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Unification modulo a partial theory of exponentiation

Deepak Kapur, Andrew Marshall, Paliath Narendran
2010 Electronic Proceedings in Theoretical Computer Science  
Here, we consider 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.  ... 
doi:10.4204/eptcs.42.2 fatcat:q6wrmmosgjgg7bsioa3vai5bxq

Unification and Narrowing in Maude 2.4 [chapter]

Manuel Clavel, Francisco Durán, Steven Eker, Santiago Escobar, Patrick Lincoln, Narciso Martí-Oliet, José Meseguer, Carolyn Talcott
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).  ... 
doi:10.1007/978-3-642-02348-4_27 fatcat:adxberqkxrhnviqr4ce2aflcfy

Algebraic Intruder Deductions [chapter]

David Basin, Sebastian Mödersheim, Luca Viganò
2005 Lecture Notes in Computer Science  
simple algebraic 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.  ... 
doi:10.1007/11591191_38 fatcat:mta2bkpwargsbdkylp3zeoy5si

A Unification Algorithm for Analysis of Protocols with Blinded Signatures [chapter]

Deepak Kapur, Paliath Narendran, Lida Wang
2005 Lecture Notes in Computer Science  
It is proved that the 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  ... 
doi:10.1007/978-3-540-32254-2_25 fatcat:a5tcdldv2bdohd4u3xlnexsrpq

Building and Combining Matching Algorithms [chapter]

Christophe Ringeissen
2019 Lecture Notes in Computer Science  
First, we survey mutation-based techniques as 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]  ... 
doi:10.1007/978-3-030-22102-7_24 fatcat:6nx7ollvnzchrcuacrpa522f6q

On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System [chapter]

Miki Hermann, Laurent Juban, Phokion G. Kolaitis
1999 Lecture Notes in Computer Science  
We investigate the computational complexity 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] .  ... 
doi:10.1007/3-540-48242-3_2 fatcat:e46mov7eanemhigafonx7kaaji

Unification and Matching in Hierarchical Combinations of Syntactic Theories [chapter]

Serdar Erbatur, Deepak Kapur, Andrew M. Marshall, Paliath Narendran, Christophe Ringeissen
2015 Lecture Notes in Computer Science  
We investigate 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  ... 
doi:10.1007/978-3-319-24246-0_18 fatcat:24wjjgrewrgmjjcgpss7ntteni

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

Andrew Marshall, Catherine Meadows, Paliath Narendran, Franz Baader
2015 Logical Methods in Computer Science  
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.  ...  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.  ... 
doi:10.2168/lmcs-11(2:11)2015 fatcat:tcjmrfmvnzghbbbzsgqpsnidla

The CL-Atse Protocol Analyser [chapter]

Mathieu Turuani
2006 Lecture Notes in Computer Science  
less limitations than other tools, thanks to 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  ... 
doi:10.1007/11805618_21 fatcat:srvr347jh5gv7onieagjvi3sxy

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
2012 Lecture Notes in Computer Science  
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.  ...  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  ... 
doi:10.1007/978-3-642-33167-1_5 fatcat:ptueva5cwvfj3ccvbqbwntdqbu

More problems in rewriting [chapter]

Nachum Dershowitz, Jean-Pierre Jouannaud, Jan Willem Klop
1993 Lecture Notes in Computer Science  
Is satisfiability 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.  ... 
doi:10.1007/3-540-56868-9_39 fatcat:cibthhywyrgmvcsv73tryp3v2e

Matching with multiplication and exponentiation (extended abstract)

BERNARD LANG
2005 Mathematical Structures in Computer Science  
We develop 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 "×"  ... 
doi:10.1017/s0960129505004883 fatcat:ud5kinnk75bzvlbceyipxi3yru

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  ... 

Bounded ACh Unification [article]

Ajay Kumar Eeralla, Christopher Lynch
2019 arXiv   pre-print
Since the 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.  ... 
arXiv:1811.05602v2 fatcat:eajtulodjzftnloisosohkswm4

Deciding Unifiability and Computing Local Unifiers in the Description Logic $\mathcal{E\!L}$ without Top Constructor

Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, Barbara Morawska
2016 Notre Dame Journal of Formal Logic  
On the other hand, 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] .  ... 
doi:10.1215/00294527-3555507 fatcat:furoxuvajnhbtdgqhqbeakoo24
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