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Unification modulo a partial theory of exponentiation
2010
Electronic Proceedings in Theoretical Computer Science
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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]
2009
Lecture Notes in Computer Science
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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]
2005
Lecture Notes in Computer Science
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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]
2005
Lecture Notes in Computer Science
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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]
2019
Lecture Notes in Computer Science
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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]
1999
Lecture Notes in Computer Science
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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]
2015
Lecture Notes in Computer Science
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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
2015
Logical Methods in Computer Science
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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]
2006
Lecture Notes in Computer Science
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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]
2012
Lecture Notes in Computer Science
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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]
1993
Lecture Notes in Computer Science
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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)
2005
Mathematical Structures in Computer Science
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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
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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]
2019
arXiv
pre-print
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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
2016
Notre Dame Journal of Formal Logic
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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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