Complexity of Linear Order Computation in Performance Grammar, TAG and HPSG

This paper investigates the time and space complexity of word order computatio11 ill the psycholinguistically motivated grammar formalism of Performance Gramrnar (PG). In PG, the jirst stage of syntax assembly yields an u11ordered tree (inobile ') co11sisti11g of a hierarchy of lexical f rames (lexically anchored elementary trees). Associated with each lexical frame is a linearizer-a Finite-State Automaton that locally comp11tes the left-to-right order of the bra11ches of the frame. li11earizatio11 takes place after the promotion compo11ent may have raised certai11 constiwents (e.g. Whor focused phrases) into the domain of lexicnl frames lrigher uμ i1, ;h,; syntactic mobile. We show that the worst-case time a11d space complexity of a11alyzi11g input strings of length n is 0(n) and O(n'), respectively. This result compares favorably with the time complexity of word-order comp11tations in Tree Adjoi11i11g Grammar (TAG). A compariso11 with Head-Driven Phrase Structure Gra111111ar (HPSG) reveals that PG yields a more declarative linearization method, provided that the FSA is rewritte11 as an equivale11t regular expressio11. 1. Performance Grammar Perfonnance Grammar (PG; Kempen, 1999) is a psycholinguistically motivated grammar fonnalism for analysis and generation. Somewhat simplified, and in the terminology of TAGs (cf. Joshi & Schabes, 1997), PG defines Jexically anchored initial trees and generates derived trees synchronously Iinked to conceptual structures described in the same formalism (as in Synchronous TAGs; Shieber & Schabes, 1990) and it factors dorninance relationships and linear precedence in surface structure trees (Joshi, 1987). PG differs from recent TAG versions in that there are no auxiliary trees, and that adjunction is replaced by a combination of substitution-the Gerard Kempen Dept. of Psychology, Leiden Univ. PO Box 9555, NL-2300 RB Leiden/NL [email protected] only composition operation-and finite-state linearizers that take caie of V\!ttic.:il rr:ovement ('promotion') of phrases and of the linear order of branches of deri ved trees. s su~o· 1 1 1 1 N p 1 s, AD V p 1PP1 s