{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T00:18:19Z","timestamp":1777940299372,"version":"3.51.4"},"reference-count":10,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3238,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a notion of a real game (a generalisation of the Karchmer\u2010Wigderson game (cf. [3]) and of real communication complexity, and relate this complexity to the size of monotone real formulas and circuits. We give an exponential lower bound for tree\u2010like monotone protocols (defined in [4, Definition 2.2]) of small real communication complexity solving the monotone communication complexity problem associated with the bipartite perfect matching problem. This work is motivated by a research in interpolation theorems for prepositional logic (by a problem posed in [5, Section 8], in particular). Our main objective is to extend the communication complexity approach of [4, 5] to a wider class of proof systems. In this direction we obtain an effective interpolation in a form of a protocol of small real communication complexity. Together with the above mentioned lower bound for tree\u2010like protocols this yields as a corollary a lower bound on the number of steps for particular semantic derivations of Hall's theorem (these include tree\u2010like cutting planes proofs for which an exponential lower bound was demonstrated in [2]).<\/jats:p>","DOI":"10.1002\/malq.19980440403","type":"journal-article","created":{"date-parts":[[2007,5,31]],"date-time":"2007-05-31T08:19:21Z","timestamp":1180599561000},"page":"450-458","source":"Crossref","is-referenced-by-count":11,"title":["Interpolation by a Game"],"prefix":"10.1002","volume":"44","author":[{"given":"Jan","family":"Kra\u00ed\u010dek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","article-title":"An exponential lower bound for the size of monotone real circuits","author":"Cook S. A.","journal-title":"J. Comp. Syst. 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N."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19980440403","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19980440403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T00:11:11Z","timestamp":1698538271000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19980440403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1002\/malq.19980440403"],"URL":"https:\/\/doi.org\/10.1002\/malq.19980440403","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}