Unsorted Functional Translations

Unsorted Functional Translations

In this article we first show how the functional and the optimized functional translation from modal logic to many-sorted first-order logic can be naturally extended to the hybrid language H(@, ↓). The translation is correct not only when reasoning over the class of all models, but for any firstorder definable class. We then show that sorts can be safely removed (i.e., without affecting the sat...

Splines and unsorted knot sequences

The definition of a B-spline is extended to unordered knot sequences. The added flexibility implies that the resulting piecewise polynomials, named U-splines, can be negative and locally linearly dependent. It is therefore remarkable that linear combinations of U-splines retain many properties of splines in B-spline form including smoothness, polynomial reproduction, and evaluation by recurrence.

Order-Sorted Termination: The Unsorted Way

We consider the problem of proving termination of ordersorted rewrite systems. The dominating method for proving termination of order-sorted systems has been to simply ignore sort information, and use the techniques developed for unsorted rewriting. The problem with this approach is that many order-sorted rewrite systems terminate because of the structure of the set of sorts. In these cases the...

Translations

Incremental Construction of Minimal Acyclic Sequential Transducers from Unsorted Data

This paper presents an efficient algorithm for the incremental construction of a minimal acyclic sequential transducer (ST) for a dictionary consisting of a list of input and output strings. The algorithm generalises a known method of constructing minimal finite-state automata (Daciuk et al., 2000). Unlike the algorithm published by Mihov and Maurel (2001), it does not require the input strings...