Looking at Mean-Payoff through Foggy Windows

Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in NP-intersect-coNP. MPGs are suitable quantitative models for open reactive systems. However, in this context the assumption of perfect information is not always realistic. For the partial-observation case, the problem that asks if the first player has an observation-based winning strategy that enforces a given threshold on the mean-payoff, is undecidable. In this paper, we study the window mean-payoff objectives that were introduced recently as an alternative to the classical mean-payoff objectives. We show that, in sharp contrast to the classical mean-payoff objectives, some of the window mean-payoff objectives are decidable in games with partial-observation

On the Complexity of Heterogeneous Multidimensional Games

We study two-player zero-sum turn-based games played on multidimensional weighted graphs with heterogeneous quantitative objectives. Our objectives are defined starting from the measures Inf, Sup, LimInf, and LimSup of the weights seen along the play, as well as on the window mean-payoff (WMP) measure recently introduced in [Krishnendu,Doyen,Randour,Raskin, Inf. Comput., 2015]. Whereas multidimensional games with Boolean combinations of classical mean-payoff objectives are undecidable [Velner, FOSSACS, 2015], we show that CNF/DNF Boolean combinations for heterogeneous measures taken among {WMP, Inf, Sup, LimInf, LimSup} lead to EXPTIME-completeness with exponential memory strategies for both players. We also identify several interesting fragments with better complexities and memory requirements, and show that some of them are solvable in PTIME

Bard Observer, Vol. 1, No. 1 (February, 2007)

https://digitalcommons.bard.edu/observer/1554/thumbnail.jp

Bard Observer, Vol. 1, No. 1 (February 28, 2007)

https://digitalcommons.bard.edu/observer/1487/thumbnail.jp

Perceptions, 1987

49 pages. Editors: Jennifer Cogelia and Gene Moody. Art Editors: Jeff Dulaney and Brenda Lehett. Staff: Terry Hulsey, Sammy Lott, and Terri Osborne. Faculty Advisors: Sally Russell, creative writing; Robert F. Westervelt, art. Cover: Jeff Dulaney. Contributors-Poetry: Stacey Alexander, Doug Amis, Jennifer Cogilia, Sandra Farrer, Thelma Hall, Jessica Jackson, Robbie Lathem, Hoyt LeCroy, Brenda Lehett, Sammy Lott, Betty Maine, Gene Moody, Terri Osborne, Kenna Redding, Ricky Shaw, Robby Spriggs, Angle Sullivan, Barbara T., and Melissa Tweedell. Contributors-Prose: Doug Amis, Jennifer Cogelia, Ruby Davis, Rick Duncan, Lee McClure, Gene Moody, Marie Owens, Keena Redding, Bart Smith, Angle Sullivan, and Melissa Tweedell. Contributors-Art: Ernest Boetz, Jim Breakell, karen Corn, Doris deSha, Sabrina Dills, Jeff Dulaney, Anne Geddings, Angela Hemphill, Harriet Jackson, Jay Langford, Brenda Lehett, Susan Pardue, and Andy Parton.https://digitalcommons.northgeorgia.edu/perceptions/1005/thumbnail.jp