Associative-Commutative Deducibility Constraints

摘要

We consider deducibility constraints, which are equivalent to particular Diophantine systems, arising in the automatic verification of security protocols, in presence of associative and commutative symbols. We show that deciding such Diophantine systems is, in general, unde-cidable. Then, we consider a simple subclass, which we show decidable. Though the solutions of these problems are not necessarily semi-linear sets, we show that there are (computable) semi-linear sets whose minimal solutions are not too far from the minimal solutions of the system. Finally, we consider a small variant of the problem, for which there is a much simpler decision algorithm.