Abstraction-based Synthesis for Stochastic Systems with Omega-Regular Objectives

Dutreix, Maxence; Huh, Jeongmin; Coogan, Samuel

doi:10.48550/arxiv.2001.09236

Cited by 6 publications

(15 citation statements)

References 22 publications

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“…In the following, we first formalize the case study, which was proposed by Dutreix et al [2020]. Consider the dynamic model of a bistable switch which is a tuple Σ = (𝑋, 𝑈 ,𝑊 , 𝑓 ) with a twodimensional compact state space…”

Section: Controller Synthesis Formentioning

confidence: 99%

“…5. In Table 2, we compare both the accelerated and the non-accelerated versions of our fixpoint algorithm against the state-of-the-art algorithm for solving this problem, which is implemented in the tool called StochasticSynthesis (SS) [Dutreix et al 2020].…”

Section: 𝐴 𝐶mentioning

confidence: 99%

“…We show on a number of synthetic benchmarks from the very large transition systems benchmark suite [Garavel and Descoubes 2003] that our algorithm, with the improvements, can scale to large Rabin games and the performance scales with the number of cores. Additionally, we evaluate our tool on two case studies, one from software synthesis [Chatterjee et al 2013] and the other from stochastic control synthesis [Dutreix et al 2020]. We show that Fairsyn scales well on these case studies, and outperforms a state-of-the-art stochastic game solver by an order of magnitude.…”

Section: Introductionmentioning

confidence: 99%

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Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness

Banerjee¹,

Majumdar²,

Mallik³

et al. 2022

Preprint

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We consider fixpoint algorithms for two-player games on graphs with 𝜔-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any execution is strongly fair with respect to a specified set of live edges: whenever the source vertex of a live edge is visited infinitely often along a play, the edge itself is traversed infinitely often along the play as well.We show that, surprisingly, strong transition fairness retains the algorithmic characteristics of the fixpoint algorithms for 𝜔-regular games-the new algorithms can be obtained simply by replacing certain occurrences of the controllable predecessor by a new almost sure predecessor operator. For Rabin games with 𝑘 pairs, the complexity of the new algorithm is 𝑂 (𝑛 𝑘+2 𝑘!) symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption. Further, we show that GR(1) specifications with strong transition fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as the usual algorithm. In contrast, strong fairness necessarily requires increasing the alternation depth depending on the number of fairness assumptions.We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic 𝜔-regular games that runs in 𝑂 (𝑛 𝑘+2 𝑘!) symbolic steps, improving the state of the art. Previous approaches for handling fairness assumptions would either increase the alternation depth of the fixpoint algorithm or require an up-front automata-theoretic construction that would increase the state space, or both.Finally, we have implemented a BDD-based synthesis engine based on our algorithm. We show on a set of synthetic and real benchmarks that our algorithm is scalable, parallelizable, and outperforms previous algorithms by orders of magnitude.All proofs can be found in the appendix.

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Section: Controller Synthesis Formentioning

confidence: 99%

Section: 𝐴 𝐶mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness

Banerjee¹,

Majumdar²,

Mallik³

et al. 2022

Preprint

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“…[10,11]) and ω-regular properties (see e.g. [12,13]). These techniques require constructing symbolic models (a.k.a.…”

Section: Introductionmentioning

confidence: 99%

Formal Synthesis of Controllers for Uncertain Linear Systems against $ω$-Regular Properties: A Set-based Approach

Zhong¹,

Caccamo²

2021

Preprint

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In this paper, we present how to synthesize controllers to enforce ω-regular properties over linear control systems affected by bounded disturbances. In particular, these controllers are synthesized based on socalled hybrid controlled invariant (HCI) sets. To compute these sets, we first construct a product system using the linear control system and the deterministic Rabin automata (DRA) modeling the negation of the desired property. Then, we compute the maximal HCI set over the state set of the product system by leveraging a set-based approach. To ensure termination of the computation of the HCI sets within a finite number of iterations, we also propose two iterative schemes to compute approximations of the maximal HCI set. Finally, we show the effectiveness of our approach on two case studies.

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“…An alternate approach to ours would be to assign probability values to disturbances: The ones in W high \ W normal occur with low probability, and the ones in W normal occur with high probability. Then an optimal controller that maximizes the probability of satisfaction of the given specification [7], [16], [24] would perhaps behave similarly to the optimally resilient controller in our setup. In contrast to our approach, there are two drawbacks of the probabilistic treatment of unexpected disturbances: First, an explicit probabilistic model of the disturbance is required, which is often difficult to obtain.…”

Section: Introductionmentioning

confidence: 99%

Resilient Abstraction-Based Controller Design

Samuel

Mallik

Schmuck

et al. 2020

2020 59th IEEE Conference on Decision and Control (CDC)

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We consider the computation of resilient controllers for perturbed non-linear dynamical systems w.r.t. linear-time temporal logic specifications. We address this problem through the paradigm of Abstraction-Based Controller Design (ABCD) where a finite state abstraction of the perturbed system dynamics is constructed and utilized for controller synthesis. In this context, our contribution is twofold: (I) We construct abstractions which model the impact of occasional high disturbance spikes on the system via so called disturbance edges. (II) We show that the application of resilient reactive synthesis techniques to these abstract models results in closed loop systems which are optimally resilient to these occasional high disturbance spikes. We have implemented this resilient ABCD workflow on top of SCOTS and showcase our method through multiple robot planning examples.

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Abstraction-based Synthesis for Stochastic Systems with Omega-Regular Objectives

Cited by 6 publications

References 22 publications

Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness

Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness

Formal Synthesis of Controllers for Uncertain Linear Systems against $ω$-Regular Properties: A Set-based Approach

Resilient Abstraction-Based Controller Design

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