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Streaming Complexity of Checking Priority Queues Francois, Nathanael Magniez, Frédéric Streaming Algorithms Communication Complexity Priority Queue This work is in the line of designing efficient checkers for testing the reliability of some massive data structures. Given a sequential access to the insert/extract operations on such a structure, one would like to decide, a posteriori only, if it corresponds to the evolution of a reliable structure. In a context of massive data, one would like to minimize both the amount of reliable memory of the checker and the number of passes on the sequence of operations. Chu, Kannan and McGregor (M. Chu, S. Kannan, and A. McGregor, 2007) initiated the study of checking priority queues in this setting. They showed that the use of timestamps allows to check a priority queue with a single pass and memory space \tilde{\Order}(\sqrt{N}). Later, Chakrabarti, Cormode, Kondapally and McGregor (A. Chakrabarti, G. Cormode, R. Kondapally, and A. McGregor, 2010) removed the use of timestamps, and proved that more passes do not help. We show that, even in the presence of timestamps, more passes do not help, solving an open problem of (M. Chu, S. Kannan, and A. McGregor, 2007; A. Chakrabarti, G. Cormode, R. Kondapally, and A. McGregor). On the other hand, we show that a second pass, but in reverse direction shrinks the memory space to \tilde{\Order}((\log N)^2), extending a phenomenon the first time observed by Magniez, Mathieu and Nayak (F. Magniez, C. Mathieu, and A. Nayak, 2010) for checking well-parenthesized expressions. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nathanael Francois and Frédéric Magniez 2013 Is Part Of LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2013.454 urn:nbn:de:0030-drops-39561 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.454 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode