A Canonicity Test for Configuration

Advances in Polytime Isomorph Elimination for Configuration

“…Also experimented is the substitution of connecting actual objects by counting them according to their target types [8]. A pseudo-linear time canonicity test that complies with the canonical retractability property is given in [9] when the configuration problem only involves composition relations (in which case all structural solutions are trees). This result was generalized to generic configuration problems in [10], by describing a weak canonicity criterion compatible with canonical retractability, in the case of DAGS.…”

“…However, as seen at the end of section 2, it has to be chosen according to the canonicity criterion to ensure completeness. We hence sort trees according to the total order from [9], and define as canonical a tree being the -minimal in its isomorphism class. [9] proves that this canonicity criterion has the canonical retractability property.…”

“…We hence sort trees according to the total order from [9], and define as canonical a tree being the -minimal in its isomorphism class. [9] proves that this canonicity criterion has the canonical retractability property. To ensure completeness, the edges of E must be sorted as follows: edge e i is before e j in E iff T ∪ {e i } T ∪ {e j }.…”

“…Starting from this procedure, we generalize it to another able to generate all type of structures (DAGs), in a complete and non redundant way, while still avoiding the generation of an important number of isomorphic structures. This work is based upon the results obtained in [9] and [10], which demonstrated necessary existence conditions for such procedures but did not explicit any of them, leaving the crucial point of how defining them unmentioned.…”