Abstract
Recently, new libraries, such as Grand Central Dispatch (GCD), have been proposed to directly harness the power of multicore platforms and to make the development of concurrent software more accessible to software engineers. When using such a library, the programmer writes so-called blocks, which are chunks of code, and dispatches them using synchronous or asynchronous calls to several types of waiting queues. A scheduler is then responsible for dispatching those blocks among the available cores. Blocks can synchronize via a global memory. In this article, we propose Queue-Dispatch Asynchronous Systems as a mathematical model that faithfully formalizes the synchronization mechanisms and behavior of the scheduler in those systems. We study in detail their relationships to classical formalisms such as pushdown systems, Petri nets, Fifo systems, and counter systems. Our main technical contributions are precise worst-case complexity results for the Parikh coverability problem and the termination problem for several subclasses of our model. We also consider an extension of Qdas with a fork-join mechanism. Adding fork-join to any of the subclasses that we have identified leads to undecidability of the coverability problem. This motivates the study of over-approximations. Finally, we consider handmade abstractions as a practical way of verifying programs that cannot be faithfully modeled by decidable subclasses of Qdas.
- Apple. 2009. DispatchWebServer in Mac Developper Library. Retreived from https://developer.apple.com/library/mac/.Google Scholar
- Apple. 2010. Grand Central Dispatch (GCD) Reference. Technical Report.Google Scholar
- Apple. 2011. Concurrency Programming Guide. Technical Report.Google Scholar
- A. Bouajjani and M. Emmi. 2012. Analysis of recursively parallel programs. In Proceedings of POPL’12. 203--214. Google ScholarDigital Library
- A. Bouajjani, J. Esparza, and O. Maler. 1997. Reachability analysis of pushdown automata: Application to model-checking. In Proceedings of CONCUR’97 (LNCS), Vol. 1243. Springer, 135--150. Google ScholarDigital Library
- D. Brand and P. Zafiropulo. 1983. On communicating finite-state machines. Journal of the ACM 30, 2 (1983), 323--342. Google ScholarDigital Library
- P. Cousot and R. Cousot. 1977. Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In POPL’77. ACM, New York, NY, 238--252. DOI:http://dx.doi.org/10.1145/512950.512973 Google ScholarDigital Library
- J. Esparza. 1998. Decidability and complexity of Petri net problems—an introduction. In Lectures on Petri nets I. LNCS, Vol. 1491. Springer. Google ScholarDigital Library
- J. Esparza, D. Hansel, P. Rossmanith, and S. Schwoon. 2000. Efficient algorithms for model checking pushdown systems. In Proceedings of CAV’00 (LNCS), Vol. 1855. Springer, 232--247. Google ScholarDigital Library
- P. Ganty and R. Majumdar. 2012. Algorithmic verification of asynchronous programs. TOPLAS 34, 1 (2012). Google ScholarDigital Library
- P. Ganty, R. Majumdar, and A. Rybalchenko. 2009. Verifying liveness for asynchronous programs. In Proceedings of POPL’09. ACM, 102--113. Google ScholarDigital Library
- G. Geeraerts, A. Heußner, M. Praveen, and J.-F. Raskin. 2013b. ω-Petri nets. In Proceedings of Petri Nets 2013 (LNCS), Vol. 7927. Springer, 49--69. Google ScholarDigital Library
- G. Geeraerts, A. Heußner, and J.-F. Raskin. 2013a. Queue-dispatch asynchronous systems. In Proceedings of ACSD’13. IEEE, 150--159. Google ScholarDigital Library
- A. Heußner, J. Leroux, A. Muscholl, and G. Sutre. 2012. Reachability analysis of communicating pushdown systems. Logical Methods in Computer Science 8, 3 (2012).Google Scholar
- S. Schwoon J. Esparza, and A. Kučera. 2003. Model checking LTL with regular valuations for pushdown systems. Information and Computation 186, 2 (2003), 355--376. Google ScholarDigital Library
- R. Jhala and R. Majumdar. 2007. Interprocedural analysis of asynchronous programs. In Proceedings of POPL’07. ACM, 339--350. Google ScholarDigital Library
- J. Kochems and C.-H. L. Ong. 2013. Safety verification of asynchronous pushdown systems with shaped stacks. In Proceedings of CONCUR’13 (LNCS), Vol. 8052. SV, 288--302. Google ScholarDigital Library
- S. La Torre, P. Madhusudan, and G. Parlato. 2008. Context-bounded analysis of concurrent queue systems. In Proceedings of TACAS’08 (LNCS), Vol. 4963. Springer, 299--314. Google ScholarDigital Library
- libdispatch. 2013. Project Web Page. Retrieved from http://libdispatch.macosforge.org/.Google Scholar
- R. Lipton. 1976. The Reachability Problem Requires Exponential Space. Technical Report 62. Yale University.Google Scholar
- M. Minsky. 1967. Computation: Finite and Infinite Machines. Prentice Hall Int. Google ScholarDigital Library
- mist2. 2014. Tool repository and web page. (2014). https://github.com/pierreganty/mist.Google Scholar
- QDAS. 2014. mist2 Example Code. Retrieved from http://www.swt-bamberg.de/aheussner/research/qdas.html.Google Scholar
- C. Rackoff. 1978. The covering and boundedness problem for vector addition systems. Theoretical Computer Science 6 (1978), 233--231.Google ScholarCross Ref
- K. Sen and M. Viswanathan. 2006. Model checking multithreaded programs with asynchronous atomic methods. In Proceedings of CAV’06 (LNCS), Vol. 4144. 300--314. Google ScholarDigital Library
- SPIN. 2014. Project Web Page. Retrieved from http://www.spinroot.com.Google Scholar
Index Terms
- On the Verification of Concurrent, Asynchronous Programs with Waiting Queues
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