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