Fairness for Infinitary Control

Abstract

In 1988, Olderog and Apt developed a fair scheduler for a system with finitely many processes based on the concept of explicit scheduling. In 2010, Hoenicke, Olderog, and Podelski extended the fair scheduler from static to dynamic control. In systems with dynamic control, processes can be created dynamically. Thus, the overall number of processes can be infinite, but the number of created processes is finite at each step of an execution of the system. In this paper we extend the fair scheduler to infinitary control. In systems with infinitary control, the number of created processes can be infinite. The fair scheduler for infinitary control is perhaps interesting for its apparent unfairness: instead of treating all processes equal, the scheduler discriminates each process against finitely many other processes. However, it also privileges each process against infinitely many other processes (in fact, all but finitely many).