The Undecidability of the First-Order Theories of One Step Rewriting in Linear Canonical Systems

The Undecidability of the First-Order Theories of One Step Rewriting in Linear Canonical Systems

By reduction from the halting problem for Minsky's two-register machines we prove that there is no algorithm capable of deciding the ∃∀∀∀-theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixe...

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Veröffentlicht in:Information and computation 2002-06, Vol.175 (2), p.182-213
1. Verfasser: Vorobyov, Sergei
Format: Artikel
Sprache:eng
Schlagworte:
Applied sciences
Computer science
control theory
systems
Exact sciences and technology
Programming theory
Theoretical computing
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Zusammenfassung:By reduction from the halting problem for Minsky's two-register machines we prove that there is no algorithm capable of deciding the ∃∀∀∀-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 ∃∀*-theory of one step rewriting (strong undecidability). This improves over all previously known results of the same kind.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.2002.3151