Stack Size Analysis for Interrupt-Driven Programs

Abstract

We study the problem of determining stack boundedness and the exact maximum stack size for three classes of interrupt-driven programs. Interrupt-driven programs are used in many real-time applications that require responsive interrupt handling. In order to ensure responsiveness, programmers often enable interrupt processing in the body of lower-priority interrupt handlers. In such programs a programming error can allow interrupt handlers to be interrupted in cyclic fashion to lead to an unbounded stack, causing the system to crash. For a restricted class of interrupt-driven programs, we show that there is a polynomial-time procedure to check stack boundedness, while determining the exact maximum stack size is PSPACE-complete. For a larger class of programs, the two problems are both PSPACE-complete, and for the largest class of programs we consider, the two problems are PSPACE-hard and can be solved in exponential time.

Jens Palsberg, Di Ma, and Tian Zhao were supported by the NSF ITR award 0112628. Thomas A. Henzinger, Krishnendu Chatterjee, and Rupak Majumdar were supported by the AFOSR grant F49620-00-1-0327, the DARPA grants F33615-C-98-3614 and F33615-00-C-1693, the MARCO grant 98-DT-660, and the NSF grants CCR-0208875 and CCR-0085949.