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Author, Editor(s)

Author(s):

Levy, Jordi
Veanes, Margus

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BibTeX cite key*:

LevyVeanes99

Title

Title*:

On the Undecidability of Second-Order Unification

Journal

Journal Title*:

Information and Computation

Journal's URL:

http://www.academicpress.com/i&c

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Language:

English

Publisher

Publisher's
Name:

Academic Press

Publisher's URL:

http://www.apnet.com/

Publisher's
Address:

London, UK

ISSN:

0890-5401

Vol, No, pp, Date

Volume*:

159

Number:


Publishing Date:

2000

Pages*:

125-150

Number of
VG Pages:


Page Start:


Page End:


Sequence Number:


DOI:


Note, Abstract, ©

Note:


(LaTeX) Abstract:

There is a close relationship between word unification and second-order unification. This similarity has been exploited, for instance, for proving decidability of monadic second-order unification, and decidability of linear second-order unification when no second-order variable occurs more than twice. The attempt to prove the second result for (non-linear) second-order unification failed, and lead instead to a natural reduction from simultaneous rigid E-unification to this problem. This reduction is the first main result of this paper, and it is the starting point for proving some novel results about the undecidability of second-order unification presented in the rest of the paper.

We prove that second-order unification is \emph{undecidable} in the following three cases: 1) each second-order variable occurs at most twice and there are only two second-order variables; 2) there is only one second-order variable and it is unary; 3) the conditions (i--iv) hold for some fixed integer $n$: (i) the arguments of all second-order variables are ground terms of size less than $n$, (ii) the arity of all second-order variables is less than $n$, (iii) the number of occurrences of second-order variables is at most 5, (iv) there is either a single second-order variable, or there are two second-order variables and no first-order variables.

URL for the Abstract:


Categories,
Keywords:

Second-Order Unification

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Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Programming Logics Group

Audience:

experts only

Appearance:

MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat


BibTeX Entry:

@ARTICLE{LevyVeanes99,
AUTHOR = {Levy, Jordi and Veanes, Margus},
TITLE = {On the Undecidability of Second-Order Unification},
JOURNAL = {Information and Computation},
PUBLISHER = {Academic Press},
YEAR = {2000},
VOLUME = {159},
PAGES = {125--150},
ADDRESS = {London, UK},
ISBN = {0890-5401},
}


Entry last modified by Christine Kiesel, 03/12/2010
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Editor(s)
Margus Veanes
Created
04/22/1999 08:39:40 PM
Revisions
10.
9.
8.
7.
6.
Editor(s)
Christine Kiesel
Uwe Brahm
Uwe Brahm
Uwe Brahm
Uwe Brahm
Edit Dates
04.09.2001 11:19:29
04/04/2001 06:29:31 PM
04/04/2001 06:28:48 PM
04/04/2001 05:32:10 PM
14.03.2001 13:42:45