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Journal ArticleDOI

Parameter synthesis for probabilistic timed automata using stochastic game abstractions

11 May 2017-Theoretical Computer Science (Elsevier)-Vol. 735, pp 64-81
TL;DR: In the parametric setting, the method is able to determine all the possible maximum or minimum reachability probabilities that arise for different values of timing parameters, and yields optimal valuations represented as a set of symbolic constraints between parameters.
About: This article is published in Theoretical Computer Science.The article was published on 2017-05-11 and is currently open access. It has received 3 citations till now. The article focuses on the topics: PRISM model checker & Reachability.

Summary (1 min read)

1 Introduction

  • Stochastic aspect is very important for modelling numerous classes of systems, such as communication and security protocols, due to component failures, unreliable channels or randomisation.
  • The goal is then to automatically synthesize the values of model’s parameters such that the specification is guaranteed.
  • The authors are dealing with the synthesis of timing parameters for probabilistic real-time systems modelled as probabilistic timed automata (PTA) [18].
  • Subsequent research has thus concentrated on finding subclasses for which certain problems would be decidable by restricting the use of parameters [9] or by restricting the parameter domain [11].

2 Preliminaries

  • The authors now define Markov decision processes, a formalism for modelling systems which exhibit both nondeterministic and probabilistic behaviour.
  • Player 2 then selects a probability distribution µ from the set StepsGps, δ, s1q.
  • Let R, Rě0 and Z be the sets of reals, non-negative reals and integers, respectively.
  • The authors now give a formal definition of Parametric Probabilistic Timed Automata (PPTA), which are PTA extended with timing parameters.
  • In the case of property “the maximum probability of an airbag failing to deploy”, the authors would want to choose the timing parameters that minimise this probability value.

3 Synthesis with Forward Reachability

  • A naive approach to parameter synthesis for PTA is to restrict parameter values to bounded intervals of integers (or rationals that can be scaled to integers) and perform verification for each such (non-parametric) model using a probabilistic model checker, e.g. Prism [16].
  • In Fig. 1 the authors present their extension of the forward reachability algorithm from [18] to parametric probabilistic timed automata.
  • Let us highlight the differences between their algorithm and its non-parametric counterpart from [18].
  • In their setting, the authors are interested in finding the optimal parameter valuations (that maximise or minimise some reachability probability).
  • The authors divide the set Reached into subsets Reached i, each of which contains the symbolic states pli, ζiq with equivalent parameter values (obtained by projection onto parameters ζi|P ).

5 Conclusion

  • The authors presented a technique for PPTA which derives symbolic constraints on parameters of the model, such that the max/min probability of reaching some set of locations is optimised.
  • The authors focused on probabilistic reachability, but can easily consider more expressive target sets that refer to locations and clocks by syntactically modifying the model as in [18].
  • Unlike for TA/PTA, where the extrapolation operator on zones can be used, in the parametric case the authors need to impose certain restrictions to ensure termination.
  • The authors are currently implementing the algorithm in Prism.
  • This research is supported by ERC AdG VERIWARE.

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Citations
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Journal ArticleDOI
TL;DR: A systematic review on AVS implementing deep learning methods that only rely on RGB camera vision rather than complex sensor fusion is expected to offer a pathway for the rapid development of cost-efficient and more secure practical autonomous vehicle systems.
Abstract: In the past decade, autonomous vehicle systems (AVS) have advanced at an exponential rate, particularly due to improvements in artificial intelligence, which have had a significant impact on social as well as road safety and the future of transportation systems. However, the AVS is still far away from mass production because of the high cost of sensor fusion and a lack of combination of top-tier solutions to tackle uncertainty on roads. To reduce sensor dependency and to increase manufacturing along with enhancing research, deep learning-based approaches could be the best alternative for developing practical AVS. With this vision, in this systematic review paper, we broadly discussed the literature of deep learning for AVS from the past decade for real-life implementation in core fields. The systematic review on AVS implementing deep learning is categorized into several modules that cover activities including perception analysis (vehicle detection, traffic signs and light identification, pedestrian detection, lane and curve detection, road object localization, traffic scene analysis), decision making, end-to-end controlling and prediction, path and motion planning and augmented reality-based HUD, analyzing research works from 2011 to 2021 that focus on RGB camera vision. The literature is also analyzed for final representative outcomes as visualization in augmented reality-based head-up display (AR-HUD) with categories such as early warning, road markings for improved navigation and enhanced safety with overlapping on vehicles and pedestrians in extreme visual conditions to reduce collisions. The contribution of the literature review includes detailed analysis of current state-of-the-art deep learning methods that only rely on RGB camera vision rather than complex sensor fusion. It is expected to offer a pathway for the rapid development of cost-efficient and more secure practical autonomous vehicle systems.

8 citations

Journal ArticleDOI
TL;DR: It is shown that the existence of timing parameter valuations ensuring consistency is undecidable in the general context, but still exhibit a syntactic condition on parameters to ensure decidability.

1 citations


Cites methods from "Parameter synthesis for probabilist..."

  • ...aluations preserving the same minimum and maximum probabilities for reachability properties as the reference valuation? Parametric probabilistic timed automata were then given a symbolic semantics in [JK14]; a method has been proposed in that same work to synthesize optimal parameter valuations to maximize or minimize the probability of reaching a discrete location. In the purely probabilistic setting, ...

    [...]

Journal Article
TL;DR: In this article, the authors present PRISM-PSY, a tool that performs precise GPU-accelerated parameter synthesis for continuous-time Markov chains and time-bounded temporal logic specifications.
Abstract: In this paper we present PRISM-PSY, a novel tool that performs precise GPU-accelerated parameter synthesis for continuous-time Markov chains and time-bounded temporal logic specifications. We redesign, in terms of matrix-vector operations, the recently formulated algorithms for precise parameter synthesis in order to enable effective dataparallel processing, which results in significant acceleration on many-core architectures. High hardware utilisation, essential for performance and scalability, is achieved by state space and parameter space parallelisation: the former leverages a compact sparse-matrix representation, and the latter is based on an iterative decomposition of the parameter space. Our experiments on several biological and engineering case studies demonstrate an overall speedup of up to 31-fold on a single GPU compared to the sequential implementation.
References
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01 Jan 1990
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Abstract: From the Publisher: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Like the first edition,this text can also be used for self-study by technical professionals since it discusses engineering issues in algorithm design as well as the mathematical aspects. In its new edition,Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity,and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage. As in the classic first edition,this new edition of Introduction to Algorithms presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers. Further,the algorithms are presented in pseudocode to make the book easily accessible to students from all programming language backgrounds. Each chapter presents an algorithm,a design technique,an application area,or a related topic. The chapters are not dependent on one another,so the instructor can organize his or her use of the book in the way that best suits the course's needs. Additionally,the new edition offers a 25% increase over the first edition in the number of problems,giving the book 155 problems and over 900 exercises thatreinforcethe concepts the students are learning.

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Journal ArticleDOI
TL;DR: Alur et al. as discussed by the authors proposed timed automata to model the behavior of real-time systems over time, and showed that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the non-deterministic case and PSPACE-complete in deterministic case.

7,096 citations

Book ChapterDOI
14 Jul 2011
TL;DR: A major new release of the PRISMprobabilistic model checker is described, adding, in particular, quantitative verification of (priced) probabilistic timed automata.
Abstract: This paper describes a major new release of the PRISMprobabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and real-time characteristics. In many application domains, all three aspects are essential; this includes, for example, embedded controllers in automotive or avionic systems, wireless communication protocols such as Bluetooth or Zigbee, and randomised security protocols. PRISM, which is open-source, also contains several new components that are of independent use. These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicit-state probabilistic model checking library; a discrete-event simulation engine for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite.

2,377 citations

Journal ArticleDOI
TL;DR: A detailed user guide is given which describes how to use the various tools of Uppaal version 2.02 to construct abstract models of a real-time system, to simulate its dynamical behavior, to specify and verify its safety and bounded liveness properties in terms of its model.
Abstract: This paper presents the overal structure, the design criteria, and the main features of the tool box Uppaal. It gives a detailed user guide which describes how to use the various tools of Uppaal version 2.02 to construct abstract models of a real-time system, to simulate its dynamical behavior, to specify and verify its safety and bounded liveness properties in terms of its model. In addition, the paper also provides a short review on case-studies where Uppaal is applied, as well as references to its theoretical foundation.

2,358 citations

Frequently Asked Questions (2)
Q1. What contributions have the authors mentioned in the paper "Parameter synthesis for probabilistic timed automata using stochastic game abstractions" ?

The authors propose a method to synthesise optimal values of timing parameters for probabilistic timed automata, in the sense that the probability of reaching some set of states is either maximised or minimised. 

One possibility is to restrict the parameter domain to bounded integers as in [ 11 ].