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- W2218882686 abstract "This note studies structural aspects concerning Optimal Positional Strategies (OPSs) in Mean Payoff Games (MPGs), it is a contribution to understanding the relationship between OPSs in MPGs and Small Energy-Progress Measures (SEPMs) in reweighted Energy Games (EGs). Firstly, it is observed that the space of all OPSs, $texttt{opt}_{Gamma}Sigma^M_0$, admits a unique complete decomposition in terms of so-called extremal-SEPM{s} in reweighted EG{s}; this points out what we called the Energy-Lattice $mathcal{X}^*_{Gamma}$ of Secondly, it is offered a pseudo-polynomial total-time recursive procedure for enumerating (w/o repetitions) all the elements of $mathcal{X}^*_{Gamma}$, and for computing the corresponding partitioning of $texttt{opt}_{Gamma}Sigma^M_0$. It is observed that the corresponding recursion tree defines an additional lattice $mathcal{B}^*_{Gamma}$, whose elements are certain subgames $Gamma'subseteq Gamma$ that we call basic subgames. The extremal-SEPMs of a given MPG $Gamma$ coincide with the least-SEPMs of the basic subgames of $Gamma$; so, $mathcal{X}^*_{Gamma}$ is the energy-lattice comprising all and only the least-SEPMs of the emph{basic} subgames of $Gamma$. The complexity of the proposed enumeration for both $mathcal{B}^*_{Gamma}$ and $mathcal{X}^*_{Gamma}$ is $O(|V|^3|E|W |mathcal{B}^*_{Gamma}|)$ total time and $O(|V||E|)+Thetabig(|E| mathcal{B}^*_{Gamma}|big)$ working space. Finally, it is constructed an MPG $Gamma$ for which $|mathcal{B}^*_{Gamma}| > |mathcal{X}^*_Gamma|$, this proves that $mathcal{B}^*_{Gamma}$ and $mathcal{X}^*_Gamma$ are not isomorphic." @default.
- W2218882686 created "2016-06-24" @default.
- W2218882686 creator A5037223268 @default.
- W2218882686 date "2015-08-10" @default.
- W2218882686 modified "2023-09-27" @default.
- W2218882686 title "Energy Structure of Optimal Positional Strategies in Mean Payoff Games." @default.
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