Erika Ábrahám

RWTH Aachen University · Department of Computer Science

We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability which is easier to guarantee computationally. We prove results about this which can allow reduced CAD computations.

Different stochastic extensions of hybrid automata have been proposed in the past, with unclear expressivity relations between them. In previous work, we related these modelling languages with regard to two alternative (composed and decomposed) approaches to extend hybrid automata with stochastic choices of discrete events and their time points. Th...

This paper introduces ROSAR, a novel framework enhancing the robustness of deep learning object detection models tailored for side-scan sonar (SSS) images, generated by autonomous underwater vehicles using sonar sensors. By extending our prior work on knowledge distillation (KD), this framework integrates KD with adversarial retraining to address t...

In this paper we present YOLOX-ViT, a novel object detection model, and investigate the efficacy of knowledge distillation for model size reduction without sacrificing performance. Focused on underwater robotics, our research addresses key questions about the viability of smaller models and the impact of the visual transformer layer in YOLOX. Furth...

Markov chain analysis is a key technique in formal verification. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not—or only partially—known. This motivates considering parametric models with transitions labeled with functions ov...

SMT (Satisfiability Modulo Theories) solving is a technology for the fully automated solution of logical formulas. Due to their impressive efficiency, SMT solvers are nowadays frequently used in a wide variety of applications. These tools are general purpose and as off-the-shelf solvers, their usage is truly integrated. A typical application (i) en...

Different stochastic extensions of hybrid automata have been proposed in the past, with unclear expressivity relations between them. To structure and relate these modeling languages, in this paper we formalize two alternative approaches to extend hybrid automata with stochastic choices of discrete events and their time points. The first approach, w...

Probabilistic hyperproperties express probabilistic relations between different executions of systems with uncertain behavior. HyperPCTL [3] allows to formalize such properties, where quantification over probabilistic schedulers resolves potential non-determinism. In this paper we propose an extension named AHyperPCTL to additionally introduce asyn...

In this paper we introduce a novel quantifier elimination method for conjunctions of linear real arithmetic constraints. Our algorithm is based on the Fourier-Motzkin variable elimination procedure, but by case splitting we are able to reduce the worst-case complexity from doubly to singly exponential. The adaption of the procedure for SMT solving...

Different stochastic extensions of hybrid automata have been proposed in the past, with unclear expressivity relations between them. To structure and relate these modeling languages, in this paper we formalize two alternative approaches to extend hybrid automata with stochastic choices of discrete events and their time points. The first approach, w...

Probabilistic hyperproperties express probabilistic relations between different executions of systems with uncertain behavior. HyperPCTL allows to formalize such properties, where quantification over probabilistic schedulers resolves potential non-determinism. In this paper we propose an extension named AHyperPCTL to additionally introduce asynchro...

Traditionally, extensive vehicle testing is applied to assure the robustness and safety of automotive systems. This approach is highly challenged by increasing system complexity. Formal verification lends a powerful framework for model-based safety assurance, but due to the mixed discrete–continuous behavior of automotive systems, traditional tools...

One of the few available complete methods for checking the satisfiability of sets of polynomial constraints over the reals is the cylindrical algebraic covering (CAlC) method. In this paper, we propose an extension for this method to exploit the strictness of input constraints for reducing the computational effort. We illustrate the concepts on a m...

This paper proposes an algorithm to maximize reachability probabilities for rectangular automata with random clocks via a history-dependent prophetic scheduler. This model class incorporates time-induced nondeterminism on discrete behavior and nondeterminism in the dynamic behavior. After computing reachable state sets via a forward flowpipe constr...

A wide range of problems from aerospace engineering and other application areas can be encoded logically and solved using satisfiability modulo theories (SMT) tools, which themselves use dedicated decision procedures for the underlying theories.Subtropical satisfiability is such a decision procedure for the theory of real arithmetic. Though incompl...

This paper proposes an algorithm to maximize reachability probabilities for rectangular automata with random clocks via a history-dependent prophetic scheduler. This model class incorporates time-induced nondeterminism on discrete behavior and nondeterminism in the dynamic behavior. After computing reachable state sets via a forward flowpipe constr...

Over the past decades, underwater robotics has enjoyed growing popularity and relevance. While performing a mission, one crucial task for Autonomous Underwater Vehicles (AUVs) is bottom tracking, which should keep a constant distance from the seabed. Since static obstacles like walls, rocks, or shipwrecks can lie on the sea bottom, bottom tracking...

Due to the pandemic, we had to switch our satisfiability checking lecture to an online format. To create space for interaction, we gave the students the opportunity to earn bonus points for the final exam by correctly answering some questions during the lecture. It turned out to be challenging to design these questions in a way that makes them rele...

Satisfiability Modulo Theories (SMT) solvers check the satisfiability of quantifier-free first-order logic formulas. We consider the theory of non-linear real arithmetic where the formulae are logical combinations of polynomial constraints. Here a commonly used tool is the Cylindrical Algebraic Decomposition (CAD) to decompose real space into cells...

We study the problem of formalizing and checking probabilistic hyperproperties for Markov decision processes (MDPs). We introduce the temporal logic HyperPCTL that allows explicit and simultaneous quantification over schedulers as well as probabilistic computation trees. We show that the logic can express important quantitative requirements in secu...

The European Erasmus+ project ARC – Automated Reasoning in the Class aims at improving the academic education in disciplines related to Computational Logic by using Automated Reasoning tools. We present the technical aspects of the tools as well as our education experiments, which took place mostly in virtual lectures due to the COVID pandemics. Ou...

A swarm robotic system consists of a team of robots performing cooperative tasks without any centralized coordination. In principle, swarms enable flexible and scalable solutions; however, designing individual control algorithms that can guarantee a required global behavior is difficult. Formal methods have been suggested by several researchers as...

Over the last decades, the development of algorithms and tools for the safety verification of hybrid systems has been content of intensive research. Numerous novel ideas have been presented and implemented in different tools. Whereas the majority of these tools offer implementations for fixed algorithms, only few general libraries have been provide...

Probabilistic hyperproperties describe system properties involving probability measures over multiple runs and have numerous applications in information-flow security. However, the poor scalability of existing model checking algorithms for probabilistic hyperproperties limits their use to small models. In this paper, we propose a model checking alg...

Probabilistic hyperproperties describe system properties that are concerned with the probability relation between different system executions. Likewise, it is desirable to relate performance metrics (e.g., energy, execution time, etc.) between multiple runs. This paper introduces the notion of rewards to the temporal logic HyperPCTL by extending th...

In this paper, we improve the scalability of an exact symbolic simulation method to compute the impact of stochastic delays in railway systems. We present transformation rules that allow minimizing the size of the system state representation (which train is where with which probability), without losing exactness. Based on these transformation rules...

We present HyperProb, a model checker to verify probabilistic hyperproperties on Markov Decision Processes (MDP). Our tool receives as input an MDP expressed as a PRISM model and a formula in Hyper Probabilistic Computational Tree Logic (HyperPCTL). By restricting the domain of scheduler quantification to memoryless non-probabilistic schedulers, ou...

Satisfiability Modulo Theories (SMT) and SAT solvers are critical components in many formal software tools, primarily due to the fact that they are able to easily solve logical problem instances with millions of variables and clauses. This efficiency of solvers is in surprising contrast to the traditional complexity theory position that the problem...

In this paper we propose an exact symbolic simulation method to compute the impact of delays in railway systems. We use macroscopic railway infrastructure models and model primary delays of trains in a timetable by discrete probability distributions. Our method is capable of computing exact probabilistic quantities like delay probability distributi...

We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not sufficient. We note that the new breed of local search based algorithms for this domain may offer an easier path fo...

We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real arithmetic. The algorithm is a variant of Cylindrical Algebraic Decomposition (CAD) adapted for satisfiability, whe...

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 al...

We present a transformation of Hybrid Petri nets extended with stochastic firings (HPnGs) into a subclass of Stochastic Hybrid Automata (SHA), thereby making HPnGs amenable to techniques from that domain. While (non-stochastic) Hybrid Petri nets have previously been transformed into Hybrid Automata, we consider also stochastic aspects and transform...

We consider the problem of planning with arithmetic theories, and focus on generating optimal plans for numeric domains with constant and state-dependent action costs. Solving these problems efficiently requires a seamless integration between propositional and numeric reasoning. We propose a novel approach that leverages Optimization Modulo Theorie...

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 al...

Passenger train timetables in Europe are often periodical and predetermined for longer periods of time to facilitate the planning of travel. Freight train schedules, however, depend on the actual demand. Therefore it is a common problem in railway systems to schedule additional freight train requests, under consideration of a given timetable for pa...

Collins introduced the cylindrical algebraic decomposition method for eliminating quantifiers in real arithmetic formulas. In our work we use this method for satisfiability checking in satisfiability modulo theories solver technologies, and tune it by trying to avoid some computation steps that are needed for quantifier elimination but not for sati...

In industrial model-based development (MBD) frameworks, requirements are typically specified informally using textual descriptions. To enable the application of formal methods, these specifications need to be formalized in the input languages of all formal tools that should be applied to analyse the models at different development levels. In this p...

In industrial model-based development (MBD) frameworks, requirements are typically specified informally using textual descriptions. To enable the application of formal methods, these specifications need to be formalized in the input languages of all formal tools that should be applied to analyse the models at different development levels. In this p...

Markov chain analysis is a key technique in reliability engineering. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not---or only partially---known. This motivates considering parametric models with transitions labeled with func...

Model-based synthesis allows to generate plans to achieve high-level tasks while satisfying certain properties of interest. However, when such plans are executed on concrete systems, several modeling assumptions may be challenged, jeopardizing their real applicability. This paper presents an integrated system for generating, executing and monitorin...

In this paper, we propose a new temporal 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 syste...

We present the latest developments in SMT-RAT, a tool for the automated check of quantifier-free real and integer arithmetic formulas for satisfiability. As a distinguishing feature, \smtrat provides a set of solving modules and supports their strategic combination. We describe our CArL library for arithmetic computations, the available modules imp...

This paper presents our experience with formal verification of C code that is automatically generated from Simulink open-loop controller models. We apply the state-of-the-art commercial model checker BTC EmbeddedPlatform to two Ford R&D prototype case studies: a next-gen Driveline State Request and a next-gen E-Clutch Control. These case studies co...

The automotive industry makes increasing usage of Simulink-based software development. Typically, automotive Simulink designs are analyzed using non-formal test methods, which do not guarantee the absence of errors. In contrast, formal verification techniques aim at providing formal guarantees or counterexamples that the analyzed designs fulfill th...

Smart factories are on the verge of becoming the new industrial paradigm, wherein optimization permeates all aspects of production, from concept generation to sales. To fully pursue this paradigm, flexibility in the production means as well as in their timely organization is of paramount importance. AI is planning a major role in this transition, b...

To decide whether a set of states is reachable in a hybrid system, over-approximative symbolic successor computations can be used, where the symbolic representation of state sets as well as the successor computations have several parameters which determine the efficiency and the precision of the computations. Naturally, faster computations come wit...

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.,...

Two approaches have been presented for the analysis of HPnGs, (i) a tree-based approach and (ii) a state-space representation based on computational geometry. We present a translation of the tree-based representation into a geometric representation using the C++ library HyPro, which has been developed for the analysis of hybrid automata. This allow...

In manufacturing, the increasing involvement of autonomous robots in production processes poses new challenges on the production management. In this paper we report on the usage of Optimization Modulo Theories (OMT) to solve certain multi-robot scheduling problems in this area. Whereas currently existing methods are heuristic, our approach guarante...

In this paper we propose an improvement for flowpipe-construction-based reachability analysis techniques for hybrid systems. Such methods apply iterative successor computations to pave the reachable region of the state space by state sets in an over-approximative manner. As the computational costs steeply increase with the dimension, in this work w...

In this paper we propose an improvement for flowpipe-construction-based reachability analysis techniques for hybrid systems. Such methods apply iterative successor computations to pave the reachable region of the state space by state sets in an over-approximative manner. As the computational costs steeply increase with the dimension, in this work w...

In this tool paper we introduce HyPro, our free and open-source C++ programming library, which offers implementations for the most prominent state set representations used by flowpipe-construction-based reachability analysis techniques for hybrid systems.

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...

Symbolic Computation and Satisfiability Checking are viewed as individual research areas, but they share common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite these commonalities, the two communities are currently only weakly connected. We introduce a new project SC 2 to build a...

Modern cloud applications consist of software components deployed on multiple virtual machines. Deploying such applications is error prone and requires detailed system expertise. The deployment optimization problem is about how to configure and deploy applications correctly while at the same time minimizing resource cost on the cloud. This problem...

The seminar focused on satisfiability checking for combinations of first-order logic and sub-classes thereof with arithmetic theories in a very liberal sense, also covering quantifiers andparameters. It gathered members of the two communities of symbolic computation (or computeralgebra) and satisfiability checking (including satisfiability modulo t...

Due to its complexity, the standing-up task for robots is highly challenging, and often implemented by scripting the strategy that the robot should execute per hand. In this paper we aim at improving the approach of a scripted stand-up strategy by making it more stable and safe. To achieve this aim, we apply both static and runtime methods by integ...

The exploitation of solar power for energy supply is of increasing importance. While technical development mainly takes place in the engineering disciplines, computer science offers adequate techniques for optimization. This work addresses the problem of finding an optimal heliostat field arrangement for a solar tower power plant. We propose a solu...

The branch-and-bound framework has already been successfully applied in SAT-modulo-theories (SMT) solvers to check the satisfiability of linear integer arithmetic formulas. In this paper we study how it can be used in SMT solvers for non-linear integer arithmetic on top of two real-algebraic decision procedures: the virtual substitution and the cyl...

Symbolic Computation and Satisfiability Checking are two research areas, both having their individual scientific focus but sharing also common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite their commonalities, the two communities are rather weakly connected. The aim of our newly...

Symbolic Computation and Satisfiability Checking are two research areas, both having their individual scientific focus but sharing also common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite their commonalities, the two communities are rather weakly connected. The aim of our newly...

In this paper we address the safety analysis of chemical plants controlled by programmable logic controllers (PLCs). We consider a specification of the control program of the PLCs, extended with the specification of the dynamic plant behavior. The resulting hybrid models can be transformed to hybrid automata, for which advanced techniques for reach...

Satisfiability checking aims to develop algorithms and tools for checking the satisfiability of existentially quantified logical formulas. Besides powerful SAT solvers for solving propositional logic formulas, sophisticated SAT-modulo-theories (SMT) solvers are available for a wide range of theories, and are applied as black-box engines for many te...

2016 SC-Square Project Poster

Due to the increasing complexity of software systems, there is a growing need for automated and scalable software synthesis and analysis. In the last decade, active research in the formal methods community brought interesting results and valuable tools. However, there are still challenges to face and hard problems that need to be solved. We briefly...