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The Complexity of Model Checking Higher Order Fixpoint Logic
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology. Faculty of Science and Technology, Biology, Department of Ecology and Evolution, Computing Science. CSD.
2005 (English)In: Mathematical Foundations of Computer Science 2005: 30th International Symposium, MFCS 2005, Gdansk, Poland, August 29–September 2, 2005. Proceedings, 2005Conference paper (Refereed)
Place, publisher, year, edition, pages
URN: urn:nbn:se:uu:diva-80124DOI: doi:10.1007/11549345_55ISBN: 3-540-28702-7OAI: oai:DiVA.org:uu-80124DiVA: diva2:108038
Available from: 2006-04-25 Created: 2006-04-25 Last updated: 2013-01-22
In thesis
1. Logics and Algorithms for Verification of Concurrent Systems
Open this publication in new window or tab >>Logics and Algorithms for Verification of Concurrent Systems
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we investigate how the known framework of automatic formal verification by model checking can be extended in different directions. One extension is to go beyond the common limitation of the existing specification formalisms, that they can describe only regular properties of components. This can be achieved using logics capable of expressing non-regular properties, such as the Propositional Dynamic Logic of Context-free Programs (PDLCF), Fixpoint Logic with Chop (FLC) or the Higher-order Fixpoint Logic (HFL). Our main result in this area is proving that the problem of model checking HFL formulas of order bounded by k is k-EXPTIME complete. In the proofs we demonstrate two model checking algorithms for that logic. We also show that PDLCF is equivalent to a proper fragment of FLC.

The standard model checking algorithms, which are run on a single computer, are severely limited by the amount of available computing resources. A way to overcome this limitation is to develop distributed algorithms, which can be run on a cluster of computers and use their joint resources. In this thesis we show how a distributed model checking algorithm for the alternation-free fragment of the modal μ-calculus can be extended to handle formulas with one level of alternation. This is an important extension, since Lμ formulas with one level of alternation can express the same properties as logics LTL and CTL commonly used in formal verification.

Finally, we investigate stochastic games which can be used to model additional aspects of components, such as their interaction with environment and their quantitative properties. We describe new algorithms for finding optimal values and strategies in turn-based stochastic games with reachability winning conditions. We prove their correctness and report on experiments where we compare them against each other and against other known algorithms, such as value iteration and strategy improvement.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 48 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 964
National Category
Computer Science
Research subject
Computer Science
urn:nbn:se:uu:diva-179847 (URN)978-91-554-8447-7 (ISBN)
Public defence
2012-10-01, Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 13:15 (English)
Available from: 2012-09-11 Created: 2012-08-24 Last updated: 2014-07-21Bibliographically approved

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