Probabilistic Couplings For Probabilistic Reasoning

This thesis explores proofs by coupling from the perspective of formal verification. Long employed in probability theory and theoretical computer science, these proofs construct couplings between the output distributions of two probabilistic processes. Couplings can imply various probabilistic relational properties, guarantees that compare two runs of a probabilistic computation. To give a formal account of this clean proof technique, we first show that proofs in the program logic pRHL (probabilistic Relational Hoare Logic) describe couplings. We formalize couplings that establish various probabilistic properties, including distribution equivalence, convergence, and stochastic domination. Then we deepen the connection between couplings and pRHL by giving a proofs-as-programs interpretation: a coupling proof encodes a probabilistic product program, whose properties imply relational properties of the original two programs. We design the logic xpRHL (product pRHL) to build the product program, with extensions to model more advanced constructions including shift coupling and path coupling. We then develop an approximate version of probabilistic coupling, based on approximate liftings. It is known that the existence of an approximate lifting implies differential privacy, a relational notion of statistical privacy. We propose a corresponding proof technique---proof by approximate coupling---inspired by the logic apRHL, a version of pRHL for building approximate liftings. Drawing on ideas from existing privacy proofs, we extend apRHL with novel proof rules for constructing new approximate couplings. We give approximate coupling proofs of privacy for the Report-noisy-max and Sparse Vector mechanisms, well-known algorithms from the privacy literature with notoriously subtle privacy proofs, and produce the first formalized proof of privacy for these algorithms in apRHL. Finally, we enrich the theory of approximate couplings with several more sophisticated constructions: a principle for showing accuracy-dependent privacy, a generalization of the advanced composition theorem from differential privacy, and an optimal approximate coupling relating two subsets of samples. We also show equivalences between approximate couplings and other existing definitions. These ingredients support the first formalized proof of privacy for the Between Thresholds mechanism, an extension of the Sparse Vector mechanism

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Choice and chance:model-based testing of stochastic behaviour

Probability plays an important role in many computer applications. A vast number of algorithms, protocols and computation methods uses randomisation to achieve their goals. A crucial question then becomes whether such probabilistic systems work as intended. To investigate this, such systems are often subjected to a large number of well-designed test cases, that compare a observed behaviour to a requirements specification. Model-based testing is an innovative testing technique rooted in formal methods, that aims at automating this labour intense and often error-prone manual task. By providing faster and more thorough testing at lower cost, it has gained rapid popularity in industry and academia alike. However, classic model-based testing methods are insufficient when dealing with inherently stochastic systems. This thesis introduces a rigorous model-based testing framework, that is capable to automatically test such systems. The presented methods are capable of judging functional correctness, discrete probability choices, and hard and soft-real time constraints. The framework is constructed in a clear step-by-step approach. First, the model-based testing landscape is laid out, and related work is discussed. Next, we instantiate a model-based testing framework to highlight the purpose of individual theoretical components like, e.g., a conformance relation, test cases, and practical test generation algorithms. This framework is then conservatively extended by introducing discrete probability choices to the specification language. A last step further extends this probabilistic framework by adding hard and soft real time constraints. Classical functional correctness verdicts are thus extended with goodness of fit methods known from statistics. Proofs of the framework’s correctness are presented before its capabilities are exemplified by studying smaller scale case studies known from the literature. The framework reconciles non-deterministic and probabilistic choices in a fully-fledged way via the use of schedulers. Schedulers then become a subject worthy to study in their own rights. This is done in the second part of this thesis; we introduce a most natural equivalence relation based on schedulers for Markov automata, and compare its distinguishing power to notions of trace distributions and bisimulation relations. Lastly, the power of different scheduler classes of stochastic automata is investigated. We compare reachability probabilities of different schedulers by altering the information available to them. A hierarchy of scheduler classes is established, with the intent to reduce complexity of related problems by gaining near optimal results for smaller scheduler classes

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

On Distributed Verification and Verified Distribution

Fokkink, W.J. [Promotor]Pol, J.C. van de [Copromotor