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Hilbert's tenth problem is of unification type zero

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Abstract

We show that the problem of finding integer solutions to a polynomial equation over the integers has unification type zero, i.e. there exist polynomial equations which have unifiers, but which have no minimal and complete set of unifiers: In particular, it is shown that the equation uv=w+z has no minimal and complete set of solutions.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 90024-1555, Los Angeles, CA, U.S.A.

    Mark Franzen

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  1. Mark Franzen
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Franzen, M. Hilbert's tenth problem is of unification type zero. J Autom Reasoning 9, 169–178 (1992). https://doi.org/10.1007/BF00245459

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  • DOI: https://doi.org/10.1007/BF00245459

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