Contract-Based Distributed Synthesis in Two-Objective Parity Games
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911799906926592 |
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| author | Anand, Ashwani Nayak, Satya Prakash Schmuck, Anne-Kathrin |
| author_facet | Anand, Ashwani Nayak, Satya Prakash Schmuck, Anne-Kathrin |
| contents | We present a novel method to compute $\textit{assume-guarantee contracts}$ in non-zerosum two-player games over finite graphs where each player has a different $ ω$-regular winning condition. Given a game graph $G$ and two parity winning conditions $Φ_0$ and $Φ_1$ over $G$, we compute $\textit{contracted strategy-masks}$ ($\texttt{csm}$) $(Ψ_{i},Φ_{i})$ for each Player $i$. Within a $\texttt{csm}$, $Φ_{i}$ is a $\textit{permissive strategy template}$ which collects an infinite number of winning strategies for Player $i$ under the assumption that Player $1-i$ chooses any strategy from the $\textit{permissive assumption template}$ $Ψ_{i}$. The main feature of $\texttt{csm}$'s is their power to $\textit{fully decentralize all remaining strategy choices}$ -- if the two player's $\texttt{csm}$'s are compatible, they provide a pair of new local specifications $Φ_0^\bullet$ and $Φ_1^\bullet$ such that Player $i$ can locally and fully independently choose any strategy satisfying $Φ_i^\bullet$ and the resulting strategy profile is ensured to be winning in the original two-objective game $(G,Φ_0,Φ_1)$.
In addition, the new specifications $Φ_i^\bullet$ are $\textit{maximally cooperative}$, i.e., allow for the distributed synthesis of any cooperative solution. Further, our algorithmic computation of $\texttt{csm}$'s is complete and ensured to terminate.
We illustrate how the unique features of our synthesis framework effectively address multiple challenges in the context of \enquote{correct-by-design} logical control software synthesis for cyber-physical systems and provide empirical evidence that our approach possess desirable structural and computational properties compared to state-of-the-art techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06212 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Contract-Based Distributed Synthesis in Two-Objective Parity Games Anand, Ashwani Nayak, Satya Prakash Schmuck, Anne-Kathrin Computer Science and Game Theory We present a novel method to compute $\textit{assume-guarantee contracts}$ in non-zerosum two-player games over finite graphs where each player has a different $ ω$-regular winning condition. Given a game graph $G$ and two parity winning conditions $Φ_0$ and $Φ_1$ over $G$, we compute $\textit{contracted strategy-masks}$ ($\texttt{csm}$) $(Ψ_{i},Φ_{i})$ for each Player $i$. Within a $\texttt{csm}$, $Φ_{i}$ is a $\textit{permissive strategy template}$ which collects an infinite number of winning strategies for Player $i$ under the assumption that Player $1-i$ chooses any strategy from the $\textit{permissive assumption template}$ $Ψ_{i}$. The main feature of $\texttt{csm}$'s is their power to $\textit{fully decentralize all remaining strategy choices}$ -- if the two player's $\texttt{csm}$'s are compatible, they provide a pair of new local specifications $Φ_0^\bullet$ and $Φ_1^\bullet$ such that Player $i$ can locally and fully independently choose any strategy satisfying $Φ_i^\bullet$ and the resulting strategy profile is ensured to be winning in the original two-objective game $(G,Φ_0,Φ_1)$. In addition, the new specifications $Φ_i^\bullet$ are $\textit{maximally cooperative}$, i.e., allow for the distributed synthesis of any cooperative solution. Further, our algorithmic computation of $\texttt{csm}$'s is complete and ensured to terminate. We illustrate how the unique features of our synthesis framework effectively address multiple challenges in the context of \enquote{correct-by-design} logical control software synthesis for cyber-physical systems and provide empirical evidence that our approach possess desirable structural and computational properties compared to state-of-the-art techniques. |
| title | Contract-Based Distributed Synthesis in Two-Objective Parity Games |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2307.06212 |