Bounded Context Switching for Valence Systems

TL;DR

This paper introduces a new notion of bounded context switching for valence systems, showing that reachability under this constraint is NP-complete regardless of memory type, with some cases solvable in polynomial time.

Contribution

It generalizes existing BCS notions to valence systems and provides an algebraic proof that reachability is NP-complete, with special cases in P.

Findings

Reachability with bounded context switches is in NP for valence systems.

The algebraic proof offers a new perspective on BCS.

Certain storage mechanisms allow BCS reachability in polynomial time.

Abstract

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