The Complexity of Bounded Context Switching with Dynamic Thread Creation

Baumann, Pascal; Majumdar, Rupak; Thinniyam, Ramanathan S.; Zetzsche, Georg

doi:10.4230/lipics.icalp.2020.111

Cited by 2 publications

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“…If furthermore the global states are defined explicitly and there are no local variables, then this results in a setting, which has been studied before: Atig et al [2009] showed that the context-bounded reachability problem is in 2EXPSPACE for a fixed 𝐾 (or when 𝐾 is given in unary). A matching lower bound for all fixed 𝐾 ≥ 1 (or equivalently, for 𝐾 given in unary) was provided by Baumann et al [2020]. We study the problem when 𝐾 is given in binary and states are defined in a succinct manner via global and local Boolean variables.…”

Section: Decision Problems and Main Resultsmentioning

confidence: 99%

“…The 3EXPSPACE upper bound follows from a relatively simple analysis of the upper bound of Atig et al [2009]. For the lower bound, we extend the 2EXPSPACE-hardness result of Baumann et al [2020] with new encodings.…”

Section: Decision Problems and Main Resultsmentioning

confidence: 99%

“…They show that the problem is in 2EXPSPACE for a fixed context bound, or if the context bound is given in unary. Baumann et al [2020] show a matching lower bound for this case. We improve upon these results to show that safety verification (without thread pooling) is 3EXPSPACE-complete when the context bound is given in binary.…”

Section: Introductionmentioning

confidence: 90%

“…(We note that we consider a model in which Boolean parameters are only allowed to be passed to recursive calls within a thread, but not to newly spawned tasks. Allowing formal parameters to spawns as well would result in a 2EXPSPACE-complete problem: membership follows from our methods, whereas hardness can be shown by applying the techniques of Baumann et al [2020] to our slightly different problem and setting. )…”

Section: Introductionmentioning

confidence: 99%

“…The hard part is the lower bound. We extend the encoding of Baumann et al [2020] to perform an łexponentially largerž computation when 𝐾 is in binary. Interestingly, succinct computations are now used in this proof to show lower bounds and hardness!…”

Section: Introductionmentioning

confidence: 99%

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Context-bounded verification of thread pools

Baumann

Majumdar

Thinniyam

et al. 2022

Proc. ACM Program. Lang.

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Thread pooling is a common programming idiom in which a fixed set of worker threads are maintained to execute tasks concurrently. The workers repeatedly pick tasks and execute them to completion. Each task is sequential, with possibly recursive code, and tasks communicate over shared memory. Executing a task can lead to more new tasks being spawned. We consider the safety verification problem for thread-pooled programs. We parameterize the problem with two parameters: the size of the thread pool as well as the number of context switches for each task. The size of the thread pool determines the number of workers running concurrently. The number of context switches determines how many times a worker can be swapped out while executing a single task---like many verification problems for multithreaded recursive programs, the context bounding is important for decidability. We show that the safety verification problem for thread-pooled, context-bounded, Boolean programs is EXPSPACE-complete, even if the size of the thread pool and the context bound are given in binary. Our main result, the EXPSPACE upper bound, is derived using a sequence of new succinct encoding techniques of independent language-theoretic interest. In particular, we show a polynomial-time construction of downward closures of languages accepted by succinct pushdown automata as doubly succinct nondeterministic finite automata. While there are explicit doubly exponential lower bounds on the size of nondeterministic finite automata accepting the downward closure, our result shows these automata can be compressed. We show that thread pooling significantly reduces computational power: in contrast, if only the context bound is provided in binary, but there is no thread pooling, the safety verification problem becomes 3EXPSPACE-complete. Given the high complexity lower bounds of related problems involving binary parameters, the relatively low complexity of safety verification with thread-pooling comes as a surprise.

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Section: Decision Problems and Main Resultsmentioning

confidence: 99%

Section: Decision Problems and Main Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Context-bounded verification of thread pools

Baumann

Majumdar

Thinniyam

et al. 2022

Proc. ACM Program. Lang.

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Context-Bounded Verification of Context-Free Specifications

Baumann

Ganardi

Majumdar

et al. 2023

Proc. ACM Program. Lang.

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A fundamental problem in refinement verification is to check that the language of behaviors of an implementation is included in the language of the specification. We consider the refinement verification problem where the implementation is a multithreaded shared memory system modeled as a multistack pushdown automaton and the specification is an input-deterministic multistack pushdown language. Our main result shows that the context-bounded refinement problem, where we ask that all behaviors generated in runs of bounded number of context switches belong to a specification given by a Dyck language, is decidable and coNP-complete. The more general case of input-deterministic languages follows, with the same complexity. Context-bounding is essential since emptiness for multipushdown automata is already undecidable, and so is the refinement verification problem for the subclass of regular specifications. Input-deterministic languages capture many non-regular specifications of practical interest and our result opens the way for algorithmic analysis of these properties. The context-bounded refinement problem is coNP-hard already with deterministic regular specifications; our result demonstrates that the problem is not harder despite the stronger class of specifications. Our proof introduces several general techniques for formal languages and counter programs and shows that the search for counterexamples can be reduced in non-deterministic polynomial time to the satisfiability problem for existential Presburger arithmetic. These techniques are essential to ensure the coNP upper bound: existing techniques for regular specifications are not powerful enough for decidability, while simple reductions lead to problems that are either undecidable or have high complexities. As a special case, our decidability result gives an algorithmic verification technique to reason about reference counting and re-entrant locking in multithreaded programs.

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The Complexity of Bounded Context Switching with Dynamic Thread Creation

Cited by 2 publications

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Context-bounded verification of thread pools

Context-bounded verification of thread pools

Context-Bounded Verification of Context-Free Specifications

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