Simulating perfect channels with probabilistic lossy channels

AbstractWe consider the problem of deciding whether an infinite-state system (expressed as a Markov chain) satisfies a correctness property with probability 1. This problem is, of course, undecidable for general infinite-state systems. We focus our attention on the model of probabilistic lossy channel systems consisting of finite-state processes that communicate over unbounded lossy FIFO channels. Abdulla and Jonsson have shown that safety properties are decidable while progress properties are undecidable for non-probabilistic lossy channel systems. Under assumptions of “sufficiently high” probability of loss, Baier and Engelen have shown how to check whether a property holds of probabilistic lossy channel system with probability 1. In this paper, we consider a model of probabilistic lossy channel systems, where messages can be lost only during send transitions. In contrast to the model of Baier and Engelen, once a message is successfully sent to channel, it can only be removed through a transition which receives the message. We show that checking whether safety properties hold with probability 1 is undecidable for this model. Our proof depends upon simulating a perfect channel, with a high degree of confidence, using lossy channels

Solving Stochastic B\"uchi Games on Infinite Arenas with a Finite Attractor

We consider games played on an infinite probabilistic arena where the first player aims at satisfying generalized B\"uchi objectives almost surely, i.e., with probability one. We provide a fixpoint characterization of the winning sets and associated winning strategies in the case where the arena satisfies the finite-attractor property. From this we directly deduce the decidability of these games on probabilistic lossy channel systems.Comment: In Proceedings QAPL 2013, arXiv:1306.241

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Refactorings are meaning-preserving transformations of object-oriented programs carried out with the aim of improving their design. Sometimes refactorings accomplish just cosmetic improvements. At other times, they make programs easier to modify. Many systems for refactoring programs have been described in the literature. The past few years have seen a plethora of object-oriented languages that enforce strict static type-checking and use explicit type declarations (type annotations). Type annotations add to the expense of modification. Our first result is a categorisation of refactorings by their effect on type annotations. In the second part of this thesis, we study a tool that makes it easier to change programs with type annotations. The tool uses type inference to automate the management of type annotations. The third part of the thesis concerns the use of type inference tools to select candidate refactorings. In particular, these refactorings are recommended when type inconsistencies are found in a program. Thus, refactorings and type inference can mutually benefit each other

Probabilistic and Nondeterministic Systems

Probabilistic and nondeterministic systems are important to model systems such as distributed network protocols, concurrent systems and randomized algorithms, where nondeterminism is inherently present along with probabilistic choices. Probabilistic transi-tion systems without any nondeterminism have been explored over the past decade. Several logics have been proposed to express the probabilistic behavior of systems. Nondetermin-istic systems differ from their probabilistic counterparts in that there behavior needs a notion of scheduler which resolves the nondeterministic choices. The probability space of observations of such systems is dependent on the choice of scheduler. In the absence of unique probability space the system properties can only be measured in intervals. The methods proposed in literature for quantitative analysis of nondeterministic systems use approximations for conjunction and disjunction to avoid the nonlinearity in the equations for measures. The contribution of this thesis is three fold. In the initial part we present a model checking method for quantitative analysis of nondeterministic systems. We generate a set of constraints and compute the minimum and maximum measure for the property without using any approximations. Secondly, we present an abstraction and probabilistic bi-simulation based approach to model and analyze randomized token stabilization protocol. In the end we present a method for compositional verification of PNS where in we describe weak predicate transformers which can be used to generate sub-specification for the unknown systems from the specification of the composite system