Sergiy Bogomolov

Newcastle University | NCL · School of Computing

Digital twin is a technology that facilitates a real-time coupling of a cyber–physical system and its virtual representation. The technology is applicable to a variety of domains and facilitates more intelligent and dependable system design and operation, but it relies heavily on the existence of digital models that can be depended upon. In realist...

Koopman operator linearization approximates nonlinear systems of differential equations with higher-dimensional linear systems. For formal verification using reachability analysis, this is an attractive conversion, as highly scalable methods exist to compute reachable sets for linear systems. However, two main challenges are present with this appro...

While Koopman operator linearization has brought many advances for prediction, control, and verification of dynamical systems, its main disadvantage is that the quality of the resulting model heavily depends on the correct tuning of hyper-parameters such as the number of observables. Our toolbox is a Python package that automates learning accurate...

Digital Twins are an emerging technology which makes it possible to couple cyber-physical assets with their virtual representation in real-time. The technology is applicable to a variety of domains and facilitates a more intelligent and dependable system design and operation. In this paper, we address the challenge of analysing Digital Twins by pro...

For years formal methods have been successfully applied in the railway domain to formally demonstrate safety of railway systems. Despite that little has been done in the field of formal methods to address the cyber-physical nature of modern railway signalling systems. In this paper, we present an approach for a formal development of cyber-physical...

Koopman operator linearization approximates nonlinear systems of differential equations with higher-dimensional linear systems. For formal verification using reachability analysis, this is an attractive conversion, as highly scalable methods exist to compute reachable sets for linear systems. However, two main challenges are present with this appro...

The development of cyber-physical systems has become one of the biggest challenges in the field of model-based system engineering. The difficulty stems from the complex nature of cyber-physical systems which have deeply intertwined physical processes, computation and networking system aspects. To provide the highest level of assurance, cyber-physic...

Approximating the set of reachable states of a dynamical system is an algorithmic way to rigorously reason about its safety. Despite progress on efficient algorithms for affine dynamical systems, available algorithms still lack scalability to ensure their wide adoption in practice. While modern linear algebra packages are efficient for matrices wit...

The falsification of a hybrid system aims at finding trajectories that violate a given safety property. This is a challenging problem, and the practical applicability of current falsification algorithms still suffers from their high time complexity. In contrast to falsification, verification algorithms aim at providing guarantees that no such traje...

Planning as model checking based on source-to-source compilations has found increasing attention. Previously proposed approaches for temporal and hybrid planning are based on static translations, in the sense that the resulting model checking problems are uniquely defined by the given input planning problems. As a drawback, the translations can bec...

Reachability analysis of nonlinear dynamical systems is a challenging and computationally expensive task. Computing the reachable states for linear systems, in contrast, can often be done efficiently in high dimensions. In this paper, we explore verification methods that leverage a connection between these two classes of systems based on the concep...

Reachability analysis of nonlinear dynamical systems is a challenging and computationally expensive task. Computing the reachable states for linear systems, in contrast, can often be done efficiently in high dimensions. In this paper, we explore verification methods that leverage a connection between these two classes of systems based on the concep...

Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respec...

Reachability analysis computes an envelope encompassing the reachable states of a hybrid automaton within a given time horizon. It is known to be a computationally intensive task. In this case study paper, we consider the application of reachability analysis on a mathematical model unifying two key warfighting functions: Combat, and Command-and-Con...

Reachability analysis techniques aim to compute which states a dynamical system can enter. The analysis of systems described by nonlinear differential equations is known to be particularly challenging. Hybridization methods tackle this problem by abstracting nonlinear dynamics with piecewise linear dynamics around the reachable states, with additio...

Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) that contain a stochastic process in their vector field functions. They have been used for many years in a wide range of applications, but have been a shadow existence to stochastic differential equations (SDEs) despite being able to model a wider and often ph...

The problem of safety verification for a subclass of hybrid systems, namely for impulsive systems with fixed moments of jumps is considered. Sufficient conditions are derived for the safety of impulsive systems whose continuous dynamics may steer the state outside the safe region. For this purpose auxiliary barrier certificates with nonlinear rates...

Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally hard for hybrid systems. One of the main challenges is the handling of discrete transitions, including computation of intersections with invariants and guards. In this paper, we address this problem by proposi...

Hybrid automata are an important formalism for modeling dynamical systems exhibiting mixed discrete–continuous behavior such as control systems and are amenable to formal verification. However, hybrid automata lack expressiveness compared to integrated model-based design frameworks such as the MathWorks’ Simulink/Stateflow (SlSf). In this paper, we...

We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and LazySets, a standalone library that implements state-of-the-art algorithms for calculus with convex sets. The...

This paper studies an effect-abstraction based relaxation for reasoning about linear numeric planning problems. The effect-abstraction decomposes non-constant linear numeric effects into actions with conditional effects over additive constant numeric effects. With little effort, on this compiled version, it is possible to use known subgoaling based...

Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical systems, available algorithms still lack scalability to ensure their wide adoption in the industrial setting. Wh...

Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical systems, available algorithms still lack scalability to ensure their wide adoption in the industrial setting. Wh...

A promising technique for the formal verification of embedded and cyber-physical systems is flow-pipe construction, which creates a sequence of regions covering all reachable states over time. Flow-pipe construction methods can check whether specifications are met for all states, rather than just testing using a finite and incomplete set of simulat...

Despite researchers’ efforts in the last couple of decades, reachability analysis is still a challenging problem even for linear hybrid systems. Among the existing approaches, the most practical ones are mainly based on bounded-time reachable set over-approximations. For the purpose of unbounded-time analysis, one important strategy is to abstract...

A Rapidly-exploring Random Tree (RRT) is an algorithm which can search a non-convex region of space by incrementally building a space-filling tree. The tree is constructed from random points drawn from system’s state space and is biased to grow towards large unexplored areas in the system. RRT can provide better coverage of a system’s possible beha...

In this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u, x)=0, parametric in u, which can yield an infinite number of concrete invariants by assigning different values to u...

Hybrid systems are complex dynamical systems that combine discrete and continuous components. Reachability questions, regarding whether a system can run into a certain subset of its state space, stand at the core of verification and synthesis problems for hybrid systems. This volume contains papers describing new developments in this area, which we...

Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user o...

This book constitutes the refereed proceedings of the 9th InternationalWorkshop on Numerical Software Verification, NSV 2016, held in Toronto, ON, Canada in July 2011 - colocated with CAV 2016, the 28th International Conference on Computer Aided Verification. The NSV workshop is dedicated to the development of logical and mathematical techniques fo...

We propose two parallel state-space-exploration algorithms for hybrid automaton (HA), with the goal of enhancing performance on multi-core shared-memory systems. The first uses the parallel, breadth-first-search algorithm (PBFS) of the SPIN model checker, when traversing the discrete modes of the HA, and enhances it with a parallel exploration of t...

Many biological systems can be modeled as multiaffine hybrid systems. Due to the nonlinearity of multiaffine systems, it is difficult to verify their properties of interest directly. A common strategy to tackle this problem is to construct and analyze a discrete overapproximation of the original system. However, the conservativeness of a discrete a...

PDDL+ planning has its semantics rooted in hybrid automata (HA) and recent work has shown that it can be modeled as a network of HAs. Addressing the complexity of nonlinear PDDL+ planning as HAs requires both space and time efficient reasoning. Unfortunately, existing solvers either do not address nonlinear dynamics or do not natively support netwo...

Hybrid systems have both continuous and discrete dynamics and are useful for modeling a variety of control systems, from air traffic control protocols to robotic maneuvers and beyond. Recently, numerous powerful and scalable tools for analyzing hybrid systems have emerged. Several of these tools implement automated formal methods for mathematically...

Continuous-time Markov chain (CTMC) models have become a central tool for understanding the dynamics of complex reaction networks and the importance of stochasticity in the underlying biochemical processes. When such models are employed to answer questions in applications, in order to ensure that the model provides a sufficiently accurate represent...

We propose two parallel state-space exploration algorithms for hybrid systems with the goal of enhancing performance on multi-core shared memory systems. The first is an adaption of the parallel breadth first search in the SPIN model checker. We show that the adapted algorithm does not provide the desired load balancing for many hybrid systems benc...

Hybrid automata are an important formalism for modeling dynamical systems exhibiting mixed discrete-continuous behavior such as control systems and are amenable to formal verification. However, hybrid automata lack expressiveness compared to integrated model-based design (MBD) frameworks such as the MathWorks’ Simulink/Stateflow (SLSF). In this pap...

In this paper, we propose an approach to automatically compute invariant clusters for semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u,x)=0, parametric in u, which can yield an infinite number of concrete invariants by assigning different values to u so that ev...

Hybridization methods enable the analysis of hybrid automata with complex, nonlinear dynamics through a sound abstraction process. Complex dynamics are converted to simpler ones with added noise, and then analysis is done using a reachability method for the simpler dynamics. Several such recent approaches advocate that only 'dynamic' hybridization...

Hybrid systems play an important role in many application domains. A range of powerful analysis methods for this class of systems perform high-level analysis, where, iteratively, (1) a reachability computation is performed on a system model, (2) the result of the analysis is examined, and (3) the model is modified and the process repeats. For examp...

In this paper we propose a benchmark for verification of properties of fault-tolerant clock synchronization algorithms, namely, a benchmark of a TTEthernet network, where properties of the clock synchronization algorithm as implemented in a TTEthernet network can be verified, and optimization techniques for verification purposes can be applied. Our...

Algorithmically analyzing hybrid systems models is challenging in theory and in practice. Numerous sound (and sometimes complete) transformations for simplifying the analysis of hybrid systems models have been developed, and are used to show both theoretical results such as reductions to finite-state automata for certain classes and practical resul...

We present a new model of a tank network used to transfer liquid. Tanks are connected by channels. The throughput velocity of every particular channel is governed by the controller. We consider a special class of stratified controllers which are organized in several phases. Every phase can be further partitioned into multiple options. This structur...

We present XSpeed a parallel state-space exploration algorithm for continuous systems with linear dynamics and nondeterministic inputs. The motivation of having parallel algorithms is to exploit the computational power of multi-core processors to speed-up performance. The parallelization is achieved on two fronts. First, we propose a parallel imple...

Multiaffine hybrid automata (MHA) represent a powerful formalism to model complex dynamical systems. This formalism is particularly suited for the representation of biological systems which often exhibit highly non-linear behavior. In this paper, we consider the problem of parameter identification for MHA. We present an abstraction of MHA based on...

We present the first steps towards a runtime verification framework for monitoring hybrid and cyber-physical systems (CPS) development tools—such as hybrid systems reachability analysis tools, model-based development environments like Simulink/Stateflow (SLSF), etc.— based on randomized differential testing. First, hybrid automaton models are rando...

The Functional Mock-up Interface (FMI) is an industry standard which enables co-simulation of complex heterogeneous systems using multiple simulation engines. In this paper, we show how to use FMI in order to co-simulate hybrid systems modeled in the model checkers SPACEEX and UPPAAL. We show how FMI components can be automatically generated from S...

Continuous-time Markov chain (CTMC) models have become a central tool for understanding the dynamics of complex reaction networks and the importance of stochasticity in the underlying biochemical processes. When such models are employed to answer questions in applications, in order to ensure that the model provides a sufficiently accurate represent...

Hybrid systems represent an important and powerful formalism for modeling real-world applications such as embedded systems. A verification tool like SpaceEx is based on the exploration of a symbolic search space (the region space). As a verification tool, it is typically optimized towards proving the absence of errors. In some settings, e.g., when...

Planning in hybrid domains poses a special challenge due to the involved mixed discrete-continuous dynamics. A recent solving approach for such domains is based on applying model checking techniques on a translation of PDDL+ planning problems to hybrid automata. However, the proposed translation is limited because must behavior is only overapproxim...

In this poster, we present methods for randomly generating hybrid automata with affine differential equations, invariants, guards, and assignments. Selecting an arbitrary affine function from the set of all affine functions results in a low likelihood of generating hybrid automata with diverse and interesting behaviors, as there are an uncountable...

A number of powerful and scalable hybrid systems model checkers have recently emerged. Although all of them honor roughly the same hybrid systems semantics, they have drastically different model description languages. This situation (a) makes it difficult to quickly evaluate a specific hybrid automaton model using the different tools, (b) obstructs...

Computing an approximation of the reachable states of a hybrid system is a challenge, mainly because overapproximating the solutions of ODEs with a finite number of sets does not scale well. Using template polyhedra can greatly reduce the computational complexity, since it replaces complex operations on sets with a small number of optimization prob...

Planning in hybrid domains poses a special challenge due to the involved mixed discrete-continuous dynamics. A recent solving approach for such domains is based on applying model checking techniques on a translation of PDDL+ planning problems to hybrid automata. However, the proposed translation is limited because must behavior is only over-approxi...

Hybrid automata are used to model systems with both discrete and continuous dynamics. A prototypical example is a thermostat which switches between the modes “heating” and “cooling”. We present new methods to construct and utilize abstractions for the analysis of hybrid automata. For guiding the exploration of the region space of a hybrid automaton...

Compositional verification techniques in the assume-guarantee style have been successfully applied to transition systems to efficiently reduce the search space by leveraging the compositional nature of the systems under consideration. We adapt these techniques to the domain of hybrid systems with affine dynamics. To build assumptions we introduce a...

Planning in hybrid domains is an important and challenging task, and various planning algorithms have been proposed in the last years. From an abstract point of view, hybrid plan-ning domains are based on hybrid automata, which have been studied intensively in the model checking community. In par-ticular, powerful model checking algorithms and tool...

Planning in hybrid domains is an important and challenging task, and various planning algorithms have been proposed in the last years. From an abstract point of view, hybrid planning domains are based on hybrid automata, which have been studied intensively in the model checking community. In particular, powerful model checking algorithms and tools...

The concept of hybrid automata provides a powerful framework to model and analyze real-world systems. Due to the structural complexity of hybrid systems it is important to ensure the scalability of analysis algorithms. We approach this problem by providing an effective generalisation of the recently introduced notion of quasi-equal clocks to hybrid...

Hybrid systems represent an important and powerful formalism for modeling real-world applications that require both discrete and continuous behavior. A verification tool such as SpaceEx is based on the exploration of a symbolic search space (the region space). As a verification tool, it is typically optimized towards proving the absence of errors....

A recent technique used in falsification methods for hybrid systems relies on distance-based heuristics for guiding the search towards a goal state. The question is whether the technique can be carried over to reachability analyses that use regions as their basic data structure. In this paper, we introduce a box-based distance measure between regio...

We present a method to enhance the power of a given reachability analysis engine for hybrid systems. The method works by a new form of composition of reachability analyses, each on a different relaxation of the input hybrid system. We present preliminary experiments that indicate its practical potential for checking safety and stability.

The ability of some RNA molecules to switch between different metastable conformations plays an important role in cellular processes. In order to identify such molecules and to predict their conformational changes one has to investigate the refolding pathways. As a qualitative measure of these transitions, the barrier height marks the energy peak a...