Unification-based grammars and complexity classes

نویسنده

  • Anders Søgaard
چکیده

A simple unification-based formalism is identified, and it is demonstrated how small changes effect its computational complexity. Versions are defined for polynomial time (PTIME), non-deterministic polynomial time (NPTIME), polynomial space (PSPACE), exponential time (EXPTIME), and undecidability (UNDEC). If the grammar is unambiguous or deterministically copying, its recognition problem is solvable in PTIME; the same goes for the polysized and k-ambiguous fragment; if the grammar has no unary cycles, it is solvable in NPTIME; in the abscence of true path equations and global implication, if functional uncertainty is impossible, and no weak precedence is employed (no quantification over strings), the grammar is solvable in PSPACE; if true path equations are not employed, a positive result can be obtained for EXPTIME; and finally, if the grammar is unrestricted and thus subsumed by Kasper-Rounds logic with global implication, it is undecidable. In fact, when functional uncertainty is also employed, this is high undecidability.

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تاریخ انتشار 2006