Threshold counters with increments and decrements

A threshold counter is a shared data structure that assumes integer values. It provides two operations: Increment changes the current counter value from v to v+1, while Read returns the value [v/w], where v is the current counter value and w is a fixed constant. Thus, the Read operation returns the "approximate" value of the counter to within the constant w. Threshold counters have many potential uses, including software barrier synchronization. Threshold networks are a class of distributed data structures that can be used to construct highly-concurrent, low-contention implementations of shared threshold counters. In this paper, we give the first proof that any threshold network construction of a threshold counter can be extended to support a Decrement operation that changes the counter value from v to v-1.