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We study valence systems, finite-control programs over infinite-statememories modeled in terms of graph monoids. Our contribution is a notion ofbounded context switching (BCS). Valence systems generalize pushdowns,concurrent pushdowns, and Petri nets. In these settings, our definitionconservatively generalizes existing notions. The main finding is thatreachability within a bounded number of context switches is in NP, independentof the memory (the graph monoid). Our proof is genuinely algebraic, andtherefore contributes a new way to think about BCS. In addition, we exhibit aclass of storage mechanisms for which BCS reachability belongs to P.

Bounded Context Switching for Valence Systems