Concurrency Theorems for Non-linear Rewriting Theories

Sesqui-pushout (SqPO) rewriting along non-linear rules and for monic matches is well-known to permit the modeling of fusing cloning vertices edges, yet date, no construction a suitable concurrency theorem was available. The lack such theorem, in turn, rendered compositional reasoning systems largely infeasible. We develop this paper SqPO-rewriting categories that are quasi-topoi (subsuming example adhesive categories) with required be regular monomorphisms given category. Our reveals an interesting “backpropagation effect” computing rule compositions. derive addition double pushout (DPO) rm-adhesive categories. results open SqPO DPO semantics rich static analysis techniques available from concurrency, algebra tracelet theory.