Computing knowledge in equational extensions of subterm convergent theories

Abstract

We study decision procedures for two knowledge problems critical to the verification of security protocols, namely the intruder deduction and the static equivalence problems. These problems can be related to particular forms of context matching and context unification. Both problems are defined with respect to an equational theory and are known to be decidable when the equational theory is given by a subterm convergent term rewrite system (TRS). In this work, we extend this to consider a subterm convergent TRS defined modulo an equational theory, like Commutativity. We present two pairs of solutions for these important problems. The first solves the deduction and static equivalence problems in rewrite systems modulo shallow theories such as Commutativity. The second provides a general procedure that solves the deduction and static equivalence problems in subterm convergent systems modulo syntactic permutative theories, provided a finite measure is ensured. Several examples of such theories are also given.

Terminating Non-disjoint Combined Unification

“…In the short term, we plan to experiment the use of our variant-free hierarchical unification procedures (e.g., the ones introduced in Examples 3 and 7) as an alternative to variant-based unification procedures in modern protocol verification tools [6,18,25]. In the long term, we want to promote the use of non-disjoint combination procedures [16] and mutation-based procedures [17] in protocol verification tools, targeting unification problems as well as some decision problems related to the knowledge of an intruder, such as intruder deduction (a reachability problem) and indistinguishability (an equivalence problem) [1,8]. The goal is to improve automation of verification methods when theories share for instance AC symbols.…”