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Recursive Analysis Characterized as a Class of Real Recursive Functions
TLDR
We prove that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions. Expand
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Elementarily computable functions over the real numbers and R-sub-recursive functions
TLDR
We present an analog and machine-independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis: they correspond to the smallest class of functions that contains some basic functions, and closed by composition, linear integration, and a simple limit schema. Expand
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Reachability in Linear Dynamical Systems
TLDR
We show that the Skolem-Pisot problem that is undecidable in the general case is in fact decidable for a natural class of continuous-time dynamical systems: linear systems. Expand
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Polynomial differential equations compute all real computable functions on computable compact intervals
TLDR
We show that, in an appropriate framework, the GPAC and computable analysis are actually equivalent from the computability point of view, at least in compact intervals. Expand
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Real Recursive Functions and Real Extensions of Recursive Functions
TLDR
We extend this result to all computable functions: functions over the reals that extend total recursive functions over integers are proved to correspond to the smallest class of real functions containing some basic functions and closed by composition, linear integration and a natural unique minimization schema. Expand
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An Analog Characterization of Elementarily Computable Functions over the Real Numbers
TLDR
We present an analog and machine-independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis: we prove that they correspond to the smallest class of functions that contains some basic functions and closed by composition, linear integration, and a simple limit schema. Expand
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The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation
TLDR
We show that if we change the notion of GPAC-computability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Expand
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Interpretation of Stream Programs: Characterizing Type 2 Polynomial Time Complexity
TLDR
We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). Expand
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Type-Based Complexity Analysis for Fork Processes
TLDR
We introduce a type system for concurrent programs described as a parallel imperative language using while loops and fork/wait instructions, in which processes do not share a global memory, in order to analyze computational complexity. Expand
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Characterizing polynomial time complexity of stream programs using interpretations
TLDR
This paper provides a criterion based on interpretation methods on term rewrite systems in order to characterize the polynomial time complexity of second order functionals. Expand
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