The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Sergei Soloviev - One of the best experts on this subject based on the ideXlab platform.
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a deciding algorithm for Linear Isomorphism of types with complexity o n log2 n
Lecture Notes in Computer Science, 1997Co-Authors: Alexander E. Andreev, Sergei SolovievAbstract:It is known, that ordinary Isomorphisms (associativity and commutativity of “times”, Isomorphisms for “times” unit and currying) provide a complete axiomatisation of Isomorphism of types in multiplicative Linear lambda calculus (Isomorphism of objects in a free symmetric monoidal closed category). One of the reasons to consider Linear Isomorphism of types instead of ordinary Isomorphism was that better complexity could be expected. Meanwhile, no upper bounds reasonnably close to Linear were obtained. We describe an algorithm deciding if two types are Linearly isomorphic with complexity O(nlog 2(n)).
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Category Theory and Computer Science - A Deciding Algorithm for Linear Isomorphism of Types with Complexity O (n log2(n))
Category Theory and Computer Science, 1997Co-Authors: Alexander E. Andreev, Sergei SolovievAbstract:It is known, that ordinary Isomorphisms (associativity and commutativity of “times”, Isomorphisms for “times” unit and currying) provide a complete axiomatisation of Isomorphism of types in multiplicative Linear lambda calculus (Isomorphism of objects in a free symmetric monoidal closed category). One of the reasons to consider Linear Isomorphism of types instead of ordinary Isomorphism was that better complexity could be expected. Meanwhile, no upper bounds reasonnably close to Linear were obtained. We describe an algorithm deciding if two types are Linearly isomorphic with complexity O(nlog 2(n)).
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A Decision Algorithm for Linear Isomorphism of Types with Complexity Cn(log2(n))
BRICS Report Series, 1996Co-Authors: Alexander E. Andreev, Sergei SolovievAbstract:It is known that ordinary Isomorphisms (associativity and commutativity of "times", Isomorphisms for "times" unit and currying) provide a complete axiomatisation for Linear Isomorphism of types. One of the reasons to consider Linear Isomorphism of types instead of ordinary Isomorphism was that better complexity could be expected. Meanwhile, no upper bounds reasonably close to Linear were obtained. We describe an algorithm deciding if two types are Linearly isomorphic with complexity Cn(log2(n)).
Jeffrey Considine - One of the best experts on this subject based on the ideXlab platform.
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POPL - Efficient algorithms for Isomorphisms of simple types
Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '03, 2003Co-Authors: Yoav Zibin, Joseph Gil, Jeffrey ConsidineAbstract:The first order Isomorphism problem is to decide whether two non-recursive types using product- and function-type constructors, are isomorphic under the axioms of commutative and associative products, and currying and distributivity of functions over products. We show that this problem can be solved in O(n log2 n) time and O(n) space, where is n the input size. This result improves upon the O(n log2 n) time and O(n2) space bounds of the best previous algorithm. We also describe an O(n) time algorithm for the Linear Isomorphism problem, which does not include the distributive axiom, whereby improving upon the O(n log n) time of the best previous algorithm for this problem.
Xiangyu Jiao - One of the best experts on this subject based on the ideXlab platform.
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bimodule and twisted representation of vertex operator algebras
Science China-mathematics, 2016Co-Authors: Qifen Jiang, Xiangyu JiaoAbstract:In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number \(n \in \tfrac{1} {T}\mathbb{Z}_ +\), we construct an A g,n (V)-bimodule A g,n (M) and study its properties, discuss the connections between bimodule A g,n (M) and intertwining operators. Especially, bimodule \(A_{g,n - \tfrac{1} {T}} (M)\) (M) is a natural quotient of A g,n (M) and there is a Linear Isomorphism between the space \(\mathcal{I}_{M M^j }^{M^k }\) of intertwining operators and the space of homomorphisms \(Hom_{A_{g,n} (V)} \left( {A_{g,n} \left( M \right) \otimes _{A_{g,n} (V)} M^j \left( s \right),M^k \left( t \right)} \right)\) for s, t ⩽ n, M j , M k are g-twisted V modules, if V is g-rational.
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bimodule and twisted representation of vertex operator algebras
arXiv: Representation Theory, 2015Co-Authors: Qifen Jiang, Xiangyu JiaoAbstract:In this paper, for a vertex operator algebra $V$ with an automorphism $g$ of order $T,$ an admissible $V$-module $M$ and a fixed nonnegative rational number $n\in\frac{1}{T}\Bbb{Z}_{+},$ we construct an $A_{g,n}(V)$-bimodule $\AA_{g,n}(M)$ and study its some properties, discuss the connections between bimodule $\AA_{g,n}(M)$ and intertwining operators. Especially, bimodule $\AA_{g,n-\frac{1}{T}}(M)$ is a natural quotient of $\AA_{g,n}(M)$ and there is a Linear Isomorphism between the space ${\cal I}_{M\,M^j}^{M^k}$ of intertwining operators and the space of homomorphisms $\rm{Hom}_{A_{g,n}(V)}(\AA_{g,n}(M)\otimes_{A_{g,n}(V)}M^j(s), M^k(t))$ for $s,t\leq n, M^j, M^k$ are $g$-twisted $V$ modules, if $V$ is $g$-rational.
Alexander E. Andreev - One of the best experts on this subject based on the ideXlab platform.
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a deciding algorithm for Linear Isomorphism of types with complexity o n log2 n
Lecture Notes in Computer Science, 1997Co-Authors: Alexander E. Andreev, Sergei SolovievAbstract:It is known, that ordinary Isomorphisms (associativity and commutativity of “times”, Isomorphisms for “times” unit and currying) provide a complete axiomatisation of Isomorphism of types in multiplicative Linear lambda calculus (Isomorphism of objects in a free symmetric monoidal closed category). One of the reasons to consider Linear Isomorphism of types instead of ordinary Isomorphism was that better complexity could be expected. Meanwhile, no upper bounds reasonnably close to Linear were obtained. We describe an algorithm deciding if two types are Linearly isomorphic with complexity O(nlog 2(n)).
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Category Theory and Computer Science - A Deciding Algorithm for Linear Isomorphism of Types with Complexity O (n log2(n))
Category Theory and Computer Science, 1997Co-Authors: Alexander E. Andreev, Sergei SolovievAbstract:It is known, that ordinary Isomorphisms (associativity and commutativity of “times”, Isomorphisms for “times” unit and currying) provide a complete axiomatisation of Isomorphism of types in multiplicative Linear lambda calculus (Isomorphism of objects in a free symmetric monoidal closed category). One of the reasons to consider Linear Isomorphism of types instead of ordinary Isomorphism was that better complexity could be expected. Meanwhile, no upper bounds reasonnably close to Linear were obtained. We describe an algorithm deciding if two types are Linearly isomorphic with complexity O(nlog 2(n)).
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A Decision Algorithm for Linear Isomorphism of Types with Complexity Cn(log2(n))
BRICS Report Series, 1996Co-Authors: Alexander E. Andreev, Sergei SolovievAbstract:It is known that ordinary Isomorphisms (associativity and commutativity of "times", Isomorphisms for "times" unit and currying) provide a complete axiomatisation for Linear Isomorphism of types. One of the reasons to consider Linear Isomorphism of types instead of ordinary Isomorphism was that better complexity could be expected. Meanwhile, no upper bounds reasonably close to Linear were obtained. We describe an algorithm deciding if two types are Linearly isomorphic with complexity Cn(log2(n)).
Quanyuan Chen - One of the best experts on this subject based on the ideXlab platform.
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NonLinear Maps Preserving Mixed Product on Factors
Bulletin of the Iranian Mathematical Society, 2020Co-Authors: Yuanyuan Zhao, Quanyuan ChenAbstract:Let $${\mathcal {A}}$$ and $${\mathcal {B}}$$ be two factors with dim $${\mathcal {A}}>4$$ . In this article, it is proved that a bijective map $$\Phi : {\mathcal {A}}\rightarrow {\mathcal {B}}$$ satisfies $$\Phi ([A\bullet B, C])=[\Phi (A)\bullet \Phi (B), \Phi (C)]$$ for all $$A, B, C\in {\mathcal {A}}$$ if and only if $$\Phi $$ is a Linear $$*$$ -Isomorphism, or a conjugate Linear $$*$$ -Isomorphism, or the negative of a Linear $$*$$ -Isomorphism, or the negative of a conjugate Linear $$*$$ -Isomorphism.
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NonLinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras
Chinese Annals of Mathematics Series B, 2018Co-Authors: Quanyuan Chen, Ting WangAbstract:Let \(\mathcal{A}\) and \(\mathcal{B}\) be two factor von Neumann algebras. For \(A,B \in \mathcal{A}\), define by [A,B]* = AB − BA* the skew Lie product of A and B. In this article, it is proved that a bijective map \(\Phi :\mathcal{A} \to \mathcal{B}\) satisfies Φ([[A,B]*,C]*) = [[Φ(A),Φ(B)]*,Φ(C)]* for all \(A,B,C \in \mathcal{A}\) if and only if Φ is a Linear *-Isomorphism, or a conjugate Linear *- Isomorphism, or the negative of a Linear *-Isomorphism, or the negative of a conjugate Linear *-Isomorphism.
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NonLinear Maps Preserving Product $$X^{*}Y+Y^{*}X$$ on von Neumann Algebras
Bulletin of the Iranian Mathematical Society, 2018Co-Authors: F. Zhao, Quanyuan ChenAbstract:Let $$\mathcal {A}$$ and $$\mathcal {B}$$ be two von Neumann algebras with no central abelian projections. In this paper, it is proved that if a not necessarily Linear bijective map $$\Phi :\mathcal {A}\rightarrow \mathcal {B}$$ satisfies $$\Phi (A^{*}B+B^{*}A)=\Phi (A)^{*}\Phi (B)+\Phi (B)^{*}\Phi (A)$$ for all $$A, B\in \mathcal {A}$$ , then $$\Phi $$ is a sum of a Linear $$*$$ -Isomorphism and a conjugate Linear $$*$$ -Isomorphism.