Unification grammars and off-line parsability

Unification grammars are known to be Turing-equivalent; given a grammar G and a word w, it is undecidable whether w L(G). In order to ensure decidability, several constraints on grammars, commonly known as off-line parsability (OLP), were suggested, such that the recognition problem is decidable for grammars which satisfy OLP. An open question is whether it is decidable if a given grammar satisfies OLP. In this paper we investigate various definitions of OLP and discuss their interrelations, proving that some of the OLP variants are indeed undecidable. We then present a novel, decidable OLP constraint which is more liberal than the existing decidable ones.
Keywords off-line parsability  parsing termination  unification grammars
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DOI 10.1007/s10849-005-4511-1
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Daniel Feinstein & Shuly Wintner (2008). Highly Constrained Unification Grammars. Journal of Logic, Language and Information 17 (3):345-381.
Anders Søgaard & Martin Lange (2009). Polyadic Dynamic Logics for Hpsg Parsing. Journal of Logic, Language and Information 18 (2):159-198.

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