Pierre Flener

Breaking Row and Column Symmetries in Matrix Models

We identify an important class of symmetries in constraint programming, arising from matrices of decision variables where rows and columns can be swapped. Whilst lexicographically ordering the rows (columns) breaks all the row (column) symmetries, lexicographically ordering both the rows and the columns fails to break all the compositions of the row and column symmetries. Nevertheless, our experimental results show that this is effective at dealing with these compositions of symmetries. We extend these results to cope with symmetries in any number of dimensions, with partial symmetries, and with symmetric values. Finally, we identify special cases where all compositions of the row and column symmetries can be eliminated by the addition of only a linear number of symmetry-breaking constraints.

Introducing ESRA, a relational language for modelling combinatorial problems

Current-generation constraint programming languages are considered by many, especially in industry, to be too low-level, difficult, and large. We argue that solver-independent, high-level relational constraint modelling leads to a simpler and smaller language, to more concise, intuitive, and analysable models, as well as to more efficient and effective model formulation, maintenance, reformulation, and verification. All this can be achieved without sacrificing the possibility of efficient solving, so that even time-pressed or less competent modellers can be well assisted. Towards this, we propose the esra relational constraint modelling language, showcase its elegance on some well-known problems, and outline a compilation philosophy for such languages.

The tree constraint

This article presents an arc-consistency algorithm for the tree constraint, which enforces the partitioning of a digraph

Logic Program Synthesis from Incomplete Information

\mathcal{G}

Inductive synthesis of recursive logic programs: Achievements and prospects

= (

Synthesis of Programs in Computational Logic

\mathcal{V},\mathcal{E}

Specifications are necessarily informal or: some more myths of formal methods

) into a set of vertex-disjoint anti-arborescences. It provides a necessary and sufficient condition for checking the tree constraint in

Logic program synthesis from incomplete specifications

\mathcal{O}(|\mathcal{V}| + |\mathcal{E}|)

An Abstract Formalization of Correct Schemas for Program Synthesis

time, as well as a complete filtering algorithm taking

On Correct Program Schemas

\mathcal{O}(|\mathcal{V}| \cdot |\mathcal{E}|)