Volume 184, Issue 2

1. Right Buchberger algorithm over bijective skew PBW extensions

W. Fajardo.
In this paper we present a right version of the algorithms developed for to compute Gröbner bases over bijective skew PBW extensions in the left case given in [3]. In particular, we adapt the theory of reduction and we build a right division algorithm and generate a right version of Buchberger algorithm over bijective skew PBW extensions, finally we illustrate some examples using the SPBWE.lib library implemented in Maple (see [1], [4]). It is important to note that the development of this theory is fundamental to complete the SPBWE.lib library and to be able to develop many of the homological applications that arise as result of obtaining the right Gröbner bases over skew PBW extensions.

2. A Non-Deterministic Multiset Query Language

Bartosz Zielinski.
We develop a multiset query and update language executable in a term rewriting system. Its most remarkable feature, besides non-standard approach to quantification and introduction of fresh values, is non-determinism - a query result is not uniquely determined by the database. We argue that this feature is very useful, e.g., in modelling user choices during simulation or reachability analysis of a data-centric business process - the intended application of our work. Query evaluation is implemented by converting the query into a terminating term rewriting system and normalizing the initial term which encapsulates the current database. A normal form encapsulates a query result. We prove that our language can express any relational algebra query. Finally, we present a simple business process specification framework (and an example specification). Both syntax and semantics of our query language is implemented in Maude.