In this paper, an idea for improvement of suffix array construction using lazy evaluation is presented. Evaluation of the suffix array is based on the searching queries; only the necessary part of the suffix array is built when unevaluated part of the suffix array is referred during the searching process. This is less time consuming than constructing complete suffix array. We propose lazy evaluation of Schürmann-Stoye algorithm. Experimental results show that lazy Schürmann-Stoye algorithm runs faster than Maniscalco, which is well-recognized as the fastest suffix sorting algorithm, under the constraint of small LCP (longest common prefix) and a limited number of searching queries.

We propose a user-defined on-demand matching strategy, called O-matching, in which users can control the order of matching arguments of each operation symbol. In ordinary matching schemes it is not important to set the order of matching, however, in on-demand matching schemes, it is very important since an input term may be changed while doing the on-demand matching process. O-matching is suitable to combine with the E-strategy, which is a user-defined reduction strategy in which users can control the order of reducing arguments. We show a sufficient condition under which the E-strategy with O-matching is correct for head normal forms, that is, any reduced term is a head normal form.

This paper surveys two methods for designing numerically robust geometric algorithms. The first method is the exact-arithmetic method, in which numerical computations are done in sufficiently high precision so that all the topological judgements can be done correctly. This method is usually accompanied with lazy evaluation and symbolic perturbation in order to reduce the computational cost and the implementation cost. The second method is the topology-oriented method, in which the consistency of the topological structure is considered as higher-priority information than numerical computation, and thus inconsistency is avoided. Both of the methods are described with the implementation examples.

This paper extends left-incompatible term rewriting systems defined by Toyama et al. It is also shown that the functional strategy is normalizing in the class, where the functional strategy is the reduction strategy that finds index by some rule selection method and top-down and left-to-right lazy pattern matching method.