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The size of a formula as a measure of complexity

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.

preprint2012arXivOpen access
Lauri HellaJouko Väänänen
Logic in Computer Sciencemath.LO
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Lauri HellaJouko Väänänen

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