Jiilka Cidhiidhiga ah iyo Naxwaha-Hagayay

A language model supplies scores for continuation tokens, while a hard-constrained decoder limits which tokens remain eligible. The restriction acts during decoding rather than requiring the model weights to change for each request. A stateful rule system tracks the emitted prefix and allows only continuations compatible with its covered language. Formal representations can include regular expressions or context-free grammars, with support and implementation details identified by the engine. A regex can be handled with finite-state machinery, while general nested context-free structure can require stack-like or richer parser state. Calling every grammar decoder a simple finite-state machine therefore loses an important expressivity distinction. Tokenization also matters: one vocabulary token can contain text spanning several grammar elements. The decoder must consider its contribution to the parsing state rather than assume each token is one grammar symbol. The cited research includes efficient guided generation, input-dependent grammar-constrained decoding, and the XGrammar structured-generation engine. Their mechanisms and evaluations differ. A valid prefix is not necessarily a complete accepted output. An opening JSON brace can be a possible start, while a complete object still requires the rest of the structure, including its closing brace. Interruption or a length limit can leave an incomplete prefix. Likewise, grammar-conforming data can contain unsupported facts or fail an application rule outside the covered grammar. Masking also changes probabilities: if a stated distribution assigns A 0.2, B 0.3, and C 0.5, and only A and B remain allowed, renormalization gives A probability 0.4 and B 0.6.