Phonology does not require the power of center-embedding, which is a property of context-free languages. Recursively enumerable grammars are as powerful as any theoretically possible computer and generate languages such as a^n, where n is a prime number.īoth phonology and morphology frequently display properties of regular languages.Context-sensitive grammars can handle non-linear patterns such as a^2^n for n > 0.Mildly context-sensitive grammars are powerful enough to handle cross-serial dependencies such as some types of copying.Context-free grammars have access to potentially infinite stack that allows them to reproduce patterns that involve center embedding.Regular grammars are as powerful as finite-state devices or regular expressions: they can "count" only until a certain threshold (no a^n b^n patterns).The Chomsky hierarchy aligns the main classes of formal languages with respect to their expressive power (Chomsky 1959). It also allows one to compare different grammars regarding parameters such as expressivity. Why theoretical linguists might be interested in formal language theory?įormal language theory explains how potentially infinite string sets, or formal languages,Ĭan be generalized to grammars encoding the desired patterns and what properties those This toolkit is relevant for anyone who is working or going to work with subregular grammars both from the perspectives of theoretical linguistics and formal language theory. ![]() generate_sample( n = 3) # Subregular languages and mappings in phonology Import sigmapie # learning UTP pattern with an SP grammar language = sigmapie.
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