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Register a new userConformance Relations and Hyperproperties for Doping Detection in Time and Space
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Added by
Sebastian Biewer
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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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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.
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.
We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with $n$ vertices and $m$ edges, the classical symbolic algorithm from the 1990s for the MEC decomposition requires $O(n^2)$ symbolic operations and $O(1)$ symbolic space. The only other symbolic algorithm for the MEC decomposition requires $O(n sqrt{m})$ symbolic operations and $O(sqrt{m})$ symbolic space. A main open question is whether the worst-case $O(n^2)$ bound for symbolic operations can be beaten. We present a symbolic algorithm that requires $widetilde{O}(n^{1.5})$ symbolic operations and $widetilde{O}(sqrt{n})$ symbolic space. Moreover, the parametrization of our algorithm provides a trade-off between symbolic operations and symbolic space: for all $0<epsilon leq 1/2$ the symbolic algorithm requires $widetilde{O}(n^{2-epsilon})$ symbolic operations and $widetilde{O}(n^{epsilon})$ symbolic space ($widetilde{O}$ hides poly-logarithmic factors). Using our techniques we present faster algorithms for computing the almost-sure winning regions of $omega$-regular objectives for MDPs. We consider the canonical parity objectives for $omega$-regular objectives, and for parity objectives with $d$-priorities we present an algorithm that computes the almost-sure winning region with $widetilde{O}(n^{2-epsilon})$ symbolic operations and $widetilde{O}(n^{epsilon})$ symbolic space, for all $0 < epsilon leq 1/2$.
Several notions of conformance have been proposed for checking the behavior of cyber-physical systems against their hybrid systems models. In this paper, we explore the initial idea of a notion of approximate conformance that allows for comparison of both observable discrete actions and (sampled) continuous trajectories. As such, this notion will consolidate two earlier notions, namely the notion of Hybrid Input-Output Conformance (HIOCO) by M. van Osch and the notion of Hybrid Conformance by H. Abbas and G.E. Fainekos. We prove that our proposed notion of conformance satisfies a semi-transitivity property, which makes it suitable for a step-wise proof of conformance or refinement.
Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into infinitely many equivalence classes. The present work investigates the infinite one-one numbered recursively enumerable (r.e.) families realised by such relations and asks how the choice of the equivalence relation impacts the learnability properties of these classes when studying learnability in the limit from positive examples, also known as learning from text. For all choices of such positive equivalence relations, for each of the following entries, there are one-one numbered r.e. families which satisfy it: (a) they are behaviourally correctly learnable but not vacillatorily learnable; (b) they are explanatorily learnable but not confidently learnable; (c) they are not behaviourally correctly learnable. Furthermore, there is a positive equivalence relation which enforces that (d) every vacillatorily learnable one-one numbered family of languages closed under this equivalence relation is already explanatorily learnable and cannot be confidently learnable.
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