The fixed initial credit problem for partial-observation energy games is Ack-complete

Abstract In this paper we study two-player games with asymmetric partial observation and an energy objective. Such games are played on a weighted automaton by Eve, choosing actions, and Adam, choosing a transition labelled with the given action. Eve attempts to maintain the sum of the weights (of the transitions taken) non-negative while Adam tries to do the opposite. Eve does not know the exact state of the game, she is only given an equivalence class of states which contains it. In contrast, Adam has full observation. We show the fixed initial credit problem for these games is Ack -complete.

[1]  Szymon Torunczyk,et al.  Energy and Mean-Payoff Games with Imperfect Information , 2010, CSL.

[2]  S. S. Wainer,et al.  A classification of the ordinal recursive functions , 1970 .

[3]  Marcin Jurdzinski,et al.  Fixed-Dimensional Energy Games are in Pseudo-Polynomial Time , 2015, ICALP.

[4]  Stanley S. Wainer,et al.  Chapter III - Hierarchies of Provably Recursive Functions , 1998 .

[5]  Guillermo A. Pérez,et al.  Mean-Payoff Games with Partial-Observation - (Extended Abstract) , 2014, RP.

[6]  Sylvain Schmitz,et al.  Complexity Hierarchies beyond Elementary , 2013, TOCT.

[7]  Krzysztof R. Apt,et al.  Lectures in Game Theory for Computer Scientists , 2011 .

[8]  Thomas A. Henzinger,et al.  Resource Interfaces , 2003, EMSOFT.

[9]  Philippe Schnoebelen,et al.  Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma , 2010, 2011 IEEE 26th Annual Symposium on Logic in Computer Science.

[10]  Kim G. Larsen,et al.  Infinite Runs in Weighted Timed Automata with Energy Constraints , 2008, FORMATS.

[11]  Krishnendu Chatterjee,et al.  Generalized Mean-payoff and Energy Games , 2010, FSTTCS.

[12]  S. Wainer,et al.  Hierarchies of number-theoretic functions. I , 1970 .

[13]  Uri Zwick,et al.  The Complexity of Mean Payoff Games , 1995, COCOON.

[14]  S. Schmitz,et al.  Algorithmic Aspects of WQO Theory , 2012 .

[15]  Marcin Jurdziński,et al.  Deciding the Winner in Parity Games is in UP \cap co-Up , 1998, Inf. Process. Lett..

[16]  Patrick Totzke,et al.  Trace Inclusion for One-Counter Nets Revisited , 2014, RP.

[17]  Uri Zwick,et al.  The Complexity of Mean Payoff Games on Graphs , 1996, Theor. Comput. Sci..

[18]  Philippe Schnoebelen,et al.  Revisiting Ackermann-Hardness for Lossy Counter Machines and Reset Petri Nets , 2010, MFCS.