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Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/6658
Title: Definability with Bounded Number of Bound Variables
Authors: Immerman, Neil
Kozen, Dexter
Keywords: computer science
technical report
Issue Date: Mar-1987
Publisher: Cornell University
Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR87-818
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.
URI: http://hdl.handle.net/1813/6658
Appears in Collections:Computer Science Technical Reports

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