# The 3 Frenchmen method proves undecidability of the uniform boundedness for single recursive rule ternary DATALOG Programs

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## Abstract

*DATALOG is the language of logic programs without function symbols. It is considered to be the paradigmatic database query language. If it is possible to eliminate the recursion from the program then it is* uniformly bounded. *We show that the uniform boundedness is undecidable for ternary DATALOG programs containing only one recursive rule, and for linear programs of arity 3. The proof is based on the discovery of, how we call it*, Achilles-Turtle machine. *It computes the subsequent iterations of a Conway function and is, up to our knowledge, the simplest known universal machine*.

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