Fei He
ABSTRACT
Analyzing multi-threaded programs is hard due to the number of thread interleavings. Partial orders can be used for modeling and analyzing multi-threaded programs. However, there is no dedicated decision procedure for solving partial-order constraints. In this paper, we propose a novel ordering consistency theory for multi-threaded program verification under sequential consistency, and we elaborate its theory solver, which realizes incremental consistency checking, minimal conflict clause generation, and specialized theory propagation to improve the efficiency of SMT solving. We conducted extensive experiments on credible benchmarks; the results show significant promotion of our approach.
- Parosh Abdulla, Stavros Aronis, Bengt Jonsson, and Konstantinos Sagonas. 2014. Optimal Dynamic Partial Order Reduction. In Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL ’14). Association for Computing Machinery, New York, NY, USA. 373–384. isbn:9781450325448 https://doi.org/10.1145/2535838.2535845 Google Scholar
Digital Library
- Parosh Aziz Abdulla, Stavros Aronis, Mohamed Faouzi Atig, Bengt Jonsson, Carl Leonardsson, and Konstantinos Sagonas. 2015. Stateless Model Checking for TSO and PSO. In Tools and Algorithms for the Construction and Analysis of Systems, Christel Baier and Cesare Tinelli (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 353–367. isbn:978-3-662-46681-0 https://doi.org/10.1007/978-3-662-46681-0_28 Google ScholarDigital Library
- Parosh Aziz Abdulla, Mohamed Faouzi Atig, Bengt Jonsson, and Carl Leonardsson. 2016. Stateless Model Checking for POWER. In Computer Aided Verification, Swarat Chaudhuri and Azadeh Farzan (Eds.). Springer International Publishing, Cham. 134–156. isbn:978-3-319-41540-6 https://doi.org/10.1007/978-3-319-41540-6_8 Google ScholarCross Ref
- Parosh Aziz Abdulla, Mohamed Faouzi Atig, Bengt Jonsson, Magnus Lång, Tuan Phong Ngo, and Konstantinos Sagonas. 2019. Optimal Stateless Model Checking for Reads-from Equivalence under Sequential Consistency. Proc. ACM Program. Lang., 3, OOPSLA (2019), Article 150, Oct., 29 pages. https://doi.org/10.1145/3360576 Google ScholarDigital Library
- Parosh Aziz Abdulla, Mohamed Faouzi Atig, Bengt Jonsson, Magnus Lång, Tuan Phong Ngo, and Konstantinos Sagonas. 2019. Optimal Stateless Model Checking for Reads-from Equivalence under Sequential Consistency. Proc. ACM Program. Lang., 3, OOPSLA (2019), Article 150, Oct., 29 pages. https://doi.org/10.1145/3360576 Google ScholarDigital Library
- Sarita V Adve and Kourosh Gharachorloo. 1996. Shared memory consistency models: A tutorial. computer, 29, 12 (1996), 66–76. https://doi.org/10.1109/2.546611 Google ScholarDigital Library
- Deepak Ajwani and Tobias Friedrich. 2007. Average-Case Analysis of Online Topological Ordering. In Proceedings of the 18th International Conference on Algorithms and Computation (ISAAC’07). Springer-Verlag, Berlin, Heidelberg. 464–475. isbn:3540771182 https://doi.org/10.1007/978-3-540-77120-3_41 Google ScholarCross Ref
- Deepak Ajwani, Tobias Friedrich, and Ulrich Meyer. 2008. An O(N2.75) Algorithm for Incremental Topological Ordering. ACM Trans. Algorithms, 4, 4 (2008), Article 39, Aug., 14 pages. issn:1549-6325 https://doi.org/10.1145/1383369.1383370 Google ScholarDigital Library
- Jade Alglave, Daniel Kroening, Vincent Nimal, and Daniel Poetzl. 2014. Don’t Sit on the Fence. In Computer Aided Verification, Armin Biere and Roderick Bloem (Eds.). Springer International Publishing, Cham. 508–524. isbn:978-3-319-08867-9 https://doi.org/10.1007/978-3-319-08867-9_33 Google ScholarDigital Library
- Jade Alglave, Daniel Kroening, and Michael Tautschnig. 2013. Partial Orders for Efficient Bounded Model Checking of Concurrent Software. In Computer Aided Verification, Natasha Sharygina and Helmut Veith (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 141–157. isbn:978-3-642-39799-8 https://doi.org/10.1007/978-3-642-39799-8_9 Google ScholarCross Ref
- Jade Alglave, Luc Maranget, Susmit Sarkar, and Peter Sewell. 2010. Fences in Weak Memory Models. In Computer Aided Verification, Tayssir Touili, Byron Cook, and Paul Jackson (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 258–272. isbn:978-3-642-14295-6 https://doi.org/10.1007/978-3-642-14295-6_25 Google ScholarDigital Library
- Clark Barrett and Cesare Tinelli. 2018. Satisfiability Modulo Theories. Springer International Publishing, Cham. 305–343. isbn:978-3-319-10575-8 https://doi.org/10.1007/978-3-319-10575-8_11 Google ScholarCross Ref
- Michael A. Bender, Jeremy T. Fineman, Seth Gilbert, and Robert E. Tarjan. 2015. A New Approach to Incremental Cycle Detection and Related Problems. ACM Trans. Algorithms, 12, 2 (2015), Article 14, Dec., 22 pages. issn:1549-6325 https://doi.org/10.1145/2756553 Google ScholarDigital Library
- Dirk Beyer, Thomas A. Henzinger, and Grégory Théoduloz. 2007. Configurable Software Verification: Concretizing the Convergence of Model Checking and Program Analysis. In Computer Aided Verification, Werner Damm and Holger Hermanns (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 504–518. isbn:978-3-540-73368-3 https://doi.org/10.1007/978-3-540-73368-3_51 Google ScholarCross Ref
- Dirk Beyer and M. Erkan Keremoglu. 2011. CPAchecker: A Tool for Configurable Software Verification. In Computer Aided Verification, Ganesh Gopalakrishnan and Shaz Qadeer (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 184–190. isbn:978-3-642-22110-1 https://doi.org/10.1007/978-3-642-22110-1_16 Google ScholarCross Ref
- Armin Biere, Alessandro Cimatti, Edmund Clarke, and Yunshan Zhu. 1999. Symbolic Model Checking without BDDs. In Tools and Algorithms for the Construction and Analysis of Systems, W. Rance Cleaveland (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg. 193–207. isbn:978-3-540-49059-3 https://doi.org/10.1007/3-540-49059-0_14 Google ScholarCross Ref
- Marek Chalupa, Krishnendu Chatterjee, Andreas Pavlogiannis, Nishant Sinha, and Kapil Vaidya. 2017. Data-Centric Dynamic Partial Order Reduction. Proc. ACM Program. Lang., 2, POPL (2017), Article 31, Dec., 30 pages. https://doi.org/10.1145/3158119 Google ScholarDigital Library
- Marek Chalupa, Krishnendu Chatterjee, Andreas Pavlogiannis, Nishant Sinha, and Kapil Vaidya. 2017. Data-Centric Dynamic Partial Order Reduction. Proc. ACM Program. Lang., 2, POPL (2017), Article 31, Dec., 30 pages. https://doi.org/10.1145/3158119 Google ScholarDigital Library
- Edmund Clarke, Armin Biere, Richard Raimi, and Yunshan Zhu. 2001. Bounded Model Checking Using Satisfiability Solving. Form. Methods Syst. Des., 19, 1 (2001), July, 7–34. issn:0925-9856 https://doi.org/10.1023/A:1011276507260 Google ScholarDigital Library
- Lucas Cordeiro and Bernd Fischer. 2011. Verifying Multi-Threaded Software Using Smt-Based Context-Bounded Model Checking. In Proceedings of the 33rd International Conference on Software Engineering (ICSE ’11). Association for Computing Machinery, New York, NY, USA. 331–340. isbn:9781450304450 https://doi.org/10.1145/1985793.1985839 Google ScholarDigital Library
- Ron Cytron, Jeanne Ferrante, Barry K. Rosen, Mark N. Wegman, and F. Kenneth Zadeck. 1991. Efficiently computing static single assignment form and the control dependence graph. ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS, 13 (1991), 451–490. https://doi.org/10.1145/115372.115320 Google ScholarDigital Library
- Martin Davis, George Logemann, and Donald Loveland. 1962. A Machine Program for Theorem-Proving. Commun. ACM, 5, 7 (1962), July, 394–397. issn:0001-0782 https://doi.org/10.1145/368273.368557 Google ScholarDigital Library
- Leonardo de Moura and Nikolaj Bjørner. 2008. Z3: An Efficient SMT Solver. In Tools and Algorithms for the Construction and Analysis of Systems, C. R. Ramakrishnan and Jakob Rehof (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 337–340. isbn:978-3-540-78800-3 https://doi.org/10.1007/978-3-540-78800-3_24 Google ScholarCross Ref
- Leonardo De Moura and Nikolaj Bjørner. 2011. Satisfiability modulo Theories: Introduction and Applications. Commun. ACM, 54, 9 (2011), Sept., 69–77. issn:0001-0782 https://doi.org/10.1145/1995376.1995394 Google ScholarDigital Library
- Thomas Dinsdale-Young, Mike Dodds, Philippa Gardner, Matthew J. Parkinson, and Viktor Vafeiadis. 2010. Concurrent Abstract Predicates. In ECOOP 2010 – Object-Oriented Programming, Theo D’Hondt (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg. 504–528. isbn:978-3-642-14107-2 https://doi.org/10.1007/978-3-642-14107-2_24 Google ScholarCross Ref
- Cormac Flanagan and Patrice Godefroid. 2005. Dynamic Partial-Order Reduction for Model Checking Software. In Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL ’05). Association for Computing Machinery, New York, NY, USA. 110–121. isbn:158113830X https://doi.org/10.1145/1040305.1040315 Google ScholarDigital Library
- Malay K. Ganai and Aarti Gupta. 2008. Efficient Modeling of Concurrent Systems in BMC. In Model Checking Software, Klaus Havelund, Rupak Majumdar, and Jens Palsberg (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 114–133. isbn:978-3-540-85114-1 https://doi.org/10.1007/978-3-540-85114-1_10 Google ScholarDigital Library
- Natalia Gavrilenko, Hernán Ponce-de León, Florian Furbach, Keijo Heljanko, and Roland Meyer. 2019. BMC for Weak Memory Models: Relation Analysis for Compact SMT Encodings. In Computer Aided Verification, Isil Dillig and Serdar Tasiran (Eds.). Springer International Publishing, Cham. 355–365. isbn:978-3-030-25540-4 https://doi.org/10.1007/978-3-030-25540-4_19 Google ScholarCross Ref
- Cunjing Ge, Feifei Ma, Jeff Huang, and Jian Zhang. 2016. SMT Solving for the Theory of Ordering Constraints. In Languages and Compilers for Parallel Computing, Xipeng Shen, Frank Mueller, and James Tuck (Eds.). Springer International Publishing, Cham. 287–302. isbn:978-3-319-29778-1 https://doi.org/10.1007/978-3-319-29778-1_18 Google ScholarDigital Library
- Patrice Godefroid. 1997. Model Checking for Programming Languages Using VeriSoft. In Proceedings of the 24th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL ’97). Association for Computing Machinery, New York, NY, USA. 174–186. isbn:0897918533 https://doi.org/10.1145/263699.263717 Google ScholarDigital Library
- Ashutosh Gupta, Corneliu Popeea, and Andrey Rybalchenko. 2011. Predicate Abstraction and Refinement for Verifying Multi-Threaded Programs. In Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL ’11). Association for Computing Machinery, New York, NY, USA. 331–344. isbn:9781450304900 https://doi.org/10.1145/1926385.1926424 Google ScholarDigital Library
- Bernhard Haeupler, Telikepalli Kavitha, Rogers Mathew, Siddhartha Sen, and Robert E. Tarjan. 2012. Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance. ACM Trans. Algorithms, 8, 1 (2012), Article 3, Jan., 33 pages. issn:1549-6325 https://doi.org/10.1145/2071379.2071382 Google ScholarDigital Library
- Alex Horn and Jade Alglave. 2014. Concurrent Kleene Algebra of Partial Strings. arxiv:1407.0385. arxiv:1407.0385Google Scholar
- Alex Horn and Daniel Kroening. 2015. On partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency. arxiv:1504.00037. arxiv:1504.00037Google Scholar
- Jeff Huang. 2015. Stateless Model Checking Concurrent Programs with Maximal Causality Reduction. In Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI ’15). Association for Computing Machinery, New York, NY, USA. 165–174. isbn:9781450334686 https://doi.org/10.1145/2737924.2737975 Google ScholarDigital Library
- Omar Inverso, Ermenegildo Tomasco, Bernd Fischer, Salvatore La Torre, and Gennaro Parlato. 2014. Bounded Model Checking of Multi-threaded C Programs via Lazy Sequentialization. In Computer Aided Verification, Armin Biere and Roderick Bloem (Eds.). Springer International Publishing, Cham. 585–602. isbn:978-3-319-08867-9 https://doi.org/10.1007/978-3-319-08867-9_39 Google ScholarDigital Library
- Irit Katriel and Hans L. Bodlaender. 2006. Online Topological Ordering. ACM Trans. Algorithms, 2, 3 (2006), July, 364–379. issn:1549-6325 https://doi.org/10.1145/1159892.1159896 Google ScholarDigital Library
- Michalis Kokologiannakis, Ori Lahav, Konstantinos Sagonas, and Viktor Vafeiadis. 2017. Effective Stateless Model Checking for C/C++ Concurrency. Proc. ACM Program. Lang., 2, POPL (2017), Article 17, Dec., 32 pages. https://doi.org/10.1145/3158105 Google ScholarDigital Library
- Michalis Kokologiannakis, Azalea Raad, and Viktor Vafeiadis. 2019. Model Checking for Weakly Consistent Libraries. In Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2019). Association for Computing Machinery, New York, NY, USA. 96–110. isbn:9781450367127 https://doi.org/10.1145/3314221.3314609 Google ScholarDigital Library
- Michalis Kokologiannakis, Azalea Raad, and Viktor Vafeiadis. 2019. Model Checking for Weakly Consistent Libraries. In Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2019). Association for Computing Machinery, New York, NY, USA. 96–110. isbn:9781450367127 https://doi.org/10.1145/3314221.3314609 Google ScholarDigital Library
- Daniel Kroening and Michael Tautschnig. 2014. CBMC – C Bounded Model Checker. In Tools and Algorithms for the Construction and Analysis of Systems, Erika Ábrahám and Klaus Havelund (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 389–391. isbn:978-3-642-54862-8 https://doi.org/10.1007/978-3-642-54862-8_26 Google ScholarCross Ref
- Leslie Lamport. 1979. How to make a multiprocessor computer that correctly executes multiprocess programs. IEEE Computer Architecture Letters, 28, 09 (1979), 690–691. http://doi.org/10.1109/TC.1979.1675439 Google ScholarDigital Library
- Alberto Marchetti-Spaccamela, Umberto Nanni, and Hans Rohnert. 1996. Maintaining a topological order under edge insertions. Inform. Process. Lett., 59, 1 (1996), 53 – 58. issn:0020-0190 https://doi.org/10.1016/0020-0190(96)00075-0 Google ScholarDigital Library
- Antoni Mazurkiewicz. 1987. Trace theory. In Petri Nets: Applications and Relationships to Other Models of Concurrency, W. Brauer, W. Reisig, and G. Rozenberg (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 278–324. isbn:978-3-540-47926-0Google Scholar
- Matthew W. Moskewicz, Conor F. Madigan, Ying Zhao, Lintao Zhang, and Sharad Malik. 2001. Chaff: Engineering an Efficient SAT Solver. In Proceedings of the 38th Annual Design Automation Conference (DAC ’01). Association for Computing Machinery, New York, NY, USA. 530–535. isbn:1581132972 https://doi.org/10.1145/378239.379017 Google ScholarDigital Library
- Robert Nieuwenhuis, Albert Oliveras, and Cesare Tinelli. 2006. Solving SAT and SAT Modulo Theories: From an Abstract Davis–Putnam–Logemann–Loveland Procedure to DPLL(T). J. ACM, 53, 6 (2006), Nov., 937–977. issn:0004-5411 https://doi.org/10.1145/1217856.1217859 Google ScholarDigital Library
- David J. Pearce and Paul H. J. Kelly. 2007. A Dynamic Topological Sort Algorithm for Directed Acyclic Graphs. ACM J. Exp. Algorithmics, 11 (2007), Feb., 1.7–es. issn:1084-6654 https://doi.org/10.1145/1187436.1210590 Google ScholarDigital Library
- Alexander Schrijver. 1986. Theory of Linear and Integer Programming. John Wiley & Sons, Inc., USA. isbn:0471908541Google Scholar
- Dennis Shasha and Marc Snir. 1988. Efficient and Correct Execution of Parallel Programs That Share Memory. ACM Trans. Program. Lang. Syst., 10, 2 (1988), April, 282–312. issn:0164-0925 https://doi.org/10.1145/42190.42277 Google ScholarDigital Library
- Nishant Sinha and Chao Wang. 2011. On Interference Abstractions. In Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL ’11). Association for Computing Machinery, New York, NY, USA. 423–434. isbn:9781450304900 https://doi.org/10.1145/1926385.1926433 Google ScholarDigital Library
- Chao Wang, HoonSang Jin, Gary D. Hachtel, and Fabio Somenzi. 2004. Refining the SAT Decision Ordering for Bounded Model Checking. In Proceedings of the 41st Annual Design Automation Conference (DAC ’04). Association for Computing Machinery, New York, NY, USA. 535–538. isbn:1581138288 https://doi.org/10.1145/996566.996713 Google ScholarDigital Library
- Chao Wang, Sudipta Kundu, Malay Ganai, and Aarti Gupta. 2009. Symbolic Predictive Analysis for Concurrent Programs. In FM 2009: Formal Methods, Ana Cavalcanti and Dennis R. Dams (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 256–272. isbn:978-3-642-05089-3 https://doi.org/10.1007/978-3-642-05089-3_17 Google ScholarDigital Library
- Chao Wang, Zijiang Yang, Vineet Kahlon, and Aarti Gupta. 2008. Peephole Partial Order Reduction. In Tools and Algorithms for the Construction and Analysis of Systems, C. R. Ramakrishnan and Jakob Rehof (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 382–396. isbn:978-3-540-78800-3 https://doi.org/10.1007/978-3-540-78800-3_29 Google ScholarCross Ref
- Liangze Yin, Wei Dong, Wanwei Liu, Yunchou Li, and Ji Wang. 2018. YOGAR-CBMC: CBMC with Scheduling Constraint Based Abstraction Refinement. In Tools and Algorithms for the Construction and Analysis of Systems, Dirk Beyer and Marieke Huisman (Eds.). Springer International Publishing, Cham. 422–426. isbn:978-3-319-89963-3 https://doi.org/10.1007/978-3-319-89963-3_25 Google ScholarCross Ref
- Liangze Yin, Wei Dong, Wanwei Liu, and Ji Wang. 2018. Scheduling Constraint Based Abstraction Refinement for Weak Memory Models. In Proceedings of the 33rd ACM/IEEE International Conference on Automated Software Engineering (ASE 2018). Association for Computing Machinery, New York, NY, USA. 645–655. isbn:9781450359375 https://doi.org/10.1145/3238147.3238223 Google ScholarDigital Library
- L. Yin, W. Dong, W. Liu, and J. Wang. 2020. On Scheduling Constraint Abstraction for Multi-Threaded Program Verification. IEEE Transactions on Software Engineering, 46, 5 (2020), may, 549–565. issn:1939-3520 https://doi.org/10.1109/TSE.2018.2864122 Google ScholarCross Ref
- Naling Zhang, Markus Kusano, and Chao Wang. 2015. Dynamic Partial Order Reduction for Relaxed Memory Models. In Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI ’15). Association for Computing Machinery, New York, NY, USA. 250–259. isbn:9781450334686 https://doi.org/10.1145/2737924.2737956 Google ScholarDigital Library
Index Terms
- Satisfiability modulo ordering consistency theory for multi-threaded program verification
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