AN ORDER DEGREE ALTERNATOR FOR ARBITRARY TOPOLOGIES

Abstract

An alternator is an arbitrary set of interacting processes that satisfies three conditions. First, if a process executes its critical section, then no neighbor of that process can execute its critical section at the same state. Second, along any infinite sequence of system states, each process will execute its critical section, an infinite number of times. Third, along any maximally concurrent computation, the alternator will stabilize to a sequence of states in which the processes will execute their critical sections in alternation. A principal reason for interest in alternators is their ability to transform systems correct under serial execution semantics to systems that are correct under concurrent execution semantics. An earlier alternator for arbitrary topology required 2q states where q is the dependency graph circumference and after stabilization would wait 2q steps between critical section executions. In a synchronous environment, this alternator requires only 2d+1 states where d is the degree of the graph of process dependencies for the system and after stabilization will require a wait of 2d+1 steps between critical section executions. In an asynchronous environment, the synchronization properties of this alternator must be supplemented with an asynchronous unison algorithm. The asynchronous unison algorithm requires expansion of the required number of states to dt, where t is the longest chordless cycle in the dependency graph; however, the required wait between critical section executions remains O(d).