Rewrite Rules

Abstract

The notion of a grammar as a relation between sets of strings is quite ancient. In the 4th century BCE, Pāṇini—Pynini’s eponym—proposed a sophisticated computational system (see Penn and Kiparsky 2012) in which Sanskrit words and phrases are constructed by repeated application of rewrite rules. These rules consist of a target (for example, in Aṣṭdhyāyā 6.1.77, [i, i:, u:,ṛ, ṛ.:]), a replacement (the corresponding semivowels), and a context in which it is applied (before another vowel). Priscian, writing in the 6th century CE, proposes a system of rewrite rules generating inflectional variants of Latin verbs (Matthews 1972). In the 19th century, historical linguists—particularly those now known as the Neogrammarians—employed rewrite rules to describe language change. For instance, Grimm’s Law correctly predicts that the initial *p in the Proto-Indo-European word meaning ‘father’ (cf. Latin pater) surfaces as [f] in Germanic (e.g., Old High German fater). In the 20th century, linguists adapted rewrite rules—some of which closely resemble historical sound changes—to sketch the morphophonemics of languages such as Menomini (Bloomfield 1939), Russian (Jakobson 1948), and Modern Hebrew (Chomsky 1951), and began to formalize rewrite systems. One particularly influential formal approach is the phonological rule notation popularized by Chomsky and Halle (1968). Subsequent work, reviewed below, establishes strong connections between the notation used by Chomsky and Halle and the regular languages,1 provides algorithms to compile rewrite rules into finite-state transducers, and employs them for speech and language technology applications. This chapter formalizes rewrite rules and shows how they are compiled into finite transducers, combined into rule cascades, and applied to input strings. Their use is then illustrated with applications in speech and language technology, including grapheme-to-phoneme conversion, morphological generation, and text normalization; the latter two applications are discussed in greater detail in later chapters.