This paper presents a computational framework to approach the resilience properties of the systems in many different domains. The proposal models elementary behaviors of the systems by means of a set of recursive func...
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ISBN:
(纸本)9781479901807
This paper presents a computational framework to approach the resilience properties of the systems in many different domains. The proposal models elementary behaviors of the systems by means of a set of recursive functions defined by a few parameters. The parameter values determine wide intervals that characterize the behavioral patterns. The proposal provides a theoretical model of resilience related to the capability of a system to maintain its own pattern by displaying only minor changes when the parameter values of the model vary inside the intervals. This model lays out two powerful design principles for resilience issues, which are the parameterized form of the function and its recursive calculation. The model has been successfully applied to the study of well known system archetypes.
For recursive functions general principles of induction needs to be applied. Instead of verifying them directly using the Vienna Development Method Specification Language (VDM-SL), we suggest a translation to Isabelle...
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Given two programs p1 and p2, typically two versions of the same program, the goal of regression verification is to mark pairs of functions from p1 and p2 that are equivalent, given a definition of equivalence. The mo...
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We prove that the pattern matching problem is undecidable in polymorphic λ-calculi (as Girard's system F [8] [9]) and calculi supporting inductive types (as Gödel's system T [10] [9]) by reducing Hilbert...
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Determining the approximate degree composition for Boolean functions remains a significant unsolved problem in Boolean function complexity. In recent decades, researchers have concentrated on proving that approximate ...
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We explore recursive programming with extensible data types. Row types make the structure of data types first class, and can express a variety of type system features from subtyping to modular combination of case bran...
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One of the basic differences between the primitive recursive functions on the natural numbers and the primitive recursive ordinal functions (PR) is the nearly complete absence of constant functions in PR. Since ω is ...
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One of the basic differences between the primitive recursive functions on the natural numbers and the primitive recursive ordinal functions (PR) is the nearly complete absence of constant functions in PR. Since ω is closed under all of the functions in PR, if α is any infinite ordinal, then λξ·α is not in PR. It is easily seen, however, that if one adds to the initial functions of PR the constant function λξ·ω, then all of the ordinals up to ω#, the next largest PR-closed ordinal, have their constant functions in this class. Since, however, such collections of functions are always countable, it is also the case that if one adds to the initial functions of PR the function λξ. α for uncountable α, then there are ordinals β < α whose constant functions are not in this collection. Because of this, the following objects are of interest:Definition. For all α,(i)PR(α) is the collection of functions obtained by adding to the initial primitive recursive ordinal functions, the function λξ· α;(ii) PRsp(α), the primitive recursive spectrum of α, is the set {β < α ∣ λξβ ∈ PR(α);(iii) Λ (α)= μρ(ρ∉ PRsp(α)).
Let ƒ be a real number. It is well known [7] that the set of rational numbers which are less than ƒ is a recursive set if and only if ƒ is representable as the limit of a recursive, recursively convergent sequence of ...
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Let ƒ be a real number. It is well known [7] that the set of rational numbers which are less than ƒ is a recursive set if and only if ƒ is representable as the limit of a recursive, recursively convergent sequence of rational numbers. In this paper we replace the condition that the set of rational numbers less than ƒ is recursive by the condition that this set is at various points in the Kleene hierarchy, and we replace the recursive, recursively convergent limit by a variety of other recursive limiting processes.
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