A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis

Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing and energy consumption, and the automatic synthesis of systems from specifications. The major challenges include environment modeling, incompleteness in specifications, and the complexity of underlying decision problems. This position paper proposes sciduction, an approach to tackle these challenges by integrating inductive inference, deductive reasoning, and structure hypotheses. Deductive reasoning, which leads from general rules or concepts to conclusions about specific problem instances, includes techniques such as logical inference and constraint solving. Inductive inference, which generalizes from specific instances to yield a concept, includes algorithmic learning from examples. Structure hypotheses are used to define the class of artifacts, such as invariants or program fragments, generated during verification or synthesis. Sciduction constrains inductive and deductive reasoning using structure hypotheses, and actively combines inductive and deductive reasoning: for instance, deductive techniques generate examples for learning, and inductive reasoning is used to guide the deductive engines. We illustrate this approach with three applications: (i) timing analysis of software; (ii) synthesis of loop-free programs, and (iii) controller synthesis for hybrid systems. Some future applications are also discussed

Proving Abstractions of Dynamical Systems through Numerical Simulations

A key question that arises in rigorous analysis of cyberphysical systems under attack involves establishing whether or not the attacked system deviates significantly from the ideal allowed behavior. This is the problem of deciding whether or not the ideal system is an abstraction of the attacked system. A quantitative variation of this question can capture how much the attacked system deviates from the ideal. Thus, algorithms for deciding abstraction relations can help measure the effect of attacks on cyberphysical systems and to develop attack detection strategies. In this paper, we present a decision procedure for proving that one nonlinear dynamical system is a quantitative abstraction of another. Directly computing the reach sets of these nonlinear systems are undecidable in general and reach set over-approximations do not give a direct way for proving abstraction. Our procedure uses (possibly inaccurate) numerical simulations and a model annotation to compute tight approximations of the observable behaviors of the system and then uses these approximations to decide on abstraction. We show that the procedure is sound and that it is guaranteed to terminate under reasonable robustness assumptions

On Distributed Storage Codes

Distributed storage systems are studied. The interest in such system has become relatively wide due to the increasing amount of information needed to be stored in data centers or different kinds of cloud systems. There are many kinds of solutions for storing the information into distributed devices regarding the needs of the system designer. This thesis studies the questions of designing such storage systems and also fundamental limits of such systems. Namely, the subjects of interest of this thesis include heterogeneous distributed storage systems, distributed storage systems with the exact repair property, and locally repairable codes. For distributed storage systems with either functional or exact repair, capacity results are proved. In the case of locally repairable codes, the minimum distance is studied. Constructions for exact-repairing codes between minimum bandwidth regeneration (MBR) and minimum storage regeneration (MSR) points are given. These codes exceed the time-sharing line of the extremal points in many cases. Other properties of exact-regenerating codes are also studied. For the heterogeneous setup, the main result is that the capacity of such systems is always smaller than or equal to the capacity of a homogeneous system with symmetric repair with average node size and average repair bandwidth. A randomized construction for a locally repairable code with good minimum distance is given. It is shown that a random linear code of certain natural type has a good minimum distance with high probability. Other properties of locally repairable codes are also studied.Siirretty Doriast

Regelungstheorie

The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency

An evaluation of approximate probabilistic reachability techniques for stochastic parametric hybrid systems

Ph. D. ThesisStochastic parametric hybrid systems allow formalising automata with discrete interruptions, continuous nonlinear dynamics and parametric uncertainty (e.g. randomness and/or nondeterminism), and are a useful framework for cyber-physical systems modelling. The problem of designing safe cyber-physical systems is very timely, given that such systems are ubiquitous in modern society, often in safety-critical contexts (e.g., aircraft and cars) with possibly some level of decisional autonomy. Therefore, the verification of cyber-physical systems (and consequently of hybrid systems) is a problem urgently demanding innovative solutions. Unfortunately, this problem is also extremely challenging. Reachability checking is a crucial element of designing safe systems. Given a system model, we specify a set of "goal" states (indicating (un)wanted behaviour) and ask whether the system evolution can reach these states or not. Probabilistic reachability is the corresponding problem for stochastic systems, and it amounts to computing the probability that the system reaches a goal state. The main problem researched in this thesis is probabilistic reachability analysis of hybrid systems with random and/or nondeterministic parameters. For nondeterministic systems, this problem amounts to computing a range of reachability probabilities depending on how nondeterminism is resolved. In this thesis I have investigated and developed three distinct techniques: Statistical methods, involving Monte Carlo, Quasi-Monte Carlo and Randomised Quasi-Monte Carlo sampling with interval estimation techniques which give statistical guarantees; An analytical approximation method, utilising Gaussian Processes that offer a statistical approximation for an (unknown) smooth function over its entire domain; A promising combination of a formal approach, based on formal reasoning which provides absolute numerical guarantees, and the Gaussian Regression method. This research offers contributions on two different levels to the verification of stochastic parametric hybrid systems. From a theoretical point of view, it offers a proof that the reachability probability function is a smooth function of the uncertain parameters of the model, and hence Gaussian Processes techniques can be used to obtain an efficient analytical approximation of the function. From a practical point of view, I have implemented all the above described statistical and approximation techniques as part of the publicly available ProbReach tool, including a Gaussian Process Expectation Propagation algorithm that performs Gaussian Process classification and regression for uni-variate and multiple class labels. My empirical evaluation of the presented techniques to a number of case studies has shown a great Gaussian Process approach advantage with respect to standard statistical model checking techniques.SAgE Doctoral Training Scholarships of Newcastle Universit

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency