The size of a formula as a measure of complexity

Abstract

We introduce a refinement of the usual Ehrenfeucht-Fra\"ıssé game. The new game will help us make finer distinctions than the traditional one. In particular, it can be used to measure the size formulas needed for expressing a given property. We will give two versions of the game: the first version characterizes the size of formulas in propositional logic, and the second version works for first-order predicate logic.

25 pages