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Order, 2012 Let \(A\) and \(B\) be sets. For functions \(f:\;A^n\to B\), \(g:\;A^m\to B\) we write \(g\leq f\) if there exists an assignment \(\alpha:\;\{1,\dots,n\}\to\{1,\dots,m\}\) such that \(g(a_1,\dots,a_m)=f(a_{\alpha(1)},\dots,a_{\alpha(n)})\) for all \(a_1,\dots,a_m\in A\).
Miguel Couceiro +2 more
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Computer Languages, Systems & Structures, 2014
Higher order combinators in functional programming languages can lead to code that would be considerably more efficient if some functions' definitions were eta-expanded, but the existing analyses are not always precise enough to allow that. In particular, this has prevented foldl from efficiently taking part in list fusion.
Joachim Breitner
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Higher order combinators in functional programming languages can lead to code that would be considerably more efficient if some functions' definitions were eta-expanded, but the existing analyses are not always precise enough to allow that. In particular, this has prevented foldl from efficiently taking part in list fusion.
Joachim Breitner
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Annals of Pure and Applied Logic, 1996 For many extensions \(L\) of first-order logic considered for finite structures there is a natural notion of arity of a formula (e.g., the maximal arity of a bounded second-order variable in a formula of fixed-point logic). Denote by \(L^k\) the fragment of \(L\) consisting of the sentences of \(L\) of arity \(\leq k\).
Martin Grohe
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2011 41st IEEE International Symposium on Multiple-Valued Logic, 2011
The arity gap of a function of several variables is defined as the minimum decrease in the number of essential variables when essential variables of the function are identified. We present a brief survey on the research done on the arity gap, from the first studies of this notion up to recent developments.
Miguel Couceiro +2 more
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The arity gap of a function of several variables is defined as the minimum decrease in the number of essential variables when essential variables of the function are identified. We present a brief survey on the research done on the arity gap, from the first studies of this notion up to recent developments.
Miguel Couceiro +2 more
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Arity-Monotonic Extended Aggregation Operators
International Conference on Information Processing and Management of Uncertainty, 2010A class of extended aggregation operators, called impact functions, is proposed and their basic properties are examined. Some important classes of functions like generalized ordered weighted averaging (OWA) and ordered weighted maximum (OWMax) operators are considered.
Marek Gągolewski +1 more
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Convergence analysis of Hermite subdivision schemes of any arity
Applied Numerical Mathematics, 2022Hermite subdivision schemes are particular vector subdivision schemes which produce function vectors consisting of consecutive derivatives of a certain function.
Zeze Zhang, Hongchan Zheng, Jie Zhou
semanticscholar +1 more source
The Lexicon-Syntax Parameter: Reflexivization and Other Arity Operations
Linguistic Inquiry, 2005 Tal Siloni
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Exploring The Impact Of Switch Arity On Butterfly Fat Tree Fpga Nocs
IEEE Symposium on Field-Programmable Custom Computing Machines, 2020Overlay Networks-on-Chip (NoCs) for FPGAs based on the Butterfly-Fat Tree (BFT) topology with lightweight flow control deliver low LUT costs and features such as in-order delivery and livelock freedom.
Ian Elmor Lang +2 more
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Essential Arity Gap of Boolean Functions
Serdica Journal of Computing, 2008 In this paper we investigate the Boolean functions with maximum essential arity gap. Additionally we propose a simpler proof of an important theorem proved by M. Couceiro and E. Lehtonen in [3]. They use Zhegalkin’s polynomials as normal forms for Boolean functions and describe the functions with essential arity gap equals 2.
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Journal of Intelligent & Fuzzy Systems, 2021
The arity of convex spaces is a numerical feature which shows the ability of finite subsets spanning to the whole space via the hull operators. This paper gives it a formal and strict definition by introducing the truncation of convex spaces. The relations that between the arity of quotient spaces and the original spaces, that between the arity of ...
Yao, Wei, Chen, Ye
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The arity of convex spaces is a numerical feature which shows the ability of finite subsets spanning to the whole space via the hull operators. This paper gives it a formal and strict definition by introducing the truncation of convex spaces. The relations that between the arity of quotient spaces and the original spaces, that between the arity of ...
Yao, Wei, Chen, Ye
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