Algorithmic Verification of Asynchronous Programs

TL;DR

This paper models asynchronous programs formally, proving that safety verification is EXPSPACE-complete and liveness verification is decidable and polynomial-time equivalent to Petri Net reachability, enabling verification via Petri Nets.

Contribution

It introduces a polynomial-time reduction from asynchronous programs to Petri Nets, facilitating the use of Petri Net algorithms for verification tasks.

Findings

Safety verification is EXPSPACE-complete.

Liveness verification is decidable and equivalent to Petri Net reachability.

Extensions to the model affect decidability and verification complexity.

Abstract

Asynchronous programming is a ubiquitous systems programming idiom to manage concurrent interactions with the environment. In this style, instead of waiting for time-consuming operations to complete, the programmer makes a non-blocking call to the operation and posts a callback task to a task buffer that is executed later when the time-consuming operation completes. A co-operative scheduler mediates the interaction by picking and executing callback tasks from the task buffer to completion (and these callbacks can post further callbacks to be executed later). Writing correct asynchronous programs is hard because the use of callbacks, while efficient, obscures program control flow. We provide a formal model underlying asynchronous programs and study verification problems for this model. We show that the safety verification problem for finite-data asynchronous programs is expspace-complete. We show that liveness verification for finite-data asynchronous programs is decidable and polynomial-time equivalent to Petri Net reachability. Decidability is not obvious, since even if the data is finite-state, asynchronous programs constitute infinite-state transition systems: both the program stack and the task buffer of pending asynchronous calls can be potentially unbounded. Our main technical construction is a polynomial-time semantics-preserving reduction from asynchronous programs to Petri Nets and conversely. The reduction allows the use of algorithmic techniques on Petri Nets to the verification of asynchronous programs. We also study several extensions to the basic models of asynchronous programs that are inspired by additional capabilities provided by implementations of asynchronous libraries, and classify the decidability and undecidability of verification questions on these extensions.