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Unification modulo a partial theory of exponentiation

2010
*
Electronic Proceedings in Theoretical Computer Science
*

Here, we consider

doi:10.4204/eptcs.42.2
fatcat:q6wrmmosgjgg7bsioa3vai5bxq
*a**partial*subtheory focussing only on*exponentiation*and multiplication operators. Two main results are proved. ... The first result is positive, namely, that the*unification*problem for the above*theory*(in which no additional property is assumed*of*the multiplication operators) is decidable. ... We will use*a*propagation graph P to check for these conditions. We now give*a*general*unification*algorithm for*unification**modulo*the*partial**theory**of**exponentiation*. ...##
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Unification and Narrowing in Maude 2.4
[chapter]

2009
*
Lecture Notes in Computer Science
*

*Unification*is supported in Core Maude, the core rewriting engine

*of*Maude, with commands and metalevel functions for order-sorted

*unification*

*modulo*some frequently occurring equational axioms. ... This paper introduces novel features

*of*Maude 2.4 including support for

*unification*and narrowing. ... If we give to Maude

*a*

*unification*problem in

*a*functional module fmod (Σ, E ∪ Ax) endfm, then the equations E are ignored and we get

*a*complete set

*of*order-sorted unifiers

*modulo*the

*theory*(Σ, Ax). ...

##
###
Algebraic Intruder Deductions
[chapter]

2005
*
Lecture Notes in Computer Science
*

simple algebraic

doi:10.1007/11591191_38
fatcat:mta2bkpwargsbdkylp3zeoy5si
*theories*. ... We present*a*framework for security protocol analysis that can handle algebraic properties*of*cryptographic operators in*a*uniform and modular way. ... the protocol analysis problem, along with other parameters like the number*of*sessions. ...##
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A Unification Algorithm for Analysis of Protocols with Blinded Signatures
[chapter]

2005
*
Lecture Notes in Computer Science
*

It is proved that the

doi:10.1007/978-3-540-32254-2_25
fatcat:a5tcdldv2bdohd4u3xlnexsrpq
*unification*problem over this equational*theory*can be reduced to the*unification*problem*modulo*the*theory**of*Abelian groups with commuting homomorphisms with an additional constraint ... Following [14] ,*a*related approach is proposed here in which equation solving*modulo*most*of*these properties*of*cryptographic and numbertheoretic functions is done by developing new*unification*algorithms ... Proof: Given*a*system*of*diophantine equations, we can construct*a**unification*problem*modulo*E as outlined above. 2*Unification*over Equational*Theory**of*Blinded Signatures In this section, we consider ...##
###
Building and Combining Matching Algorithms
[chapter]

2019
*
Lecture Notes in Computer Science
*

First, we survey mutation-based techniques as

doi:10.1007/978-3-030-22102-7_24
fatcat:6nx7ollvnzchrcuacrpa522f6q
*a*way to build*a*generic matching algorithm for*a*large class*of*equational*theories*. ...*A*matching problem can be seen as*a*particular conjunction*of*equations where each equation has*a*ground side. ... The decision problems for AC-matching and AC-*unification*are both NP-complete [32] even if for ACmatching the number*of*solutions is bounded by*a*single-*exponential*while*a*double-*exponential*[33] ...##
###
On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System
[chapter]

1999
*
Lecture Notes in Computer Science
*

We investigate the computational complexity

doi:10.1007/3-540-48242-3_2
fatcat:e46mov7eanemhigafonx7kaaji
*of*counting the Hilbert basis*of**a*homogeneous system*of*linear Diophantine equations. ... Moreover, we investigate the complexity*of*variants obtciined by restricting the number*of*occurrences*of*the variables in the system. ... Furthermore, #P-complete problems are encountered in the context*of*counting the number*of*minimal complete matchers*modulo*an equational*theory*, as shown in [HK95a, HK95b] . ...##
###
Unification and Matching in Hierarchical Combinations of Syntactic Theories
[chapter]

2015
*
Lecture Notes in Computer Science
*

We investigate

doi:10.1007/978-3-319-24246-0_18
fatcat:24wjjgrewrgmjjcgpss7ntteni
*a*hierarchical combination approach to the*unification*problem in non-disjoint unions*of*equational*theories*. ... We also consider the matching problem in syntactic extensions*of**a*base*theory*. ... Example: Matching in*a**Theory**of*Distributive*Exponentiation*As an example*of*the above combination method for matching algorithms we consider in this section*a**theory**of*distributive*exponentiation*, namely ...##
###
On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry

2015
*
Logical Methods in Computer Science
*

In this paper we first present

doi:10.2168/lmcs-11(2:11)2015
fatcat:tcjmrfmvnzghbbbzsgqpsnidla
*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. ... Next we present*a*new polynomial algorithm that solves the decision problem for*unification**modulo*one-sided distributivity. ... We first present*a*new polynomial time algorithm which solves the decision problem for*a*non-trivial subcase, based on*a*typed*theory*,*of**unification**modulo*one-sided distributivity. ...##
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The CL-Atse Protocol Analyser
[chapter]

2006
*
Lecture Notes in Computer Science
*

less limitations than other tools, thanks to

doi:10.1007/11805618_21
fatcat:srvr347jh5gv7onieagjvi3sxy
*a*complete modular*unification*algorithm. ... CL-Atse takes as input*a*protocol specified as*a*set*of*rewriting rules (IF format, produced by the AVISPA compiler), and uses rewriting and constraint solving techniques to model all reachable states ... Also, while the recent implementation*of*the Baader & Schulz*unification*required*a*significant amount*of*work, the extension*of*CL-Atse with new operator properties, like Cipher block chaining, is now ...##
###
Effective Symbolic Protocol Analysis via Equational Irreducibility Conditions
[chapter]

2012
*
Lecture Notes in Computer Science
*

Contextual symbolic reachability analysis also introduces

doi:10.1007/978-3-642-33167-1_5
fatcat:ptueva5cwvfj3ccvbqbwntdqbu
*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*. ... This has led us to define*a*class*of**unification*algorithms known as asymmetric*unification*algorithms*modulo**a**theory*(R, E), which produce*a*most general set*of*unifiers which leave the right hand side ...##
###
More problems in rewriting
[chapter]

1993
*
Lecture Notes in Computer Science
*

Is satisfiability

doi:10.1007/3-540-56868-9_39
fatcat:cibthhywyrgmvcsv73tryp3v2e
*of*equations in the*theory**of*distributivity (*unification**modulo**a*distributivity axiom) decidable? The question should read "*modulo*one right-and one left-distributivity axiom". ... One*of*the handful*of*exceptions (this one on AC-*unification*) is [Kapur and Narendran, 1992] . There is room for*a*lot nmre work on this side*of**theory*. ...##
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Matching with multiplication and exponentiation (extended abstract)

2005
*
Mathematical Structures in Computer Science
*

We develop

doi:10.1017/s0960129505004883
fatcat:ud5kinnk75bzvlbceyipxi3yru
*a*matching algorithm for an equational*theory*with multiplication,*exponentiation*and*a*unit element. ... An equational*theory*with multiplication and*exponentiation*Let C be*a*denumerable set*of*constants and V*a*denumerably infinite set*of*variables. ... The bulk*of*the paper is the application*of*the above approach to the development*of**a*matching algorithm in*a**theory*with multiplication,*exponentiation*and*a*unit element, denoted respectively by "×" ...##
###
Page 7111 of Mathematical Reviews Vol. , Issue 97K
[page]

1997
*
Mathematical Reviews
*

*modulo*AC.” ... Summary: “

*A*

*unification*problem under constrained substitutions,

*a*generalization

*of*the usual

*unification*problems, is

*a*useful for- malization

*of*

*a*practical problem in which there are some con- straints ...

##
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Bounded ACh Unification
[article]

2019
*
arXiv
*
pre-print

Since the

arXiv:1811.05602v2
fatcat:eajtulodjzftnloisosohkswm4
*unification**modulo*ACh*theory*is undecidable, we define*a*variant*of*the problem called bounded ACh*unification*. ... We consider the problem*of*the*unification**modulo*an equational*theory*ACh, which consists*of**a*function symbol h that is homomorphic over an associative-commutative operator +. ... Ajay Kumar Eeralla was*partially*supported by NSF Grant CNS 1314338. ...##
###
Deciding Unifiability and Computing Local Unifiers in the Description Logic $\mathcal{E\!L}$ without Top Constructor

2016
*
Notre Dame Journal of Formal Logic
*

On the other hand,

doi:10.1215/00294527-3555507
fatcat:furoxuvajnhbtdgqhqbeakoo24
*unification*in EL has been shown to be NP-complete, and thus*of*considerably lower complexity than*unification*in other description logics*of*similarly restricted expressive power. ...*Unification*in Description Logics has been proposed as*a*novel inference service that can, for example, be used to detect redundancies in ontologies. ... One possibility could be to use*a*SAT*modulo**theories*(SMT) approach [23] . ...
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