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Computing knowledge in equational extensions of subterm convergent theories

Published online by Cambridge University Press:  02 March 2020

Serdar Erbatur Open the ORCID record for Serdar Erbatur [Opens in a new window] ,
Andrew M. Marshall Open the ORCID record for Andrew M. Marshall [Opens in a new window]  and
Christophe Ringeissen Open the ORCID record for Christophe Ringeissen [Opens in a new window]
Serdar Erbatur
Affiliation:
University of Texas at Dallas, Richardson, TX, USA
Andrew M. Marshall
Affiliation:
University of Mary Washington, Fredericksburg, VA, USA
Christophe Ringeissen*
Affiliation:
Université de Lorraine, CNRS, Inria, LORIA, F-54000Nancy, France
*
*Corresponding author. Email: [email protected]
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Abstract

We study decision procedures for two knowledge problems critical to the verification of security protocols, namely the intruder deduction and the static equivalence problems. These problems can be related to particular forms of context matching and context unification. Both problems are defined with respect to an equational theory and are known to be decidable when the equational theory is given by a subterm convergent term rewrite system (TRS). In this work, we extend this to consider a subterm convergent TRS defined modulo an equational theory, like Commutativity. We present two pairs of solutions for these important problems. The first solves the deduction and static equivalence problems in rewrite systems modulo shallow theories such as Commutativity. The second provides a general procedure that solves the deduction and static equivalence problems in subterm convergent systems modulo syntactic permutative theories, provided a finite measure is ensured. Several examples of such theories are also given.

Keywords

Equational theoriesdecision proceduressecurity protocolsdeductionstatic equivalence
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Special Issue 6: Special Issue: Unification , June 2020 , pp. 683 - 709
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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