46 research outputs found
Syzygies among reduction operators
We introduce the notion of syzygy for a set of reduction operators and relate
it to the notion of syzygy for presentations of algebras. We give a method for
constructing a linear basis of the space of syzygies for a set of reduction
operators. We interpret these syzygies in terms of the confluence property from
rewriting theory. This enables us to optimise the completion procedure for
reduction operators based on a criterion for detecting useless reductions. We
illustrate this criterion with an example of construction of commutative
Gr{\"o}bner basis
Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming
In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters
Developing a labelled object-relational constraint database architecture for the projection operator
Current relational databases have been developed in order to improve the handling of
stored data, however, there are some types of information that have to be analysed for
which no suitable tools are available. These new types of data can be represented and treated
as constraints, allowing a set of data to be represented through equations, inequations
and Boolean combinations of both. To this end, constraint databases were defined and
some prototypes were developed. Since there are aspects that can be improved, we propose
a new architecture called labelled object-relational constraint database (LORCDB). This provides
more expressiveness, since the database is adapted in order to support more types of
data, instead of the data having to be adapted to the database. In this paper, the projection
operator of SQL is extended so that it works with linear and polynomial constraints and
variables of constraints. In order to optimize query evaluation efficiency, some strategies
and algorithms have been used to obtain an efficient query plan.
Most work on constraint databases uses spatiotemporal data as case studies. However,
this paper proposes model-based diagnosis since it is a highly potential research area,
and model-based diagnosis permits more complicated queries than spatiotemporal examples.
Our architecture permits the queries over constraints to be defined over different sets
of variables by using symbolic substitution and elimination of variables.Ministerio de Ciencia y Tecnología DPI2006-15476-C02-0