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Bounded ACh unification

Published online by Cambridge University Press:  16 September 2020

Ajay Kumar Eeralla Open the ORCID record for Ajay Kumar Eeralla [Opens in a new window]  and
Christopher Lynch
Ajay Kumar Eeralla*
Affiliation:
Galois Inc, Portland, Oregon, 97204
Christopher Lynch
Affiliation:
Department of Computer Science, Clarkson University, Potsdam, NY13699, USA
*
*Corresponding author. Email: [email protected]
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Abstract

We consider the problem of the unification modulo an equational theory associativity and commutativity (ACh), which consists of a function symbol h that is homomorphic over an associative–commutative operator +. Since the unification modulo ACh theory is undecidable, we define a variant of the problem called bounded ACh unification. In this bounded version of ACh unification, we essentially bound the number of times h can be applied to a term recursively and only allow solutions that satisfy this bound. There is no bound on the number of occurrences of h in a term, and the + symbol can be applied an unlimited number of times. We give inference rules for solving the bounded version of the problem and prove that the rules are sound, complete, and terminating. We have implemented the algorithm in Maude and give experimental results. We argue that this algorithm is useful in cryptographic protocol analysis.

Keywords

Equational unificationcryptographic protocol analysisrewritinghomomorphismcommutativityMaude
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Special Issue 6: Special Issue: Unification , June 2020 , pp. 664 - 682
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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