In propositional temporal logic, the combination of the connectives "tomorrow" and "always in the future" require the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula.

Two classical semantical approaches to studying logics which combine time and modality are the T /spl times/ W-frames and Kamp-frames (Thomason (1984)). In this paper we study a new kind of frame that extends the one introduced in Burrieza et al. (2002). The motivation is twofold: theoretical, i.e., representing properties of the basic theory of functions (definability); and practical, their use in computational applications (considering time-flows as memory of computers connected in a net, each computer with its own clock). Specifically, we present a temporal /spl times/ modal (labelled) logic, whose semantics are given by ind-functional frames in which accessibility functions are used in order to interconnect time-flows. This way, we can: (i) specify to what time-flow we want to go; (ii) carry out different comparisons among worlds with different time measures; and (iii) define properties of certain kinds of functions (in particular, of total, injective, surjective, constant, increasing and decreasing functions), without the need to resort to second-order theories. In addition, we define a minimal axiomatic system and give the completeness theorem (Henkin-style).

Dynamic, parallel algorithms of the divide-and-conquer type are mapped onto static parallel computer architectures where the set of processors and their interconnections are fixed throughout the execution of a program. The approach taken is to transform a class of algorithms, expressed as functional programs, into a form that corresponds to a pipeline. The pipeline itself is then generated and the technique is illustrated by two sorting and one numeric list processing examples.