Static Analysis of Concurrent Programs Using Ordinary Differential Equations

Abstract

Static analysis may cause state space explosion problem. In this paper we demonstrate how ordinary differential equations can be used to check the deadlocks and boundedness of the programs. We hope that our method can avoid explosion of state space entirely. A concurrent program is represented by a family of differential equations of a restricted type, where each equation describes the program state change. This family of equations are shown analytically to have a unique solution. Each program state is measured by a time-dependent function that indicates the extent to which the state can be reached in execution. It is shown that 1) a program deadlocks iff every state measure converges to either 0 or 1 as time increases. Thus instead of exploring states, the solution of a family of differential equations is analyzed. 2) a program is bounded iff every state measure converges to a bounded nonnegative number.