Optimal controller synthesis for timed systems
Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the cumulative weight while reaching a target. Used in a reactive synthesis perspective, this quantitative extension of timed games allows one to measure the q...
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| Vydáno v: | Logical methods in computer science Ročník 19, Issue 1 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Logical Methods in Computer Science Association
15.03.2023
Logical Methods in Computer Science e.V |
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| ISSN: | 1860-5974, 1860-5974 |
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| Abstract | Weighted timed games are zero-sum games played by two players on a timed
automaton equipped with weights, where one player wants to minimise the
cumulative weight while reaching a target. Used in a reactive synthesis
perspective, this quantitative extension of timed games allows one to measure
the quality of controllers in real-time systems. Weighted timed games are
notoriously difficult and quickly undecidable, even when restricted to
non-negative weights. For non-negative weights, the largest class that can be
analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the
value problem is undecidable, the authors show how to approximate the value by
considering regions with a refined granularity. In this work, we extend this
class to incorporate negative weights, allowing one to model energy for
instance, and prove that the value can still be approximated, with the same
complexity. A small restriction also allows us to obtain a class of decidable
weighted timed games with negative weights and an arbitrary number of clocks.
In addition, we show that a symbolic algorithm, relying on the paradigm of
value iteration, can be used as an approximation/computation schema over these
classes. We also consider the special case of untimed weighted games, where the
same fragments are solvable in polynomial time: this contrasts with the
pseudo-polynomial complexity, known so far, for weighted games without
restrictions. |
|---|---|
| AbstractList | Weighted timed games are zero-sum games played by two players on a timed
automaton equipped with weights, where one player wants to minimise the
cumulative weight while reaching a target. Used in a reactive synthesis
perspective, this quantitative extension of timed games allows one to measure
the quality of controllers in real-time systems. Weighted timed games are
notoriously difficult and quickly undecidable, even when restricted to
non-negative weights. For non-negative weights, the largest class that can be
analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the
value problem is undecidable, the authors show how to approximate the value by
considering regions with a refined granularity. In this work, we extend this
class to incorporate negative weights, allowing one to model energy for
instance, and prove that the value can still be approximated, with the same
complexity. A small restriction also allows us to obtain a class of decidable
weighted timed games with negative weights and an arbitrary number of clocks.
In addition, we show that a symbolic algorithm, relying on the paradigm of
value iteration, can be used as an approximation/computation schema over these
classes. We also consider the special case of untimed weighted games, where the
same fragments are solvable in polynomial time: this contrasts with the
pseudo-polynomial complexity, known so far, for weighted games without
restrictions. Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the cumulative weight while reaching a target. Used in a reactive synthesis perspective, this quantitative extension of timed games allows one to measure the quality of controllers in real-time systems. Weighted timed games are notoriously difficult and quickly undecidable, even when restricted to non-negative weights. For non-negative weights, the largest class that can be analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the value problem is undecidable, the authors show how to approximate the value by considering regions with a refined granularity. In this work, we extend this class to incorporate negative weights, allowing one to model energy for instance, and prove that the value can still be approximated, with the same complexity. A small restriction also allows us to obtain a class of decidable weighted timed games with negative weights and an arbitrary number of clocks. In addition, we show that a symbolic algorithm, relying on the paradigm of value iteration, can be used as an approximation/computation schema over these classes. We also consider the special case of untimed weighted games, where the same fragments are solvable in polynomial time: this contrasts with the pseudo-polynomial complexity, known so far, for weighted games without restrictions. |
| Author | Reynier, Pierre-Alain Monmege, Benjamin Busatto-Gaston, Damien |
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| Keywords | computational game theory timed automata weighted timed games quantitative constraints |
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| Snippet | Weighted timed games are zero-sum games played by two players on a timed
automaton equipped with weights, where one player wants to minimise the
cumulative... Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the cumulative... |
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| SubjectTerms | Computer Science computer science - computer science and game theory computer science - logic in computer science Computer Science and Game Theory d.2.4 Formal Languages and Automata Theory Logic in Computer Science |
| Title | Optimal controller synthesis for timed systems |
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