Abstract
This paper presents a novel framework for decentralized monitoring of Linear Temporal Logic (LTL) formulas, under the situation where processes are synchronous and the formula is represented as a tableau. The tableau technique allows one to construct a semantic tree for the input LTL formula, which can be used to optimize the decentralized monitoring of LTL in various ways. Given a system P and an LTL formula φ, we construct a tableau Tφ. The tableau Tφ is used for two purposes: (a) to synthesize an efficient round-robin communication policy for processes, and (b) to find the minimal ways to decompose the formula and communicate observations of processes in an efficient way. In our framework, processes can propagate truth values of both atomic and compound formulas (non-atomic formulas) depending on the syntactic structure of the input LTL formula and the observation power of processes. We demonstrate that this approach of decentralized monitoring based on tableau construction is more straightforward, more flexible, and more likely to yield efficient solutions than alternative approaches.
- Hamid Alavi, George Avrunin, James Corbett, Laura Dillon, Matt Dwyer, and Corina Pasareanu. 2011. Specification patterns website. http://patterns.projects.cis.ksu.edu/.Google Scholar
- Fahiem Bacchus and Froduald Kabanza. 1996. Planning for temporally extended goals. In Proceedings of the Thirteenth National Conference on Artificial Intelligence. 1215--1222.Google Scholar
- David Basin, Felix Klaedtke, and Eugen Zalinescu. 2015. Failure-aware runtime verification of distributed systems. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015), Vol. 45, 590--603.Google Scholar
- Andreas Bauer, Martin Leucker, and Christian Schallhart. 2011. Runtime verification for LTL and TLTL. ACM Transactions on Software Engineering and Methodology (TOSEM) (2011), 14:1--14:64.Google Scholar
- Andreas Klaus Bauer and Yliès Falcone. 2012. Decentralised LTL monitoring. In FM 2012: Formal Methods - 18th International Symposium, Paris, France. 85--100.Google Scholar
Cross Ref
- E. Beth. 1955. Semantic Entailment and Formal Derivability. Mededelingen der Koninklijke Nederlandse Akad. van Wetensch.Google Scholar
- Christian Colombo and Yliès Falcone. 2016. Organising LTL monitors over distributed systems with a global clock. Formal Methods in System Design 49, 1--2 (2016), 109--158.Google Scholar
Digital Library
- Christian Colombo, Gordon J. Pace, and Gerardo Schneider. 2008. Dynamic event-based runtime monitoring of real-time and contextual properties. In Formal Methods for Industrial Critical Systems, 13th International Workshop, FMICS 2008, L’Aquila, Italy. 135--149.Google Scholar
- Ben D’Angelo, Sriram Sankaranarayanan, César Sánchez, Will Robinson, Bernd Finkbeiner, Henny B. Sipma, Sandeep Mehrotra, and Zohar Manna. 2005. LOLA: Runtime monitoring of synchronous systems. In 12th International Symposium on Temporal Representation and Reasoning (TIME 2005), 23--25 June 2005, Burlington, Vermont, USA. 166--174.Google Scholar
Digital Library
- Matthew B. Dwyer, George S. Avrunin, and James C. Corbett. 1999. Patterns in property specifications for finite-state verification. In Proceedings of the 21st International Conference on Software Engineering. 411--420.Google Scholar
- Antoine El-Hokayem and Yliès Falcone. 2017. Monitoring decentralized specifications. In Proceedings of the 26th ACM SIGSOFT International Symposium on Software Testing and Analysis (ISTA). 125--135.Google Scholar
Digital Library
- E. Allen Emerson and Joseph Y. Halpern. 1982. Decision procedures and expressiveness in the temporal logic of branching time. In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing (STOC’82). 169--180.Google Scholar
- Yliès Falcone, Tom Cornebize, and Jean-Claude Fernandez. 2014. Efficient and generalized decentralized monitoring of regular languages. In Formal Techniques for Distributed Objects, Components, and Systems. 66--83.Google Scholar
- Shokoufeh Kazemlou and Borzoo Bonakdarpour. 2018. Crash-resilient decentralized synchronous runtime verification. In 37th IEEE Symposium on Reliable Distributed Systems SRDS. 207--212.Google Scholar
Cross Ref
- Yonit Kesten, Zohar Manna, Hugh McGuire, and Amir Pnueli. 1993. A decision algorithm for full propositional temporal logic. In Proceedings of the 5th International Conference on Computer Aided Verification (CAV’93). 97--109.Google Scholar
Digital Library
- Stephen Cole Kleene. 1952. Introduction to Metamathematics. North-Holland, Amsterdam.Google Scholar
- Menna Mostafa and Borzoo Bonakdarpour. 2015. Decentralized runtime verification of LTL specifications in distributed systems. In 2015 IEEE International Parallel and Distributed Processing Symposium. 494--503.Google Scholar
Digital Library
- Lee Pike, Sebastian Niller, and Nis Wegmann. 2012. Runtime verification for ultra-critical systems. In Proceedings of the Second International Conference on Runtime Verification (RV’11). 310--324.Google Scholar
Digital Library
- Amir Pnueli. 1977. The temporal logic of programs. In Proceedings of the 18th Annual Symposium on Foundations of Computer Science (SFCS’77). IEEE Computer Society, 46--57.Google Scholar
Digital Library
- Mark Reynolds. 2016. A new rule for LTL tableaux. In Symposium on Games, Automata, Logics and Formal Verification, GandALF 2016. 287--301.Google Scholar
Cross Ref
- Torben Scheffel and Malte Schmitz. 2014. Three-valued asynchronous distributed runtime verification. In International Conference on Formal Methods and Models for System Design (MEMOCODE), Vol. 12. IEEE.Google Scholar
Digital Library
- Stefan Schwendimann. 1998. Aspects of Computational Logic. Ph.D. Dissertation. Institut für Informatik und angewandte Mathematik.Google Scholar
- Koushik Sen, Abhay Vardhan, Gul Agha, and Grigore Rosu. 2004. Efficient decentralized monitoring of safety in distributed systems. In Proceedings of the 26th International Conference on Software Engineering (ICSE’04). IEEE Computer Society, 418--427.Google Scholar
Digital Library
- Raymond Smullyan. 1968. First Order Logic. Springer-Verlag.Google Scholar
Index Terms
Efficient Decentralized LTL Monitoring Framework Using Tableau Technique
Recommendations
A Rooted Tableau for BCTL*
The existing pure tableau technique for satisfiability checking BCTL* [Reynolds, M., A Tableau for Bundled CTL*, J Logic Computation 17 (2007), pp. 117-132. URL http://logcom.oxfordjournals.org/cgi/content/abstract/17/1/117] begins by constructing all ...
A Tableau Decision Procedure for ALC With Monotonic Modal Operators and Constant Domains
Modal description logics provide a more expressive framework than their propositional counterparts by allowing one to define the individuals and concepts of a particular application domain. In the literature, tableau decision algorithms have been given ...
A tableau-based decision procedure for CTL*
AbstractWe present a sound, complete and implementable tableau method for deciding satisfiability of formulas in the propositional version of computation tree logic CTL*. This is the first such tableau. CTL* is an exceptionally important temporal logic ...






Comments