Kerianne L. Hobbs, Peter Heidlauf, Alexander Collins, Stanley Bak
Benchmark Proposal: Space debris tracking and collision prediction is a growing worldwide problem as more and more objects are placed into orbit. While traditional methods simulate particles with Gaussian uncertainty to make collision predictions, we instead analyze the problem from a reachability perspective. The problem appears to require methods capable of quickly analyzing high-dimensional nonlinear systems, but we take advantage multiple kinds of problem structure to show that reachability analysis may be viable for this problem. In particular we present an initial analysis approach that uses numerical simulation for reachability analysis, and interval arithmetic with AABB trees for fast collision detection. The analysis uses a variable size time step with a counter-example guided abstraction refinement (CEGAR) method to increase analysis speed without sacrificing accuracy. Our approach can analyze upwards of thousands of orbiting objects faster than real-time, where each object is subject to some initial state uncertainty.
{"title":"Space Debris Collision Detection using Reachability","authors":"Kerianne L. Hobbs, Peter Heidlauf, Alexander Collins, Stanley Bak","doi":"10.29007/5313","DOIUrl":"https://doi.org/10.29007/5313","url":null,"abstract":"Benchmark Proposal: Space debris tracking and collision prediction is a growing worldwide problem as more and more objects are placed into orbit. While traditional methods simulate particles with Gaussian uncertainty to make collision predictions, we instead analyze the problem from a reachability perspective. The problem appears to require methods capable of quickly analyzing high-dimensional nonlinear systems, but we take advantage multiple kinds of problem structure to show that reachability analysis may be viable for this problem. In particular we present an initial analysis approach that uses numerical simulation for reachability analysis, and interval arithmetic with AABB trees for fast collision detection. The analysis uses a variable size time step with a counter-example guided abstraction refinement (CEGAR) method to increase analysis speed without sacrificing accuracy. Our approach can analyze upwards of thousands of orbiting objects faster than real-time, where each object is subject to some initial state uncertainty.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127148491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2018. In this year, six tools CORA, CORA/SX, C2E2, Flow*, Isabelle/HOL, and SymReach (in alphabetic order) participated. They are applied to solve reachability analysis problems on four benchmarks problems, one of them with hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools.
{"title":"ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics","authors":"Fabian Immler, Matthias Althoff, Xin Chen, Chuchu Fan, Goran Frehse, Niklas Kochdumper, Yangge Li, Sayan Mitra, Mahendra Singh Tomar, Majid Zamani","doi":"10.29007/mskf","DOIUrl":"https://doi.org/10.29007/mskf","url":null,"abstract":"We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2018. In this year, six tools CORA, CORA/SX, C2E2, Flow*, Isabelle/HOL, and SymReach (in alphabetic order) participated. They are applied to solve reachability analysis problems on four benchmarks problems, one of them with hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127395659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Benchmarks Proposal: We provide benchmarks for stochastic models drawn from Building Automation Systems (BAS), specifically constructed from expertise developed on a real BAS setup. This contribution branches out of the library of general models presented in [4], specifically focussing on probabilistic models. Using this library, we generate two realistic case studies which incorporate (i) stochasticity stemming from different sources (e.g. process or observation noise on the continuous variables) and (ii) various input and output signals. We describe each model structure (syntax and semantics), identify key problems (specifications) for different analysis goals, and finally illustrate solutions for each goal.
{"title":"Benchmarks for stochastic models from building automation systems","authors":"Nathalie Cauchi, A. Abate","doi":"10.29007/trj5","DOIUrl":"https://doi.org/10.29007/trj5","url":null,"abstract":"Abstract Benchmarks Proposal: We provide benchmarks for stochastic models drawn from Building Automation Systems (BAS), specifically constructed from expertise developed on a real BAS setup. This contribution branches out of the library of general models presented in [4], specifically focussing on probabilistic models. Using this library, we generate two realistic case studies which incorporate (i) stochasticity stemming from different sources (e.g. process or observation noise on the continuous variables) and (ii) various input and output signals. We describe each model structure (syntax and semantics), identify key problems (specifications) for different analysis goals, and finally illustrate solutions for each goal.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133753609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tool Presentation: Computing guaranteed bounds of function outputs when their input variables are bounded by intervals is an essential technique for many formal methods. Due to the importance of bounding function outputs, several techniques have been proposed for this problem, such as interval arithmetic, affine arithmetic, and Taylor models. While all methods provide guaranteed bounds, it is typically unknown to a formal verification tool which approach is best suitable for a given problem. For this reason, we present an implementation of the aforementioned techniques in our MATLAB tool CORA so that advantages and disadvantages of different techniques can be quickly explored without having to compile code. In this work we present the implementation of Taylor models and affine arithmetic; our interval arithmetic implementation has already been published. We evaluate the performance of our implementation using a set of benchmarks against Flow* and INTLAB. To the best of our knowledge, we have also evaluated for the first time how a combination of interval arithmetic and Taylor models performs: our results indicate that this combination is faster and more accurate than only using Taylor models.
{"title":"Implementation of Taylor models in CORA 2018","authors":"M. Althoff, D. Grebenyuk, Niklas Kochdumper","doi":"10.29007/zzc7","DOIUrl":"https://doi.org/10.29007/zzc7","url":null,"abstract":"Tool Presentation: Computing guaranteed bounds of function outputs when their input variables are bounded by intervals is an essential technique for many formal methods. Due to the importance of bounding function outputs, several techniques have been proposed for this problem, such as interval arithmetic, affine arithmetic, and Taylor models. While all methods provide guaranteed bounds, it is typically unknown to a formal verification tool which approach is best suitable for a given problem. For this reason, we present an implementation of the aforementioned techniques in our MATLAB tool CORA so that advantages and disadvantages of different techniques can be quickly explored without having to compile code. In this work we present the implementation of Taylor models and affine arithmetic; our interval arithmetic implementation has already been published. We evaluate the performance of our implementation using a set of benchmarks against Flow* and INTLAB. To the best of our knowledge, we have also evaluated for the first time how a combination of interval arithmetic and Taylor models performs: our results indicate that this combination is faster and more accurate than only using Taylor models.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131896047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tool Presentation: We evaluate an improved reachability algorithm for linear (and affine) systems implemented in the continuous branch of the Hylaa tool. While Hylaa’s earlier approach required n simulations to verify an n-dimensional system, the new method takes advantage of additional problem structure to produce the same verification result in significantly less time. If the initial states can be defined in i dimensions, and the output variables related to the property being checked are o-dimensional, the new approach needs only min(i, o) simulations to verify the system, or produce a counter-example. In addition to reducing the number of simulations, a second improvement speeds up individual simulations when the dynamics is sparse by using Krylov subspace methods. At ARCH 2017, we used the original approach to verify nine large linear benchmarks taken from model order reduction. Here, we run the new algorithm on the same set of benchmarks, and get an identical verification result in a fraction of the time. None of the benchmarks need more than tens of seconds to complete. The largest system with 10922 dimensions, which took over 24 hours using last year’s method, is verified in 3.4 seconds.
{"title":"Numerical Verification of 10000-dimensional Linear Systems 10000x Faster","authors":"Stanley Bak","doi":"10.29007/gv5q","DOIUrl":"https://doi.org/10.29007/gv5q","url":null,"abstract":"Tool Presentation: We evaluate an improved reachability algorithm for linear (and affine) systems implemented in the continuous branch of the Hylaa tool. While Hylaa’s earlier approach required n simulations to verify an n-dimensional system, the new method takes advantage of additional problem structure to produce the same verification result in significantly less time. If the initial states can be defined in i dimensions, and the output variables related to the property being checked are o-dimensional, the new approach needs only min(i, o) simulations to verify the system, or produce a counter-example. In addition to reducing the number of simulations, a second improvement speeds up individual simulations when the dynamics is sparse by using Krylov subspace methods. At ARCH 2017, we used the original approach to verify nine large linear benchmarks taken from model order reduction. Here, we run the new algorithm on the same set of benchmarks, and get an identical verification result in a fraction of the time. None of the benchmarks need more than tens of seconds to complete. The largest system with 10922 dimensions, which took over 24 hours using last year’s method, is verified in 3.4 seconds.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130494783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zahra Ramezani, Alexandre Donzé, Martin Fabian, K. Åkesson
Falsification is a testing method for cyber-physical systems where numerical optimization is used to find counterexamples of a given specification that the system must fulfill. The falsification process uses quantitative semantics that play the role of objective functions to minimize the distance to falsifying the specification. Falsification has gained attention due to its versatile applicability, and much work exists on various ways of implementing the falsification process, often focusing on which optimization algorithm to use, or more recently, the semantics for the formal requirements. In this work, we look at some practical aspects of input generation, i.e., the mapping from parameters used as optimization variables to signals that form the actual test cases for the system. This choice is critical but often overlooked. It is assumed that problem experts can guide how to parameterize inputs; however, this assumption is often too optimistic in practice. We observe that pulse generation is a surprisingly good first option that can falsify many common benchmarks after only a few simulations while requiring only a few parameters per signal.
{"title":"Temporal Logic Falsification of Cyber-Physical Systems using Input Pulse Generators","authors":"Zahra Ramezani, Alexandre Donzé, Martin Fabian, K. Åkesson","doi":"10.29007/q4k7","DOIUrl":"https://doi.org/10.29007/q4k7","url":null,"abstract":"Falsification is a testing method for cyber-physical systems where numerical optimization is used to find counterexamples of a given specification that the system must fulfill. The falsification process uses quantitative semantics that play the role of objective functions to minimize the distance to falsifying the specification. Falsification has gained attention due to its versatile applicability, and much work exists on various ways of implementing the falsification process, often focusing on which optimization algorithm to use, or more recently, the semantics for the formal requirements. In this work, we look at some practical aspects of input generation, i.e., the mapping from parameters used as optimization variables to signals that form the actual test cases for the system. This choice is critical but often overlooked. It is assumed that problem experts can guide how to parameterize inputs; however, this assumption is often too optimistic in practice. We observe that pulse generation is a surprisingly good first option that can falsify many common benchmarks after only a few simulations while requiring only a few parameters per signal.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116994423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tool Presentation: We present ORBITADOR, a tool for stability analysis of dynamical systems. ORBITADOR uses a method that generates a bounded invariant set of a differential system with a given set of initial conditions around a point x0 to prove the existence of a limit cycle. This invariant has the form of a tube centered on the Euler approximate solution starting at x0, which has for radius an upper bound on the distance between the approximate solution and the exact ones. The method consists in finding a real T > 0 such that the “snapshot” of the tube at time t = (i+1)T is included in the snapshot at t = iT , for some integer i with adding a small bounded uncertainty. This uncertainty allows using an approximate value T of the exact period. We successfully applied ORBITADOR to several classical examples of periodical systems.
{"title":"ORBITADOR: A tool to analyze the stability of periodical dynamical systems","authors":"J. Jerray","doi":"10.29007/k6xm","DOIUrl":"https://doi.org/10.29007/k6xm","url":null,"abstract":"Tool Presentation: We present ORBITADOR, a tool for stability analysis of dynamical systems. ORBITADOR uses a method that generates a bounded invariant set of a differential system with a given set of initial conditions around a point x0 to prove the existence of a limit cycle. This invariant has the form of a tube centered on the Euler approximate solution starting at x0, which has for radius an upper bound on the distance between the approximate solution and the exact ones. The method consists in finding a real T > 0 such that the “snapshot” of the tube at time t = (i+1)T is included in the snapshot at t = iT , for some integer i with adding a small bounded uncertainty. This uncertainty allows using an approximate value T of the exact period. We successfully applied ORBITADOR to several classical examples of periodical systems.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129221144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tool presentation: Safety-critical systems often require guaranteed state estimation instead of estimating the most-likely state. While a lot of research on guaranteed state estimation has been conducted, there exists no tool for this purpose. Since guaranteed state estimation is in many cases a reachability problem or closely related to reachability analysis,this paper presents its implementation in the continuous reachability analyzer (CORA). We present how we integrated different types of observers, different set representations, and linear as well as nonlinear dynamics. The scalability and usefulness of the implementedobservers is demonstrated for a scalable tank system.
{"title":"Guaranteed State Estimation in CORA 2021","authors":"M. Althoff","doi":"10.29007/7m2k","DOIUrl":"https://doi.org/10.29007/7m2k","url":null,"abstract":"Tool presentation: Safety-critical systems often require guaranteed state estimation instead of estimating the most-likely state. While a lot of research on guaranteed state estimation has been conducted, there exists no tool for this purpose. Since guaranteed state estimation is in many cases a reachability problem or closely related to reachability analysis,this paper presents its implementation in the continuous reachability analyzer (CORA). We present how we integrated different types of observers, different set representations, and linear as well as nonlinear dynamics. The scalability and usefulness of the implementedobservers is demonstrated for a scalable tank system.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130178659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. Ernst, Paolo Arcaini, Ismail Bennani, Aniruddh Chandratre, Alexandre Donzé, Georgios Fainekos, Goran Frehse, Khouloud Gaaloul, Jun Inoue, Tanmay Khandait, L. Mathesen, C. Menghi, Giulia Pedrielli, Marc Pouzet, Masaki Waga, Shakiba Yaghoubi, Yoriyuki Yamagata, Zhenya Zhang
This report presents the results from the 2021 friendly competition in the ARCH work- shop for the falsification of temporal logic specifications over Cyber-Physical Systems. We briefly describe the competition settings, which have been inherited from the previ- ous years, give background on the participating teams and tools and discuss the selected benchmarks. Apart from new requirements and participants, the major novelty in this instalment is that falsifying inputs have been validated independently. During this pro- cess, we uncovered several issues like configuration errors and computational discrepancies, stressing the importance of this kind of validation.
{"title":"ARCH-COMP 2021 Category Report: Falsification with Validation of Results","authors":"G. Ernst, Paolo Arcaini, Ismail Bennani, Aniruddh Chandratre, Alexandre Donzé, Georgios Fainekos, Goran Frehse, Khouloud Gaaloul, Jun Inoue, Tanmay Khandait, L. Mathesen, C. Menghi, Giulia Pedrielli, Marc Pouzet, Masaki Waga, Shakiba Yaghoubi, Yoriyuki Yamagata, Zhenya Zhang","doi":"10.29007/xwl1","DOIUrl":"https://doi.org/10.29007/xwl1","url":null,"abstract":"This report presents the results from the 2021 friendly competition in the ARCH work- shop for the falsification of temporal logic specifications over Cyber-Physical Systems. We briefly describe the competition settings, which have been inherited from the previ- ous years, give background on the participating teams and tools and discuss the selected benchmarks. Apart from new requirements and participants, the major novelty in this instalment is that falsifying inputs have been validated independently. During this pro- cess, we uncovered several issues like configuration errors and computational discrepancies, stressing the importance of this kind of validation.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130949638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a benchmark for the verification of autonomous vehicles. By considering different traffic scenarios from the CommonRoad database, we obtain several thousands of different verification tasks, where the verification problem is to prove that the con- sidered tracking controller safely follows a given reference trajectory despite disturbances and measurement errors. The dynamic of the car is described by a nonlinear kinematic single-track model. Since the feedback matrix for the tracking controller is time-varying, the dynamic of the controlled system changes constantly. Because of this, the proposed benchmark is well-suited to evaluate how robustly reachability tools can handle changing system dynamics.
{"title":"Verification of Collision Avoidance for CommonRoad Traffic Scenarios","authors":"Niklas Kochdumper, Philipp Gassert, M. Althoff","doi":"10.29007/1973","DOIUrl":"https://doi.org/10.29007/1973","url":null,"abstract":"We propose a benchmark for the verification of autonomous vehicles. By considering different traffic scenarios from the CommonRoad database, we obtain several thousands of different verification tasks, where the verification problem is to prove that the con- sidered tracking controller safely follows a given reference trajectory despite disturbances and measurement errors. The dynamic of the car is described by a nonlinear kinematic single-track model. Since the feedback matrix for the tracking controller is time-varying, the dynamic of the controlled system changes constantly. Because of this, the proposed benchmark is well-suited to evaluate how robustly reachability tools can handle changing system dynamics.","PeriodicalId":236469,"journal":{"name":"ARCH@ADHS","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125654201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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