown
**Grammatical inference**: the ultimate challenge. Impossible (Gold), as hard as breaking RSA, it is the extreme case of recognition. To learn is to compress.
L19) The P-chain
The P-chain revolutionizes psycholinguistics: your brain predicts by producing to understand. Prediction error drives learning. Discover this unified model!
L18) The Sign Reversal
The slogan ‘generating is easy, analyzing is difficult’ is false. Semantic-constrained generation can be exponential, NP-complete, and exceed parsing.
L17) The complexity matrix
The **complexity matrix** dissects generation-recognition asymmetry. Explore 6 sub-problems, differential coupling, and sign reversal. Essential reading!
L16) The Paradox of Bidirectionality
Despite 50 years, bidirectionality in reversible grammars remains rare. Discover why asymmetry is structural and requires a declarative approach in NLP.
L15) The Formulas of Asymmetry
Why is generating simpler than analyzing? Discover the formulas of generation-parsing asymmetry: complexity, Catalan numbers, and surprisal.
L13) Generating or Recognizing: The Asymmetry of Formal Grammars
Explore the duality of formal grammars: why generating and parsing are not symmetric. A key issue between computer science, artificial intelligence, and music.
L13) Generating or Recognizing: Two Directions of Formal Grammars
Discover the duality of formal grammars: why generating and parsing are not symmetrical. A key analysis across computer science, linguistics, and music.
S15) Transposition Beyond Equal Temperament: Theory and Practice
Discover why classical transposition fails outside of 12-TET. Learn how BPscript transposition handles universal tonic changes across all tuning systems.