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Register a new userProbabilistic Hyperproperties with Nondeterminism
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Added by
Borzoo Bonakdarpour
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We study the problem of formalizing and checking probabilistic hyperproperties for models that allow nondeterminism in actions. We extend the temporal logic HyperPCTL, which has been previously introduced for discrete-time Markov chains, to enable the specification of hyperproperties also for Markov decision processes. We generalize HyperPCTL by allowing explicit and simultaneous quantification over schedulers and probabilistic computation trees and show that it can express important quantitative requirements in security and privacy. We show that HyperPCTL model checking over MDPs is in general undecidable for quantification over probabilistic schedulers with memory, but restricting the domain to memoryless non-probabilistic schedulers turns the model checking problem decidable. Subsequently, we propose an SMT-based encoding for model checking this language and evaluate its performance.
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In this paper, we propose a new logic for expressing and reasoning about probabilistic hyperproperties. Hyperproperties characterize the relation between different independent executions of a system. Probabilistic hyperproperties express quantitative dependencies between such executions. The standard temporal logics for probabilistic systems, i.e., PCTL and PCTL* can refer only to a single path at a time and, hence, cannot express many probabilistic hyperproperties of interest. The logic proposed in this paper, HyperPCTL, adds explicit and simultaneous quantification over multiple traces to PCTL. Such quantification allows expressing probabilistic hyperproperties. A model checking algorithm for the proposed logic is also given for discrete-time Markov chains.
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In the paper Relating Strong Behavioral Equivalences for Processes with Nondeterminism and Probabilities to appear in TCS, we present a comparison of behavioral equivalences for nondeterministic and probabilistic processes. In particular, we consider strong trace, failure, testing, and bisimulation equivalences. For each of these groups of equivalences, we examine the discriminating power of three variants stemming from three approaches that differ for the way probabilities of events are compared when nondeterministic choices are resolved via deterministic schedulers. The established relationships are summarized in a so-called spectrum. However, the equivalences we consider in that paper are only a small subset of those considered in the original spectrum of equivalences for nondeterministic systems introduced by Rob van Glabbeek. In this companion paper we we enlarge the spectrum by considering variants of trace equivalences (completed-trace equivalences), additional decorated-trace equivalences (failure-trace, readiness, and ready-trace equivalences), and variants of bisimulation equivalences (kernels of simulation, completed-simulation, failure-simulation, and ready-simulation preorders). Moreover, we study how the spectrum changes when randomized schedulers are used instead of deterministic ones.
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We present a novel and generalised notion of doping cleanness for cyber-physical systems that allows for perturbing the inputs and observing the perturbed outputs both in the time- and value-domains. We instantiate our definition using existing notions of conformance for cyber-physical systems. As a formal basis for monitoring conformance-based cleanness, we develop the temporal logic HyperSTL*, an extension of Signal Temporal Logics with trace quantifiers and a freeze operator. We show that our generalised definitions are essential in a data-driven method for doping detection and apply our definitions to a case study concerning diesel emission tests.
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