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arXiv · 1406.0349

Undecidability of satisfiability in the algebra of finite binary relations with union, composition, and difference

Tony Tan·Jan Van den Bussche·Xiaowang Zhang
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Abstract

We consider expressions built up from binary relation names using the operators union, composition, and set difference. We show that it is undecidable to test whether a given such expression $e$ is finitely satisfiable, i.e., whether there exist finite binary relations that can be substituted for the relation names so that $e$ evaluates to a nonempty result. This result already holds in restriction to expressions that mention just a single relation name, and where the difference operator can be nested at most once.

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Tony Tan, Jan Van den Bussche, Xiaowang Zhang. 2014-06-02. Undecidability of satisfiability in the algebra of finite binary relations with union, composition, and difference. https://arxiv.org/abs/1406.0349

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