Strategies in repeated games can be classified as to whether or not they use memory and/or randomization. We consider Markov decision processes and 2-player graph games, both of the deterministic and probabilistic varieties. We characterize when memory and/or randomization are required for winning with respect to various classes of w-regular objectives, noting particularly when the use of memory can be traded for the use of randomization. In particular, we show that Markov decision processes allow randomized memoryless optimal strategies for all M?ller objectives. Furthermore, we show that 2-player probabilistic graph games allow randomized memoryless strategies for winning with probability 1 those M?ller objectives which are upward-closed. Upward-closure means that if a set α of infinitely repeating vertices is winning, then all supersets of α are also winning.
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QEST: Quantitative Evaluation of Systems
Chatterjee K, De Alfaro L, Henzinger TA. Trading memory for randomness. In: IEEE; 2004:206-217. doi:10.1109/QEST.2004.10051
Chatterjee, K., De Alfaro, L., & Henzinger, T. A. (2004). Trading memory for randomness (pp. 206–217). Presented at the QEST: Quantitative Evaluation of Systems, IEEE. https://doi.org/10.1109/QEST.2004.10051
Chatterjee, Krishnendu, Luca De Alfaro, and Thomas A Henzinger. “Trading Memory for Randomness,” 206–17. IEEE, 2004. https://doi.org/10.1109/QEST.2004.10051.
K. Chatterjee, L. De Alfaro, and T. A. Henzinger, “Trading memory for randomness,” presented at the QEST: Quantitative Evaluation of Systems, 2004, pp. 206–217.
Chatterjee K, De Alfaro L, Henzinger TA. 2004. Trading memory for randomness. QEST: Quantitative Evaluation of Systems, 206–217.
Chatterjee, Krishnendu, et al. Trading Memory for Randomness. IEEE, 2004, pp. 206–17, doi:10.1109/QEST.2004.10051.