insight - Algorithms and Data Structures - # Robust Controller Synthesis in Timed Büchi Automata

Robust Controller Synthesis in Timed Büchi Automata with Punctual Guards

Q: How could the techniques developed in this paper be extended to handle a mix of reliable (non-perturbed) and unreliable (perturbed) transitions in the timed automaton

The techniques developed in the paper could be extended to handle a mix of reliable (non-perturbed) and unreliable (perturbed) transitions in the timed automaton by introducing a more nuanced approach to perturbations. Currently, the paper focuses on robustness in the presence of small perturbations, where all transitions are subject to perturbations except for punctual guards. To handle a mix of reliable and unreliable transitions, one could modify the perturbation semantics to differentiate between perturbed and non-perturbed transitions based on their reliability. This would involve defining different levels of perturbations for different types of transitions, allowing for a more flexible and realistic modeling of timed automata systems.

Q: What are the potential practical implications of allowing punctual guards in the robust controller synthesis problem

Allowing punctual guards in the robust controller synthesis problem can have significant practical implications. By permitting punctual guards, which involve exact constraints on clock values, the controller synthesis problem becomes more flexible and can model systems with a mix of reliable and unreliable components more accurately. This can lead to the development of controllers that are better suited for real-world applications where some components may have precise timing requirements. In certain domains such as critical systems, aerospace, or industrial automation, punctual guards can help in designing controllers that can handle precise timing constraints effectively, leading to more efficient and reliable system behavior.

Q: Can this lead to more efficient or realistic controllers in certain application domains

The notion of "robustly iterable" cycles introduced in this paper has connections to concepts from game theory and formal verification. In game theory, the idea of iterated strategies and repeated plays is fundamental, and the concept of robustly iterable cycles aligns with the notion of strategies that can be repeated indefinitely to achieve a desired outcome. From a formal verification perspective, the focus on ensuring that a cycle can be iterated forever despite perturbations relates to the verification of system properties under various conditions. The robustly iterable cycles can be seen as a form of temporal logic property that needs to hold under perturbations, adding a layer of complexity to the verification process. Overall, the concept bridges the gap between game theory strategies and formal verification of system behaviors.

Conceitos Básicos

The authors present a generalization of the robust controller synthesis problem for timed automata with Büchi objectives, allowing for punctual guards that can be taken by the controller without perturbation.

Resumo

The paper considers the controller synthesis problem for timed automata with Büchi objectives, where the controller's delay choices are subject to small perturbations. The authors generalize the existing work by allowing for punctual guards, i.e., transitions that can be taken after a unique delay, to be taken by the controller without perturbation.

The key contributions are:

The authors introduce a new notion of "robustly iterable" cycles, which characterizes cycles that the controller can repeat infinitely often despite the perturbations. This notion generalizes the existing characterization of winning cycles in the absence of punctual guards.
They show that the problem remains in PSPACE despite the presence of punctual guards, by adapting the reasoning about the region abstraction and the reachability relation along cycles.
The authors introduce the concept of "slices" - a partition of regions into convex polyhedra that represent equivalence classes of the reachability relation along a robustly iterable cycle. This allows them to precisely characterize the sets of valuations that the controller can enforce staying within.

The paper provides a comprehensive analysis of the robust controller synthesis problem in the presence of punctual guards, extending the existing techniques to handle this more general setting.

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Controller Synthesis in Timed Büchi Automata: Robustness and Punctual Guards

by Beno... às arxiv.org 04-30-2024

https://arxiv.org/pdf/2404.18584.pdf

Controller Synthesis in Timed Büchi Automata: Robustness and Punctual Guards

Perguntas Mais Profundas

How could the techniques developed in this paper be extended to handle a mix of reliable (non-perturbed) and unreliable (perturbed) transitions in the timed automaton

The techniques developed in the paper could be extended to handle a mix of reliable (non-perturbed) and unreliable (perturbed) transitions in the timed automaton by introducing a more nuanced approach to perturbations. Currently, the paper focuses on robustness in the presence of small perturbations, where all transitions are subject to perturbations except for punctual guards. To handle a mix of reliable and unreliable transitions, one could modify the perturbation semantics to differentiate between perturbed and non-perturbed transitions based on their reliability. This would involve defining different levels of perturbations for different types of transitions, allowing for a more flexible and realistic modeling of timed automata systems.

What are the potential practical implications of allowing punctual guards in the robust controller synthesis problem

Allowing punctual guards in the robust controller synthesis problem can have significant practical implications. By permitting punctual guards, which involve exact constraints on clock values, the controller synthesis problem becomes more flexible and can model systems with a mix of reliable and unreliable components more accurately. This can lead to the development of controllers that are better suited for real-world applications where some components may have precise timing requirements. In certain domains such as critical systems, aerospace, or industrial automation, punctual guards can help in designing controllers that can handle precise timing constraints effectively, leading to more efficient and reliable system behavior.

Can this lead to more efficient or realistic controllers in certain application domains

The notion of "robustly iterable" cycles introduced in this paper has connections to concepts from game theory and formal verification. In game theory, the idea of iterated strategies and repeated plays is fundamental, and the concept of robustly iterable cycles aligns with the notion of strategies that can be repeated indefinitely to achieve a desired outcome. From a formal verification perspective, the focus on ensuring that a cycle can be iterated forever despite perturbations relates to the verification of system properties under various conditions. The robustly iterable cycles can be seen as a form of temporal logic property that needs to hold under perturbations, adding a layer of complexity to the verification process. Overall, the concept bridges the gap between game theory strategies and formal verification of system behaviors.