Tasks in modular proofs of concurrent algorithms
Proving the correctness of distributed or concurrent algorithms is a complex process. Errors in the reasoning are hard to find, calling for computer-checked proof systems like Coq or TLA+. To use these tools, sequential specifications of base objects are required to build modular proofs by compositi...
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| Vydáno v: | Information and computation Ročník 292; číslo Selected papers from SSS’2019, the 21st International Symposium on Stabilization, Safety, and Security of Distributed Systems; s. 105040 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Inc
01.06.2023
Elsevier |
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| ISSN: | 0890-5401, 1090-2651 |
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| Abstract | Proving the correctness of distributed or concurrent algorithms is a complex process. Errors in the reasoning are hard to find, calling for computer-checked proof systems like Coq or TLA+. To use these tools, sequential specifications of base objects are required to build modular proofs by composition. Unfortunately, many concurrent objects lack a sequential specification. This article describes a method to transform any task, a specification of a concurrent one-shot distributed problem, into a sequential specification involving two calls, set and get. This enables designers to compose proofs, facilitating modular computer-checked proofs of algorithms built using tasks and sequential objects as building blocks. Moir & Anderson implementation of renaming using splitters, wait-free concurrent objects, is an algorithm designed by composition, but it is not modular. Using our transformation, a modular description of the algorithm is given in TLA+ and mechanically verified using the TLA+ Proof System. As far as we know, this is the first time this algorithm is mechanically verified. |
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| AbstractList | Proving the correctness of distributed or concurrent algorithms is a complex process. Errors in the reasoning are hard to find, calling for computer-checked proof systems like Coq or TLA+. To use these tools, sequential specifications of base objects are required to build modular proofs by composition. Unfortunately, many concurrent objects lack a sequential specification. This article describes a method to transform any task, a specification of a concurrent one-shot distributed problem, into a sequential specification involving two calls, set and get. This enables designers to compose proofs, facilitating modular computer-checked proofs of algorithms built using tasks and sequential objects as building blocks. Moir & Anderson implementation of renaming using splitters, wait-free concurrent objects, is an algorithm designed by composition, but it is not modular. Using our transformation, a modular description of the algorithm is given in TLA+ and mechanically verified using the TLA+ Proof System. As far as we know, this is the first time this algorithm is mechanically verified. Proving correctness of distributed or concurrent algorithms is a mind-challenging and complex process. Slight errors in the reasoning are difficult to find, calling for computer-checked proof systems. In order to build computer-checked proofs with usual tools, such as Coq or TLA + , having sequential specifications of all base objects that are used as building blocks in a given algorithm is a requisite to provide a modular proof built by composition. Alas, many concurrent objects do not have a sequential specification. This article describes a systematic method to transform any task, a specification method that captures concurrent one-shot distributed problems, into a sequential specification involving two calls, set and get. This transformation allows system designers to compose proofs, thus providing a framework for modular computer-checked proofs of algorithms designed using tasks and sequential objects as building blocks. Moir & Anderson implementation of renaming using splitters is an iconic example of such algorithms designed by composition, although the actual algorithm is not modular. Moir & Anderson algorithm is adaptive and non-blocking, and, being the assembly of wait-free concurrent objects, the splitters, it resists testing, because of the cost of covering all its states and transitions even with a small input set. Using the get/set transformation, a modular description of the algorithm can be obtained. A proof of the modular algorithm has been conducted in TLA + and verified with TLAPS, the TLA + Proof System. As far as we know, this is the first time this algorithm is mechanically verified. |
| ArticleNumber | 105040 |
| Author | Castañeda, Armando Hurault, Aurélie Roy, Matthieu Quéinnec, Philippe |
| Author_xml | – sequence: 1 givenname: Armando surname: Castañeda fullname: Castañeda, Armando organization: Instituto de Matemáticas, UNAM, Mexico – sequence: 2 givenname: Aurélie surname: Hurault fullname: Hurault, Aurélie organization: IRIT – Université de Toulouse, France – sequence: 3 givenname: Philippe surname: Quéinnec fullname: Quéinnec, Philippe email: philippe.queinnec@irit.fr organization: IRIT – Université de Toulouse, France – sequence: 4 givenname: Matthieu surname: Roy fullname: Roy, Matthieu organization: LAAS, CNRS, Toulouse, France |
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| Cites_doi | 10.1006/inco.1993.1043 10.1145/1506409.1506431 10.1145/79147.79158 10.1007/s002240000072 10.1145/78969.78972 10.1145/2185376.2185383 10.1145/3266457 10.1007/s00224-013-9448-1 10.1145/235543.235546 10.1016/j.cosrev.2011.04.001 10.2298/CSIS130122007A 10.1016/j.jpdc.2009.08.011 10.1007/PL00008933 10.1016/0167-6423(95)00009-H |
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| Issue | Selected papers from SSS’2019, the 21st International Symposium on Stabilization, Safety, and Security of Distributed Systems |
| Keywords | Splitter Concurrent algorithms TLA+ Distributed tasks Linearizability Verification Formal methods Renaming TLA |
| Language | English |
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| SubjectTerms | Computer Science Concurrent algorithms Distributed tasks Distributed, Parallel, and Cluster Computing Formal methods Linearizability Renaming Splitter TLA+ Verification |
| Title | Tasks in modular proofs of concurrent algorithms |
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