Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NPcomplete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiability in deterministic polynomial time. Previously, no polynomial time algorithm was known.
Abstract. Although the observation of grammaticality judgements is well acknowledged, their formal representation faces problems of different kinds: linguistic, psycholinguistic, logical, computational. In this paper we focus on addressing some of the logical and computational aspects, relegating the linguistic and psycholinguistic ones in the parameter space. We introduce a model-theoretic interpretation of Property Grammars, which lets us formulate numerical accounts of grammaticality judgements. Such a representation allows for both clear-cut binary judgements, and graded judgements. We discriminate between problems of Intersective Gradience (i.e., concerned with choosing the syntactic category of a model among a set of candidates) and problems of Subsective Gradience (i.e., concerned with estimating the degree of grammatical acceptability of a model). Intersective Gradience is addressed as an optimisation problem, while Subsective Gradience is addressed as an approximation problem.
Abstract. Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article, we propose an approach for constructing a particular generic machine for the same task. This machine deploies the Map/Reduce paradigm over a fractal structure. Moreover our approach is modular : the machine is constructed by combining modules. In this manner, we can easily create generic machines for solving satifiability variants, such as SAT, #SAT, MAX-SAT.
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