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The Complexity of Equivariant Unification
[chapter]
2004
Lecture Notes in Computer Science
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In this paper, we study the complexity of the decision problem for equivariant unification and matching. We show that these problems are NPcomplete in general. ...
However, when one of the terms is essentially firstorder, equivariant and nominal unification coincide. ...
Only those programs or rewrite systems that actually use the novel features of nominal logic need pay for them. ...
doi:10.1007/978-3-540-27836-8_30
fatcat:tgklvhk5ane45cdq7dqwxrjuvi
Constraint solving in non-permutative nominal abstract syntax
2011
Logical Methods in Computer Science
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This constraint problem has similar complexity to equivariant unification but without many of the additional complications of the equivariant unification term language. ...
However, certain problems require a constraint solver which respects the equivariance property of nominal logic, such as Cheney's equivariant unification algorithm. ...
Acknowledgements The author would like to thank Andrew Pitts for invaluable discussions on the subject matter of this paper, as well as Paul Blain Levy and an anonymous reviewer for help debugging proofs ...
doi:10.2168/lmcs-7(3:6)2011
fatcat:yyar7ud4uzbcdgbhft354dnpmq
αProlog: A Logic Programming Language with Names, Binding and α-Equivalence
[chapter]
2004
Lecture Notes in Computer Science
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However, because of the presence of types like exp that are defined via negative recursion, the semantics of deep HOAS is complex [8] and inductive proof and recursive definition principles are very difficult ...
Simplicity: The semantics of the meta-language should be as simple as possible in order to facilitate reasoning about programs. ...
the complexity of the rules is due to the need to handle scope extrusion, which occurs when restricted names "escape" their scope because of communication. ...
doi:10.1007/978-3-540-27775-0_19
fatcat:ubv7jpej2nadjhy4sk4nfhywne
A Library of Anti-unification Algorithms
[chapter]
2014
Lecture Notes in Computer Science
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In this paper we describe an open-source library of some newly developed anti-unification algorithms in various theories: for firstand second-order unranked terms, higher-order patterns, and nominal terms ...
Anti-unification is a technique used often to solve generalization problems. ...
This research has been supported by the Austrian Science Fund (FWF) under the project SToUT (P 24087-N18). ...
doi:10.1007/978-3-319-11558-0_38
fatcat:4fd2e4sksbbsjbo5fuonsd4m6i
Nominal logic programming
2008
ACM Transactions on Programming Languages and Systems
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We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. ...
Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we ...
Notes The complexity results for equivariant unification and matching reported in Section 7.1 first appeared in [19] . ...
doi:10.1145/1387673.1387675
fatcat:longqgnr75aktkwdy56eeyu4ne
Avoiding Equivariance in Alpha-Prolog
[chapter]
2005
Lecture Notes in Computer Science
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In αProlog, the nominal unification algorithm of Urban, Pitts and Gabbay is used instead of first-order unification. ...
Nevertheless, the αProlog programs we studied run correctly without equivariant unification. ...
Acknowledgements: This research was supported by a fellowship for Urban from the Alexandervon-Humboldt foundation. ...
doi:10.1007/11417170_29
fatcat:ombil5pd4nfcdcyvs7dwrdujqq
Dimensionless machine learning: Imposing exact units equivariance
[article]
2022
arXiv
pre-print
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Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional ...
Our approach can be used to impose units equivariance across a broad range of machine learning methods which are equivariant to rotations and other groups. ...
AI2AI Amazon research award, and the TRIPODS Institute for the Foundations of Graph and Deep Learning at Johns Hopkins University. ...
arXiv:2204.00887v2
fatcat:aoqlw2xfwzc57mcd6nayl6wmuu
A Formalisation of Nominal α -equivalence with A and AC Function Symbols
2017
Electronical Notes in Theoretical Computer Science
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General α-equivalence problems are log-linearly solved while AC and the combination of A and AC α-equivalence problems have the same complexity as standard first-order approaches. ...
This development is a first step towards verification of nominal matching, unification and narrowing algorithms modulo equational theories in general. ...
A further interesting analysis would be the classification of the related "nominal α-unification modulo" problems regarding their unification type and complexities. ...
doi:10.1016/j.entcs.2017.04.003
fatcat:ym72phsunrfizivtroo2khivgy
Dynamics of Spiral Waves on Unbounded Domains Using Center-Manifold Reductions
1997
Journal of Differential Equations
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An equivariant center-manifold reduction near relative equilibria of G-equivariant semiflows on Banach spaces is presented. In contrast to previous results, the Lie group G is possibly non-compact. ...
The results are applied to bifurcations of stable patterns arising in reactiondiffusion systems on the plane or in three-space modeling chemical systems such as catalysis on platinum surfaces and Belousov-Zhabotinsky ...
Thus, by an H-invariant change of coordinates, we can transform A * into complex Jordan normal form. Let K > 0 be a bound for the off-diagonal elements of the matrix A * written in normal form. ...
doi:10.1006/jdeq.1997.3326
fatcat:f266kch3tvb77ocy7jljvhr5vi
Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results
[article]
2018
arXiv
pre-print
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We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. ...
We study their bi-algebraic systems, formulate the Ax-Schanuel conjecture and explain its relation with the Ax logarithmique theorem and the Ax-Lindemann theorem which we shall prove. ...
I have benefited from discussions with Richard Pink on the first part of the paper, especially his suggestion to simplify the proof of Theorem 4.4. ...
arXiv:1607.07843v3
fatcat:mgtthvt27za43ea55hfm3e2zaa
ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS
2019
Forum of Mathematics, Sigma
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We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. ...
We study their bi-algebraic systems, formulate the Ax-Schanuel conjecture and explain its relation with the logarithmic Ax theorem and the Ax-Lindemann theorem which we shall prove. ...
I have benefited from discussions with Richard Pink on the first part of the paper, especially his suggestion to simplify the proof of Theorem 4.4. ...
doi:10.1017/fms.2019.10
fatcat:mgq77vlkdbbqjiamqjncrhig7a
Page 3236 of Mathematical Reviews Vol. , Issue 2001E
[page]
2001
Mathematical Reviews
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Summary: “This is the first part of a series of articles on equivari- ant strong shape. ...
The aim of this paper is to prove that equivariant resolutions of G-spaces are equivariant strong expansions.”
55 ALGEBRAIC TOPOLOGY
3236
constructed a functor #: 7@F7', — dgA*(Q), from the category of ...
On Nominal Syntax and Permutation Fixed Points
[article]
2020
arXiv
pre-print
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Based on this notion of equivalence, we show that C-unification is finitary and we provide a sound and complete C-unification algorithm, as a first step towards the development of nominal unification modulo ...
This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution. ...
Regarding the complexity of the C-unification algorithm based on fixed-point constraints, we observe that in the syntactic case (i.e., without α-equivalence rules), the C-unification problem is NP-complete ...
arXiv:1902.08345v4
fatcat:l3wpoq2xirgubpcwhddrxsdh7u
On Nominal Syntax and Permutation Fixed Points
2019
Logical Methods in Computer Science
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Based on this notion of equivalence, we show that C-unification is finitary and we provide a sound and complete C-unification algorithm, as a first step towards the development of nominal unification modulo ...
This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution. ...
Regarding the complexity of the C-unification algorithm based on fixed-point constraints, we observe that in the syntactic case (i.e., without α-equivalence rules), the C-unification problem is NP-complete ...
doi:10.23638/lmcs-16(1:19)2020
fatcat:nxayfkgbvbeklitsv2rahbh3ga
Logic Column 14: Nominal Logic and Abstract Syntax
[article]
2005
arXiv
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Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding ...
We also discuss applications of nominal techniques to programming, automated reasoning, and identify some future directions. ...
restrictions on the language or solve NP-complete equivariant unification problems. ...
arXiv:cs/0511025v1
fatcat:sro6jwwv65f2jnmxlzsulzr7r4
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