Some computational complexity results for synchronous context-free grammars

Abstract

This paper investigates some computational problems associated with probabilistic translation models that have recently been adopted in the literature on machine translation. These models can be viewed as pairs of probabilistic contextfree grammars working in a 'synchronous' way. Two hardness results for the class NP are reported, along with an exponential time lower-bound for certain classes of algorithms that are currently used in the literature.

Extracting synchronous grammar rules from word-level alignments in linear time

“…As an example, the tree of Figure 2 produces the rules shown in Figure 5. We adopt the SCFG notation of Satta and Peserico (2005). Each rule has a right-hand side sequence for both languages, separated by a comma.…”

Synchronous binarization for machine translation

“…The benefit of binary grammars also lies in synchronous parsing (alignment). Wu (1997) shows that parsing a binary SCFG is in O(|w| 6 ) while parsing SCFG is NP-hard in general (Satta and Peserico, 2005).…”

“…Formally speaking, we can construct an equivalent SDTS by creating a cross-product of nonterminals from two sides. See (Satta and Peserico, 2005, Sec. 4) for other details.…”

“…An alternative definition by Satta and Peserico (2005) allows co-indexed nonterminals taking different symbols in two dimensions. Formally speaking, we can construct an equivalent SDTS by creating a cross-product of nonterminals from two sides.…”

Better synchronous binarization for machine translation

“…In these systems, machine translation decoding is cast as a synchronous parsing task. Because general SCFG parsing is an NPhard problem (Satta and Peserico, 2005), practical SMT decoders based on SCFG parsing requires an equivalent binary SCFG that is directly learned from training data to achieve polynomial time complexity using the CKY algorithm (Kasami, 1965;Younger, 1967) borrowed from CFG parsing techniques. Zhang et al (2006) proposed synchronous binarization, a principled method to binarize an SCFG in such a way that both the source-side and target-side virtual non-terminals have contiguous spans.…”