#### Filter Results:

- Full text PDF available (6)

#### Publication Year

2014

2017

- This year (3)
- Last 5 years (10)
- Last 10 years (10)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Rudolf Berghammer, Peter Höfner, Insa Stucke
- RAMICS
- 2014

Software verification is essential for safety-critical systems. In this paper, we illustrate that some verification tasks can be done fully automatically. We show how to automatically verify imperative programs for relation-based discrete structures by combining relation algebra and the well-known assertion-based verification method with automated theorem… (More)

- Rudolf Berghammer, Peter Höfner, Insa Stucke
- RAMICS
- 2015

We present different approaches of using a special purpose computer algebra system and theorem provers in software verification. To this end, we first develop a purely algebraic while-program for computing a vertex coloring of an undirected (loop-free) graph. For showing its correctness, we then combine the well-known assertion-based verification method… (More)

- Rudolf Berghammer, Peter Höfner, Insa Stucke
- J. Log. Algebr. Meth. Program.
- 2016

First, we discuss three specific classes of relations, which allow to model the essential constituents of graphs, such as vertices and (directed or undirected) edges. Based on Kawahara’s characterisation of the cardinality of relations we then derive fundamental properties on their cardinalities. As main applications of these results, we formally verify… (More)

- Rudolf Berghammer, Insa Stucke, Michael Winter
- RAMICS
- 2015

- Insa Stucke, I. Stucke
- 2015

Previous work has shown that relation algebra (as introduced in [14] and further developed in [9,12,13,15], for example) is well suited for computational problems on many discrete structures. In particular, adjacency or incidence relations can be used tomodel graphs and special relations like vectors and points to represent subsets of vertices or edges, as… (More)

We present an extension of a Coq library for relation algebras, where we provide support for cardinals in a point-free way. This makes it possible to reason purely algebraically, which is well-suited for mechanisation. We discuss several applications in the area of graph theory and program verification.

- Insa Stucke
- RAMiCS
- 2017

- Rudolf Berghammer, Insa Stucke, Michael Winter
- J. Log. Algebr. Meth. Program.
- 2017

- Paul Brunet, Damien Pous, Insa Stucke
- ITP
- 2016

- Rudolf Berghammer, Nikita Danilenko, Peter Höfner, Insa Stucke
- Discrete Mathematics
- 2016

Based on Y. Kawahara’s characterisation of the cardinality of relations we derive some fundamental properties of cardinalities concerning vectors, points and mapping-related relations. As applications of these results we verify some properties of linear orders and graphs in a calculational manner. These include the cardinalities of rooted trees and some… (More)

- ‹
- 1
- ›