The Logical Meeting Point of Multiset Rewriting and Process Algebra: Progress Report

We present a revisited semantics for multiset rewriting founded on the left sequent rules of linear logic in its LV presentation. The resulting interpretation is extended with a majority of linear connectives into the language of ωmultisets. It drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication and more. The cut rules introduce finite auxiliary rewriting chains and are admissible. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. A simple translation maps process constructors of the asynchronous π-calculus to rewrite operators, while the structural equivalence corresponds directly to logically-motivated structural properties of ω-multisets (with one exception). The language of ω-multisets forms the basis for the security protocol specification language MSR 3. With relations to both multiset rewriting and process algebra, it supports specifications that are process-based, state-based, or of a mixed nature. Additionally, its deep logical underpinning makes it an ideal common ground for systematically comparing protocol specification languages, a task currently done in an ad-hoc manner.