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Incremental model checking in the modal mu-calculus [chapter]

Oleg V. Sokolsky, Scott A. Smolka
1994 Lecture Notes in Computer Science  
We present an incremental algorithm for model checking in the alternatlon-free fragment of the modal mu-calculus, the first incremental algorithm for model checking of which we are aware.  ...  The basis for oar algorithm, which we call MCI (for Model Checking Incrementally), is a linear-time algorithm due to Cleaveland and Steffen that performs global (non-incremental) computation of fixed points  ...  for model checking in the alternation-free fragment of the modal mu-calculus.  ... 
doi:10.1007/3-540-58179-0_67 fatcat:5tr237qafjcq7dlxvh23lzlqcm

HORNSAT, model checking, verification and games [chapter]

Sandeep K. Shukla, Harry B. Hunt, Daniel J. Rosenkrantz
1996 Lecture Notes in Computer Science  
It also leads naturally to diagnostic behavioral relation checking [7] algorithms. Here we use it to develop model checking algorithms for various fragments of modal mu-calculus.  ...  We also use our methodology to develop a uniform game theoretic formulations of all the relations in the linear time/branching time hierarchy of [27] .  ...  Incremental Model Checking : In [24] , an incremental algorithm for model checking alternation free mu-calculus was developed. The basic idea was the following.  ... 
doi:10.1007/3-540-61474-5_61 fatcat:kjzqwudy6fb3jbnr3qiozwrqoe

Quotient-based Control Synthesis for Non-Deterministic Plants with Mu-Calculus Specifications

Samik Basu, Ratnesh Kumar
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
Given a plant automaton model and a mu-calculus specification we provide a set of rules that computes the "quotient" of the specification against the plant, which is another mu-calculus formula such that  ...  We study the control of a nondeterministic discrete event system (DES) subject to a control specification expressed in the propositional mu-calculus, under complete observation of events.  ...  In contrast, our satisfiability checking and model identification works directly on a mu-calculus formula.  ... 
doi:10.1109/cdc.2006.376737 dblp:conf/cdc/0001006a fatcat:q3b6r65kmfewtelbyjcmhkzp2y

Local model checking for real-time systems [chapter]

Oleg V. Sokolsky, Scott A. Smolka
1995 Lecture Notes in Computer Science  
We present a local algorithm for model checking in a real-time extension of the modal mu-calcuins.  ...  To the best of our knowledge, this is the first local algorithm for the verification of real-time systems to appear in the literature.  ...  Acknowledgements We would like to thank the anonymous referees for their helpful comments.  ... 
doi:10.1007/3-540-60045-0_52 fatcat:b7nheh4hcfaq7ki2g3y7mpr7ky

Fully local and efficient evaluation of alternating fixed points [chapter]

Xinxin Liu, C. R. Ramakrishnan, Scott A. Smolka
1998 Lecture Notes in Computer Science  
The generality of PDGs subsumes that of similarly proposed models of nested fixed-point computation such as Boolean graphs, Boolean equation systems, and the propositional modal mu-calculus.  ...  Our algorithm, which we call LAFP, combines the simplicity of previously proposed induction-based algorithms (such as Winskel's tableau method for p-calculus mode] checking) with the efficiency of semantics-based  ...  In contrast, most existing model checking algorithms for the modal mu-calculus need only linear space.  ... 
doi:10.1007/bfb0054161 fatcat:kwi5gg2gj5dchm2cozqtcibp7a

Incremental Hyperproperty Model Checking via Games [chapter]

Dimiter Milushev, Dave Clarke
2013 Lecture Notes in Computer Science  
In an attempt to remedy this, we introduced the notion of incremental hyperproperties (IHPs), motivated by the observation that they have a clearer and more feasible verification methodology.  ...  The main advantage of the approach is that the games in combination with winning strategy evidence give valuable intuition about the security of a system and are very helpful when analyzing systems w.r.t  ...  The approach is a reduction of the problem of model checking L k µ to model checking the ordinary modal mu-calculus L µ on a product of the original system.  ... 
doi:10.1007/978-3-642-41488-6_17 fatcat:4yux4wpl5zbqdpxycfnhxbnxbi

PhD Abstracts

2015 Journal of functional programming  
A dissertation is eligible if parts of it have or could have appeared in JFP, that is, if it is in the general area of functional programming. The abstracts are not reviewed.  ...  Many students complete PhDs in functional programming each year, but there is currently no common location in which to promote and advertise the resulting work.  ...  Finally, we introduce Parigot's lambda mu-calculus, which extends lambda calculus with two operators called mu and bracket, and then the extended calculus by De Groote, in which the operators mu and bracket  ... 
doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna

μ-Calculus Model Checking in Maude

Bow-Yaw Wang
2005 Electronical Notes in Theoretical Computer Science  
The LTL model checker in [11] is still preferred in practice.  ...  In this paper, a rewrite theory for checking µ-calculus properties is developed.  ...  Acknowledgment The author would like to thank anonymous reviewers for their valuable suggestions and comments.  ... 
doi:10.1016/j.entcs.2004.06.025 fatcat:v3pyfjcb5bh5pd755t3hd26izi

Comparing CTL and PCTL on Labeled Markov Chains [chapter]

M. R. A. Huth, M. Z. Kwiatkowska
1998 Programming Concepts and Methods PROCOMET '98  
We interpret modal mu-calculus formulas in a non-standard way as expectations over labeled Markov chains. In this semantics fixed-points are computed in an iterative incremental/ decremental fashion.  ...  This provides the foundation for a symbolic model checking algorithm for CTL over labeled Markov chains using Multi-Terminal Binary Decision Diagrams, where expectations of until~ formulas are calculated  ...  ACKNOWLEDGMENTS We would like to thank all the anonymous referees for their constructive criticism.  ... 
doi:10.1007/978-0-387-35358-6_18 fatcat:acdkyetax5h2lmwtjg3wtpqcdy

Model checking and transitive-closure logic [chapter]

Neil Immerman, Moshe Y. Vardi
1997 Lecture Notes in Computer Science  
have been used to express queries for model checking and then translated into -calculus for symbolic evaluation.  ...  Evaluation of -calculus formulas is, however, complete for time polynomial in the (typically huge) number of states in the Kripke structure.  ...  Thus, it is very promising to do model checking and symbolic model checking using the language FO 2 (TC) rather than the more complex modal -calculus. 2 Background on Temporal Logic and the Modal -calculus  ... 
doi:10.1007/3-540-63166-6_29 fatcat:pozwqznvtbc5ff7ozncmctv37i

Static Analysis using Parameterised Boolean Equation Systems [article]

María Del Mar Gallardo, Pedro Merino
2006 arXiv   pre-print
Firstly, we describe the problem as an alternation-free value-based mu-calculus formula, whose validity can be checked on the program model expressed as a labeled transition system (LTS).  ...  In this paper, we combine the on-the-fly model-checking approach (incremental construction of the program state space) and the static analysis method called influence analysis (extraction of significant  ...  We are indebted to Radu Mateescu for its valuable feedback on the possible interaction of our proposal with Cadp model checkers.  ... 
arXiv:cs/0606092v2 fatcat:2ns7nyob4zalrg56uh6re7keei

Model checking of macro processes [chapter]

Hardi Hungar
1994 Lecture Notes in Computer Science  
The alternationfree modal mu-calculus has already been shown to be decidable for contextfree processes, with a worst case complexity which is linear in the size of the system description and exponential  ...  They too allow deciding mu-calculus formulae, as is shown in this paper by presenting both global (iterative) and local (tableaux-based) procedures.  ...  graphs, as well as the (alternation-free) modal mu-calculus as a logic for specification.  ... 
doi:10.1007/3-540-58179-0_52 fatcat:2jsibarl2faihmbb4ag7mff6qi

Observational Mu-Calculus

Julian C. Bradfield, Perdita Stevens
1999 BRICS Report Series  
We propose an extended modal mu-calculus to provide an 'assembly<br />language' for modal logics for real time, value-passing calculi,<br />and other extended models of computation.  ...  These requirements are not hard to meet: for example, in the case of model-checking the observational mu calculus, we could take the shape of (A, φ, ρ) to be φ.  ...  Abstract games for model-checking the observational mu calculus Whether it is possible to calculate a winning strategy -that is, to solve a model-checking problem -depends on the domain of interpretation  ... 
doi:10.7146/brics.v6i5.20062 fatcat:ibpehlpocbhynco7junjrv6fia

A Priori Verification of Reactive Systems [chapter]

Mila Majster-Cederbaum, Frank Salger, Maria Sorea
2000 IFIP Advances in Information and Communication Technology  
Modal Mu-Calculus.  ...  In this paper we present a refinement operator ·[a--... Q], defined both on TCSP-like process terms P and formulas <p of the Modal Mu-Calculus.  ...  The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35533-7_26  ... 
doi:10.1007/978-0-387-35533-7_3 fatcat:6xa3pm3s6zbvzawqrwdv56yafa

Local model checking and protocol analysis

Xiaoqun Du, Scott A. Smolka, Rance Cleaveland
1999 International Journal on Software Tools for Technology Transfer (STTT)  
This paper describes a local model-checking algorithm for the alternation-free fragment of the modal mucalculus that has been implemented in the Concurrency Factory and discusses its application to the  ...  Again, using local model checking, we showed that this alternative design also possesses the properties of interest.  ...  Part I: Local Model Checking in the Alternation-Free Modal Mu-Calculus 2 The Alternation-Free Modal Mu-Calculus This section describes the syntax and semantics of the L µ1 , the alternation-free modal  ... 
doi:10.1007/s100090050031 fatcat:xv5qytu45vejvpjnc62lmqqgpa
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