Computing Boundary Tuples for Lawverean Quantales
In the process of solving a certain kind of quantitative equations over a Lawverean quantale Q (with the binary tensor operation ⊗ and partial ordering ≤), one is interested in finding finite tuples of quantale elements (q_1,...,q_n) such that their tensor product is above the given quantale element λ, called the threshold. In other words, we look for tuples such that λ ≤ q_1 ⊗ ··· ⊗ q_n holds. For a given quantale Q and threshold λ, such tuples are called good (Q,λ)-tuples. Instead of computing all good (Q,λ)-tuples, we are interested in finding ≤-minimal elements among them (so called boundary tuples or a basis), where the (partial) ordering is the componentwise extension of ≤ from quantale elements to quantale tuples.
The task of this master's thesis is to investigate the problem of computing boundary tuples for Lawverean quantales, design a corresponding algorithm, analyze it, implement, and experiment with it.
Advisor: Temur Kutsia and Wolfgang Schreiner