Data structures and terminating petri nets

Abstract

Consider a collection of particles of various types, and a set of reactions that are allowed to take place among these particles. Each reaction is defined by an input linear combination of particle types, and an output linear combination of particle types. This framework (which is a Petri net) is shown to model the cost of updating several standard data structures, the amortized cost of counting in various number systems and the space consumption of persistent data structures. A proof that the system of reactions is guaranteed to terminate gives a bound on the cost of the corresponding data structure problem. I show how linear programming can be used to analyze these systems.