We study two-player zero-sum games over infinite-state graphs equipped with omega-B and finitary conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state graphs, memoryless strategies are sufficient for finitary Büchi, and finite-memory suffices for finitary parity games. We then study pushdown games with boundedness conditions, with two contributions. First we prove a collapse result for pushdown games with omega-B-conditions, implying the decidability of solving these games. Second we consider pushdown games with finitary parity along with stack boundedness conditions, and show that solving these games is EXPTIME-complete.
@InProceedings{chatterjee_et_al:LIPIcs.CSL.2013.181, author = {Chatterjee, Krishnendu and Fijalkow, Nathana\"{e}l}, title = {{Infinite-state games with finitary conditions}}, booktitle = {Computer Science Logic 2013 (CSL 2013)}, pages = {181--196}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-60-6}, ISSN = {1868-8969}, year = {2013}, volume = {23}, editor = {Ronchi Della Rocca, Simona}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.181}, URN = {urn:nbn:de:0030-drops-41970}, doi = {10.4230/LIPIcs.CSL.2013.181}, annote = {Keywords: Two-player games, Infinite-state systems, Pushdown games, Bounds in omega-regularity, Synthesis} }
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