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Register a new userModel Checking an Epistemic mu-calculus with Synchronous and Perfect Recall Semantics
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Added by
Burkhard C. Schipper
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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We identify a subproblem of the model-checking problem for the epistemic mu-calculus which is decidable. Formulas in the instances of this subproblem allow free variables within the scope of epistemic modalities in a restricted form that avoids embodying any form of common knowledge. Our subproblem subsumes known decidable fragments of epistemic CTL/LTL, may express winning strategies in two-player games with one player having imperfect information and non-observable objectives, and, with a suitable encoding, decidable instances of the model-checking problem for ATLiR.
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The notion of knowledge-based program introduced by Halpern and Fagin provides a useful formalism for designing, analysing, and optimising distributed systems. This paper formulates the two phase commit protocol as a knowledge-based program and then an iterative process of model checking and counter-example guided refinement is followed to find concrete implementations of the program for the case of perfect recall semantic in the Byzantine failures context with synchronous reliable communication. We model several different kinds of Byzantine failures and verify different strategies to fight and mitigate them. We address a number of questions that have not been considered in the prior literature, viz., under what circumstances a sender can know that its transmission has been successful, and under what circumstances an agent can know that the coordinator is cheating, and find concrete answers to these questions. The paper describes also a methodology based on temporal-epistemic model checking technology that can be followed to verify the shortest and longest execution time of a distributed protocol and the scenarios that lead to them.
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Martin Lange (School of Electrical Engineering
, Computer Science
, n University of Kassel
2012
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in polynomial time, and conversely every polynomial-time decidable problem that has a bisimulation-invariant encoding into labeled transition systems can also be defined in the higher-dimensional modal mu-calculus. We exemplify the latter connection by giving several examples of decision problems which reduce to model checking of the higher-dimensional modal mu-calculus for some fixed formulas. This way generic model checking algorithms for the logic can then be used via partial evaluation in order to obtain algorithms for theses problems which may benefit from improvements that are well-established in the field of program verification, namely on-the-fly and symbolic techniques. The aim of this work is to extend such techniques to other fields as well, here exemplarily done for process equivalences, automata theory, parsing, string problems, and games.
In this article, we give an overview of our project on higher-order program verification based on HFL (higher-order fixpoint logic) model checking. After a brief introduction to HFL, we explain how it can be applied to program verification, and summarize the current status of the project.
Ong has shown that the modal mu-calculus model checking problem (equivalently, the alternating parity tree automaton (APT) acceptance problem) of possibly-infinite ranked trees generated by order-n recursion schemes is n-EXPTIME complete. We consider two subclasses of APT and investigate the complexity of the respective acceptance problems. The main results are that, for APT with a single priority, the problem is still n-EXPTIME complete; whereas, for APT with a disjunctive transition function, the problem is (n-1)-EXPTIME complete. This study was motivated by Kobayashis recent work showing that the resource usage verification of functional programs can be reduced to the model checking of recursion schemes. As an application, we show that the resource usage verification problem is (n-1)-EXPTIME complete.
We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the considered transition system is infinite. The novel games offer alternative approaches to various constructions in the framework of the mu-calculus. For example, they have already been successfully used as a basis for an approach leading to a natural formula size game for the logic. While our main focus is introducing the new GTS, we also consider some applications to demonstrate its uses. For example, we consider a natural model transformation procedure that reduces model checking games to checking a single, fixed formula in the constructed models, and we also use the GTS to identify new alternative variants of the mu-calculus with PTime model checking.
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