Edith Spaan

A modal perspective on the computational complexity of attribute value grammar

Many of the formalisms used in Attribute Value grammar are notational variants of languages of propositional modal logic, and testing whether two Attribute Value Structures unify amounts to testing for modal satisfiability. In this paper we put this observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express re-entrancy, the ability to express generalisations, and the ability to express recursive constraints. Two main techniques are used: either Kripke models with desirable properties are constructed, or modalities are used to simulate fragments of Propositional Dynamic Logic. Further possibilities for the application of modal logic in computational linguistics are noted.

The Complexity of Propositional Tense Logics

In [4], Ladner investigated the complexity of the provability problems for modal logics. In particular, he showed that provability in all modal logics between K and S4 is PSPACE-hard, and he constructed polynomial space bounded algorithms for deciding provability in K, T, and S4, which implies that the provability problems for these logics are PSPACE-complete.

SPARSE reduces conjunctively to TALLY

Polynomials over finite fields are used to conjunctively reduce any sparse set to a tally set. This leads to the derivation of new results and to new simple proofs of known results about various classes that lie between P and P/poly.<<ETX>>

The relative power of logspace and polynomial time reductions

There exist many different formalisms to model the notion of resource bounded ‘truth-table’ reduction. Most papers in which truthtable reductions appear refer to the seminal paper of Ladner, Lynch and Selman for a definition. The definition of truth-table reductions given there however, pertains to only one of the possible incarnations of the notion. For larger resource bounds, this definition often coincides with other-often implicitly used-definitions of the notion. In this paper we focus our attention on resource bounds for which the various definitions probably donot pertain to the same notion. In particular, we show that coincidence of different notions implies coincidence of complexity classes likeNC1,LOG, andP, which are widely believed to be different.

Decidability and undecidability in stand-alone feature logics

This paper investigates the complexity of the satisfiability problem for feature logics strong enough to code entire grammars unaided. We show that feature logics capable of both enforcing re-entrancy and stating linguistic generalisations will have undecidable satisfiability problems even when most Boolean expressivity has been discarded. We exhibit a decidable fragment, but the restrictions imposed to ensure decidability render it unfit for stand-alone use. The import of these results is discussed, and we conclude that there is a need for feature logics that are less homogeneous in their treatment of linguistic structure.