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The undecidability of the first-order theories of one step rewriting in linear canonical systems

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Vorobyov,  Sergei
Programming Logics, MPI for Informatics, Max Planck Society;

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MPI-I-98-2-009.pdf
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Vorobyov, S.(1998). The undecidability of the first-order theories of one step rewriting in linear canonical systems (MPI-I-1998-2-009). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-7A84-E
Abstract
By reduction from the halting problem for Minsky's two-register machines we prove that there is no algorithm capable of deciding the EAAA-theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixed such system with undecidable EA...A-theory of one step rewriting (strong undecidability). This improves over all previously known results of the same kind.