Transition-Based Coding and Formal Language Theory for Ordered Digraphs

Abstract

Transition-based parsing of natural language uses transition systems to build directed annotation graphs (digraphs) for sentences. In this paper, we define, for an arbitrary ordered digraph, a unique decomposition and a corresponding linear encoding that are associated bijectively with each other via a new transition system. These results give us an efficient and succinct representation for digraphs and sets of digraphs. Based on the system and our analysis of its syntactic properties, we give structural bounds under which the set of encoded digraphs is restricted and becomes a context-free or a regular string language. The context-free restriction is essentially a superset of the encodings used previously to characterize properties of noncrossing digraphs and to solve maximal subgraphs problems. The regular restriction with a tight bound is shown to capture the Universal Dependencies v2.4 treebanks in linguistics.

How to embed noncrossing trees in Universal Dependencies treebanks in a low-complexity regular language

“…There is follow-up work that extends the encoding developed in this paper to all ordered digraphs (Yli-Jyrä 2019).…”

Formal and computational verification of phonological analyses

“…Although computational finite-state methods are normally associated with segmental models, the mappings in question do not necessarily have to be segmental, or string-based. Many techniques exist for producing string representations of structured information such as autosegmental models (Bird 1995, Yli-Jyrä 2013, Hulden 2015), hence what is said below will apply to a number of domains, although the focus is on models such as Optimality Theory (OT), Lexical Phonology and Morphology and general rewrite-rule models, which can be interpreted as bidirectional string-to-string translations.…”