dc.contributor.author Immerman, Neil en_US dc.contributor.author Kozen, Dexter en_US dc.date.accessioned 2007-04-23T17:18:39Z dc.date.available 2007-04-23T17:18:39Z dc.date.issued 1987-03 en_US dc.identifier.citation http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR87-818 en_US dc.identifier.uri https://hdl.handle.net/1813/6658 dc.description.abstract A theory satisfies the $k$-variable-property if every first-order formula is equivalent to a formula with at most $k$ bound variables (possibly reused). Gabbay has shown that a fixed time structure satisfies the $k$-variable property for some $k$ if and only if there exists a finite basis for the temporal connectives over that structure. We give a model-theoretic method for establishing the $k$-variable property, involving a restricted Ehrenfeucht-Fraisse game in which each player has only $k$ pebbles. We use the method to unify and simplify results in the literature for linear orders. We also establish new $k$-variable properties for various theories of bounded-degree trees, and in each case obtain tight upper and lower bounds on $k$. This gives the first finite basis theorems for branching-time models. en_US dc.format.extent 1566781 bytes dc.format.extent 279802 bytes dc.format.mimetype application/pdf dc.format.mimetype application/postscript dc.language.iso en_US en_US dc.publisher Cornell University en_US dc.subject computer science en_US dc.subject technical report en_US dc.title Definability with Bounded Number of Bound Variables en_US dc.type technical report en_US
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