Sequentiality in orthogonal term rewriting systems

AbstractFor orthogonal term rewriting systems Q. Huet and J.-J. Lévy have introduced the property of ‘strong sequentiality’. A strongly sequential orthogonal term rewriting system admits an efficiently computable normalizing one-step reduction strategy. As shown by Huet and Lévy, strong sequentiality is a decidable property. In this paper we present an alternative analysis of strongly sequential term rewriting systems, leading to two simplified proofs of the decidability of this property. We also compare some related notions of sequentiality that recently have been proposed

Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity

Unravelings are transformations from a conditional term rewriting system (CTRS, for short) over an original signature into an unconditional term rewriting systems (TRS, for short) over an extended signature. They are not sound w.r.t. reduction for every CTRS, while they are complete w.r.t. reduction. Here, soundness w.r.t. reduction means that every reduction sequence of the corresponding unraveled TRS, of which the initial and end terms are over the original signature, can be simulated by the reduction of the original CTRS. In this paper, we show that an optimized variant of Ohlebusch's unraveling for a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled TRS is left-linear or both right-linear and non-erasing. We also show that soundness of the variant implies that of Ohlebusch's unraveling. Finally, we show that soundness of Ohlebusch's unraveling is the weakest in soundness of the other unravelings and a transformation, proposed by Serbanuta and Rosu, for (normal) deterministic CTRSs, i.e., soundness of them respectively implies that of Ohlebusch's unraveling.Comment: 49 pages, 1 table, publication in Special Issue: Selected papers of the "22nd International Conference on Rewriting Techniques and Applications (RTA'11)

CoCoWeb - A Convenient Web Interface for Confluence Tools

6th International Workshop on Confluence6th International Workshop on ConfluenceWe present a useful web interface for tools that participate in the annual confluence competition

Life events, anxious depression and personality: a prospective and genetic study.

Background: The association between life events and anxious depression might be due to causality or to gene-environment correlation. We examined unidirectional and reciprocal causality and a gene-environment correlation model, in which genes that influence the vulnerability for anxious depression also increase the risk of exposure to life events. The effect of genes that influence environmental exposure might be mediated through personality and we therefore also examined the association between life events and personality (neuroticism and extraversion). Method: Information on life events, anxious depression, neuroticism and extraversion was collected in 5782 monozygotic (MZ) and dizygotic (DZ) twins who participated in a longitudinal survey study of the Netherlands Twin Register. To examine causality, data were analysed longitudinally. To examine gene-environment correlation, the co-twin control method was used. Results: Anxious depression and, to a lesser extent, neuroticism scores increased after exposure to life events. Anxious depression and neuroticism also predicted the experience of life events. Prospectively, extraversion was not associated with life events. Anxious depression, neuroticism and extraversion scores did not differ between the non-exposed subjects of MZ and DZ twin pairs and unrelated subjects discordant for life events. Conclusions: Our findings suggest that reciprocal causation explains the relationship between life events and anxious depression and between life events and neuroticism. Extraversion is not related to life events. No evidence was found for gene-environment correlation, i.e. the genes that influence anxious depression, neuroticism or extraversion do not overlap with the genes that increase the risk of exposure to life events