Regular approximation of link grammar

We present a regular approximation of Link Grammar, a dependency-type formalism with context-free expressive power, as a first step toward a finite-state joint inference system. The approximation is implemented by limiting the maximum nesting depth of links, and otherwise retains the features of the original formalism. We present a string encoding of Link Grammar parses and describe finite-state machines implementing the grammar rules as well as the planarity, connectivity, ordering and exclusion axioms constraining grammatical Link Grammar parses. The regular approximation is then defined as the intersection of these machines. Finally, we implement two approaches to finite-state parsing using the approximation and discuss their feasibility. We find that parsing in the intersection grammars framework using the approximation is feasible, although inefficient, and we discuss several approaches to improve the efficiency.