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  The Relation Between Second-Order Unification and Simultaneous Rigid E-Unification

Veanes, M. (1998). The Relation Between Second-Order Unification and Simultaneous Rigid E-Unification. In V. Pratt (Ed.), Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science (LICS-98) (pp. 264-275). Los Alamitos, USA: IEEE.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-38A1-E Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-38A2-C
Genre: Conference Paper

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 Creators:
Veanes, Margus1, Author           
Affiliations:
1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              

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 Abstract: Simultaneous rigid $E$-unification, or SREU for short, is a fundamental problem that arises in global methods of automated theorem proving in classical logic with equality. In order to do proof search in intuitionistic logic with equality one has to handle SREU as well. Furthermore, restricted forms of SREU are strongly related to word equations and finite tree automata. It was recently shown that second-order unification has a very natural reduction to simultaneous rigid $E$-unification, which constituted probably the most transparent undecidability proof of SREU. Here we show that there is also a natural encoding of SREU in second-order unification. It follows that the problems are logspace equivalent. So second-order unification plays the same fundamental role as SREU in automated reasoning in logic with equality. We exploit this connection and use finite tree automata techniques to present a very elementary undecidability proof of second-order unification, by reduction from the halting problem for Turing machines. It follows from that proof that second-order unification is undecidable for all nonmonadic second-order term languages having at least two second-order variables with sufficiently high arities.

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Language(s): eng - English
 Dates: 2010-03-121998
 Publication Status: Issued
 Pages: -
 Publishing info: Los Alamitos, USA : IEEE
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 519654
Other: Local-ID: C1256104005ECAFC-4DE191C8D886BD5FC12566730032D9ED-Veanes98
 Degree: -

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Title: Untitled Event
Place of Event: Indianapolis, Indiana
Start-/End Date: 2003-07-08 - 2003-07-12

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Title: Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science (LICS-98)
Source Genre: Proceedings
 Creator(s):
Pratt, Vaughan, Editor
Affiliations:
-
Publ. Info: Los Alamitos, USA : IEEE
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 264 - 275 Identifier: ISBN: 0-8186-8506-9/1043-6871