Interprocedural analysis of asynchronous programs

Abstract

An asynchronous program is one that contains procedure calls which are not immediately executed from the callsite, but stored and "dispatched" in a non-deterministic order by an external scheduler at a later point. We formalize the problem of interprocedural dataflow analysis for asynchronous programs as AIFDS problems, a generalization of the IFDS problems for interprocedural dataflow analysis. We give an algorithm for computing the precise meet-over-valid-paths solution for any AIFDS instance, as well as a demand-driven algorithm for solving the corresponding demand AIFDS instances. Our algorithm can be easily implemented on top of any existing interprocedural dataflow analysis framework. We have implemented the algorithm on top of BLAST, thereby obtaining the first safety verification tool for unbounded asynchronous programs. Though the problem of solving AIFDS instances is EXPSPACE-hard, we find that in practice our technique can efficiently analyze programs by exploiting standard optimizations of interprocedural dataflow analyses. ReductionWe can reduce an AIFDS instance into a standard, synchronous dataflow analysis problem where the set of dataflow facts is the product of the original set with a set of counters which track, for each of finitely many kinds of pending calls, the exact number of instances of the call that are pending. Though the reduced instance has the same solution as the AIFDS instance, we cannot use standard dataflow analyses to compute the solution as the lattice of dataflow facts is now unbounded: the counters can grow unboundedly to track the number of pending asynchronous calls. ApproximationGiven any fixed parameter k ∈ N, we can compute approximations of the meet-over-valid path solutions in the following way. We compute an under-approximation of the infinite reduced instance using a counter that counts up to k, dropping any asynchronous call if there are already k pending instances for that call. We call this problem the k-reduced IFDS problem. We compute an over-approximation of the infinite reduced instance using a counter that counts up to k, and bumps up to infinity as soon as the value exceeds k. This has the effect of tracking up to k pending calls precisely, and then supposing that an unbounded number of calls are pending if an additional asynchronous call is performed. We call this problem the k ∞reduced IFDS problem. For each k, both the over-and the under-approximations are instances of standard interprocedural dataflow analysis as the abstraction of the counters makes the set of dataflow facts finite. Thus, we can compute over-and under-approximations of the precise solution of the AIFDS instance by running standard interprocedural dataflow analysis algorithms [28]. ConvergenceIn a crucial step, we prove that for each AIFDS instance, there always exists a k for which the solutions of the over-approximate IFDS instance and the under-approximate IFDS instance coincide, thereby yielding the precise solution for the AIFDS instance. Thus, our simple algorithm for computing th...

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Delay-bounded scheduling

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