Restriction and Verbal Complexes in LFG: A Case Study for Danish

level of representation and permits grammaticali ty—as in usual LFG—to be determined on the phrasal and functional level of represent atio . A final note about the basic formal properties of the approach es. For traditional LFG grammars (satisfying the Nonbranching Dominance Conditio n) the parsing problem is decidable, since a grammar can assign to a string only a finite number of valid derivations which guarantees the composition of the (decidable) c ontext-free parsing and the (decidable) constraint satisfaction problem to be finitely bounded by the sentence length. Because of the decidability of the satisfiability problem fo r descriptions containing projection and/or restriction constraints, decidability of t he parsing problem follows for all these extensions too. With respect to generation, however, the matter is differen t. We have seen that the restriction operator permits it to remove information when this information is assumed to be irrelevant for the f-structures finally assigned to the sentences. Thereby, it produces floating structures that are not considered to be part of the a ctual f-structures. Since the inputs to the generator do not include the floating structure s p oduced by restriction, generation is here affected by the same problems as they arise in projection architectures. These assume only the f-structures, but not the complete fa nd m-structure configurations derived by the grammar to be given to the generator and d epend thus also on the assumption that the inputs to the generator are underspecifi ed. Unfortunately, the problem of whether or not there are any st rings associated with an underspecified input structure had been shown to be undeci dable in general (see, for example, Wedekind 1999). Since there is in general no struct ural relation between the (underspecified) inputs and the fully specified structures, it i in principle possible to restrict/project off structures whose size is not bounded b y the size of the actual input f-structures. And this permits the computation of some in ge eral undecidable problems to be encoded in the structures restricted/projected off th e -structures. However, for auxiliary constructions we have seen that the d epth of the requiredDEP embeddings is always finitely bounded (up to three or four, de pending on the language), so that at least for grammars analyzing those particular con structions by restriction or projection decidability of the generation problem can stil l be established. Acknowledgments Most of the research described here was supported by The Nordic Council of Ministers . We are indebted to Mary Dalrymple, Helge Dyvik, Ron Kaplan, John Maxwell and Vi ctoria Rosén for many helpful discussions. In addition, we would like to acknowledge the P alo Alto Research Center for supporting our grammar development by equipping us with the XLE platform. S pecial thanks go to John Maxwell for implementing the restriction operator and suggesting synt actic rules for passivization. References Butt, M. , M. E. Niño, and F. Segond. 1996. Multilingual Proc essing of Auxiliaries in LFG. In D. Gibbon, editor,Natural Language Processing and Speech Technology: Result s of the 3rd KONVENS Conference . Bielefeld, pages 111–122. Butt, M. , T. Holloway King, M. E. Niño, and F. Segond. 1999. A Grammar Writer’s Cookbook . CSLI Publications, Stanford, CA. Dyvik, H. 1999. The Universality of f-Structure: Discovery or Stipulation? The Case of Modals. In M. Butt and T. Holloway King, editors, The Proceedings of the LFG ’99 Conference . University of Manchester. Engdahl, E. 1999. The Choice between bli-Passive ands-Passive in Danish, Norwegian and Swedish. NORDSEM Report 3, Göteborg University.