Star-Free Picture Expressions are Strictly Weaker Than First-Order Logic
نویسنده
چکیده
We exhibit a rst-order deenable picture language which we prove is not expressible by any star-free picture expression, i. e., it is not star-free. Thus rst-order logic over pictures is strictly more powerful than star-free picture expressions are. This is in sharp contrast with the situation with words: the well-known McNaughton-Papert theorem states that a word language is expressible by a rst-order formula if and only if it is expressible by a star-free (word) expression. The main ingredients of the non-expressibility result are a Fra ss e-style algebraic characterization of star freeness for picture languages and com-binatorics on words.
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