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On Asymmetric Unification and the Combination Problem in Disjoint Theories [chapter]

Serdar Erbatur, Deepak Kapur, Andrew M. Marshall, Catherine Meadows, Paliath Narendran, Christophe Ringeissen
<span title="">2014</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Introduction We examine the disjoint combination problem in the newly developed paradigm of asymmetric unification.  ...  One important question is the problem of asymmetric unification in a combination of theories, in particular how to produce an algorithm for the combined theory by combining algorithms for the separate  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-54830-7_18">doi:10.1007/978-3-642-54830-7_18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l23piq2shbb6lcevfd53wxjuka">fatcat:l23piq2shbb6lcevfd53wxjuka</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190228123340/http://pdfs.semanticscholar.org/a2ac/0cb0dff71ec2270afa8374939e959268183c.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a2/ac/a2ac0cb0dff71ec2270afa8374939e959268183c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-54830-7_18"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Asymmetric Unification: A New Unification Paradigm for Cryptographic Protocol Analysis [chapter]

Serdar Erbatur, Santiago Escobar, Deepak Kapur, Zhiqiang Liu, Christopher A. Lynch, Catherine Meadows, José Meseguer, Paliath Narendran, Sonia Santiago, Ralf Sasse
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We also give results on the complexity and decidability of asymmetric unification.  ...  This paradigm relies on: (i) a decomposition of an equational theory into (R, E) where R is confluent, terminating, and coherent modulo E, and (ii) on reducing unification problems to a set of problems  ...  First, it is theory-generic and can be applied to many of the theories and combinations of theories that arise in cryptographic protocol analysis.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-38574-2_16">doi:10.1007/978-3-642-38574-2_16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yom3pf444rbntievnplrn4zo6i">fatcat:yom3pf444rbntievnplrn4zo6i</a> </span>
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Combining matching algorithms: The regular case

Tobias Nipkow
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
As part of that development we present a simple algorithm for solving the word problem in the combination of arbitrary equational theories with disjoint signatures.  ...  The problem of combining matching algorithms for equational theories with disjoint signatures is studied.  ...  In unification theory this is known as the combination problem: how do unification algorithms for disjoint equational theories compose to yield a unification algorithm for the combined theory?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0747-7171(08)80145-9">doi:10.1016/s0747-7171(08)80145-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/drwqjovw3jcbbd4cbtcztmnzl4">fatcat:drwqjovw3jcbbd4cbtcztmnzl4</a> </span>
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Theory Combination: Beyond Equality Sharing [chapter]

Maria Paola Bonacina, Pascal Fontaine, Christophe Ringeissen, Cesare Tinelli
<span title="">2019</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
If the formula mixes theories, the considered theory is their union, and combination of theories is the problem of combining decision procedures for the individual theories to get one for their union.  ...  This paper surveys selected approaches to the problem of reasoning in the union of disjoint theories, that aim at going beyond equality sharing, including: asymmetric extensions of equality sharing, where  ...  Acknowledgments The authors thank the co-authors of their papers covered in this survey.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-22102-7_3">doi:10.1007/978-3-030-22102-7_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ukphko527rcpthhau3ydqyw6gy">fatcat:ukphko527rcpthhau3ydqyw6gy</a> </span>
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Protocol indepedence through disjoint encryption under Exclusive-OR [article]

Sreekanth Malladi
<span title="2010-05-09">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we prove that a similar suggestion prevents these attacks under commonly used operators such as Exclusive-OR, that induce equational theories, breaking the free algebra assumption.  ...  Multi-protocol attacks due to protocol interaction has been a notorious problem for security.  ...  I am thankful to Yannick Chevalier for explaining his protocol model in [11] , Pascal Lafourcade for many useful remarks and the anonymous reviewers for their helpful suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1003.5384v2">arXiv:1003.5384v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e3s2judz4jd7tkzk7ys46pbms4">fatcat:e3s2judz4jd7tkzk7ys46pbms4</a> </span>
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How to prevent type-flaw and multi-protocol attacks on cryptographic protocols under Exclusive-OR [article]

Sreekanth Malladi
<span title="2010-06-19">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Type-flaw attacks and multi-protocol attacks on security protocols have been frequently reported in the literature.  ...  This is the problem we consider in this paper: We prove that, under certain assumptions, tagging encrypted components still prevents type-flaw and multi-protocol attacks even in the presence of the XOR  ...  I benefited greatly from the following people's help and guidance: Jon Millen (MITRE, USA) clarified numerous concepts about constraint solving and some crucial aspects of XOR unification.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1004.2522v3">arXiv:1004.2522v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/55m6moaycvb7fcwmtrvmrkrtha">fatcat:55m6moaycvb7fcwmtrvmrkrtha</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1004.2522/1004.2522.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fd/a8/fda8cbc65255c35b1829ca73d54f1b54ae70537e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1004.2522v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Algebraic Intruder Deductions [chapter]

David Basin, Sebastian Mödersheim, Luca Viganò
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
the complexity of the equational unification problems that arise during protocol analysis by bounding the depth of message terms and the operations that the intruder can perform when analyzing messages  ...  Our framework is based on two ideas: the use of modular rewriting to formalize a generalized equational deduction problem for the Dolev-Yao intruder, and the introduction of two parameters that control  ...  The equational reasoning problems that we considered in this paper are in general undecidable and hence one must introduce restrictions to regain decidability.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11591191_38">doi:10.1007/11591191_38</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mta2bkpwargsbdkylp3zeoy5si">fatcat:mta2bkpwargsbdkylp3zeoy5si</a> </span>
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Page 3473 of Mathematical Reviews Vol. , Issue 94f [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Schulz, Unification in the union of disjoint equa- tional theories: combining decision procedures (50-65); Tobias Nipkow and Zhenyu Qian, Reduction and unification in lambda calculi with subtypes (66--  ...  Leonidas Fegaras, Tim Sheard and David Stemple, Uniform traversal combinators: definition, use and properties (148-162); Tomas E. Uribe, Sorted unification using set constraints (163- 177); Alan M.  ... 
<span class="external-identifiers"> </span>
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Effective Symbolic Protocol Analysis via Equational Irreducibility Conditions [chapter]

Serdar Erbatur, Santiago Escobar, Deepak Kapur, Zhiqiang Liu, Christopher Lynch, Catherine Meadows, José Meseguer, Paliath Narendran, Sonia Santiago, Ralf Sasse
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Contextual symbolic reachability analysis also introduces a new type of unification mechanism, which we call asymmetric unification, in which any solution must leave the right side of the solution irreducible  ...  terms generated during a state exploration are in normal form with respect to the equational theory.  ...  We are working on techniques for converting standard equational unification algorithms into asymmetric algorithms, and have produced an asymmetric version of the exclusive-or algorithm in [24] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-33167-1_5">doi:10.1007/978-3-642-33167-1_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ptueva5cwvfj3ccvbqbwntdqbu">fatcat:ptueva5cwvfj3ccvbqbwntdqbu</a> </span>
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Hierarchical Combination of Intruder Theories [chapter]

Yannick Chevalier, Michaël Rusinowitch
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This has motivated us to introduce a new notion of hierarchical combination for non-disjoint intruder theories and to show decidability results for the deduction problem in these theories.  ...  This result applies to an exponentiation theory that appears to be more general than the one considered before.  ...  Related works In [10] we have extended the combination algorithm for solving E-unification problems of [34, 3] to solve intruder constraints on disjoint signatures.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11805618_9">doi:10.1007/11805618_9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rh6pmjwcmrf3jbdebfic6qikcm">fatcat:rh6pmjwcmrf3jbdebfic6qikcm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170929134140/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/7ba/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDg5MDU0MDEwNzAwMTI1Mw%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a2/57/a25750eba3c77debb52e5660537f327ec6314a24.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11805618_9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Hierarchical combination of intruder theories

Yannick Chevalier, Michael Rusinowitch
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
This has motivated us to introduce a new notion of hierarchical combination for non-disjoint intruder theories and to show decidability results for the deduction problem in these theories.  ...  This result applies to an exponentiation theory that appears to be more general than the one considered before.  ...  Related works In [10] we have extended the combination algorithm for solving E-unification problems of [34, 3] to solve intruder constraints on disjoint signatures.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2007.07.004">doi:10.1016/j.ic.2007.07.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/irlw623ui5ev3hfy2l6qijhok4">fatcat:irlw623ui5ev3hfy2l6qijhok4</a> </span>
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Theories of Homomorphic Encryption, Unification, and the Finite Variant Property

Fan Yang, Santiago Escobar, Catherine Meadows, José Meseguer, Paliath Narendran
<span title="">2014</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mht6wa2vdbg7dn6n6lws4hpzti" style="color: black;">Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming - PPDP &#39;14</a> </i> &nbsp;
However, this application requires unification algorithms that can be easily implemented and easily extended to combinations of different theories of interest.  ...  Most theories that arise in cryptographic protocols have decompositions suitable for variant unification, but there is one major exception: the theory that describes encryption that is homomorphic over  ...  This can be mitigated by the use of asymmetric unification [16] , in which only the variants of the right-hand side of a unification problems are computed, and irreducibility constraints are also enforced  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2643135.2643154">doi:10.1145/2643135.2643154</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ppdp/YangEMMN14.html">dblp:conf/ppdp/YangEMMN14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ss5awwz6wffnnlp6i67rg5svcu">fatcat:ss5awwz6wffnnlp6i67rg5svcu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829112612/http://publish.illinois.edu/science-of-security-lablet/files/2014/06/Theories-of-Homomorphic-Encryption-Unification-and-the-Finite-Variant-Property.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1e/13/1e13976be29f40532db936c37892cea90e3e78ae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2643135.2643154"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry

Andrew Marshall, Catherine Meadows, Paliath Narendran, Franz Baader
<span title="2015-06-19">2015</span> <i title="Logical Methods in Computer Science e.V."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c67srop7pbe3nciquoxzy3d6pm" style="color: black;">Logical Methods in Computer Science</a> </i> &nbsp;
A construction, employing string compression, is used to achieve the polynomial bound. Lastly, we examine the one-sided distributivity problem in the new asymmetric unification paradigm.  ...  In this paper we first present a new polynomial time algorithm that solves the decision problem for a non-trivial subcase, based on a typed theory, of unification modulo one-sided distributivity.  ...  Here we present the first asymmetric unification algorithm for the theory of one-sided distributivity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2168/lmcs-11(2:11)2015">doi:10.2168/lmcs-11(2:11)2015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tcjmrfmvnzghbbbzsgqpsnidla">fatcat:tcjmrfmvnzghbbbzsgqpsnidla</a> </span>
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Decidability and Undecidability Results for Nelson-Oppen and Rewrite-Based Decision Procedures [chapter]

Maria Paola Bonacina, Silvio Ghilardi, Enrica Nicolini, Silvio Ranise, Daniele Zucchelli
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In the context of combinations of theories with disjoint signatures, we classify the component theories according to the decidability of constraint satisfiability problems in arbitrary and in infinite  ...  We show that this result covers decision procedures based on rewriting, complementing recent work on combination of theories in the rewrite-based approach to satisfiability.  ...  In this paper, we consider combinations of theories whose signatures are disjoint and classify the component theories according to the decidability of their satisfiability problems in arbitrary and in  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11814771_42">doi:10.1007/11814771_42</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g2lx25knv5hlheu24q5xo63ely">fatcat:g2lx25knv5hlheu24q5xo63ely</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808212520/http://profs.sci.univr.it/~bonacina/papers/IJCAR2006rewsat+csp.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/97/8f/978ffd39b7ab3113f4ce6ab189cb122d11e2b21e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11814771_42"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Towards Correctness of Program Transformations Through Unification and Critical Pair Computation

Conrad Rau, Manfred Schmidt-Schauß
<span title="2010-12-21">2010</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
The unification algorithm employs many-sorted terms, the equational theory of left-commutativity modelling multi-sets, context variables of different kinds and a mechanism for compactly representing binding  ...  A successful approach to proving correctness is the combination of a context lemma with the computation of overlaps between program transformations and the reduction rules, and then of so-called complete  ...  The combined equational theory is defined on the set of terms T (S, Σ, V), using the same set of axioms. Note that the combination is disjoint on the function symbols, but not on the sort-structure.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.42.4">doi:10.4204/eptcs.42.4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2ztp2ndb2nhc3fnvbzznx5vhym">fatcat:2ztp2ndb2nhc3fnvbzznx5vhym</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171113053202/https://core.ac.uk/download/pdf/14507882.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6c/c8/6cc86c4d09b4a8860aebc51e09784abf390a670d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.42.4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>
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