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About 3,146 papers for “Computable function”

Engineering design is a computable function

Patrick A. Fitzhorn · Artificial intelligence for engineering design analysis and manufacturing · 1994

Abstract Computational abstraction of engineering design leads to an elegant theory defining (1) the process of design as an abstract model of computability, the Turing machine; (2) the artifacts of design as enumerated strings from a (possibly multidimensional) grammar; and (3) design specifications or constraints as formal state changes that govern string enumeration. Using this theory, it is shown that engineering design is a computable function. A computational methodology based on the theory is then developed that can be described as a form follows function design paradigm.

Cited by 12

When Is a Function Securely Computable?

Himanshu Tyagi, Prakash Narayan, Piyush Gupta · IEEE Transactions on Information Theory · 2011

A subset of a set of terminals that observe correlated signals seek to compute a function of the signals using public communication. It is required that the value of the function be concealed from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the capacity of a new secrecy generation model, for which a single-letter characterization is provided.

Cited by 59

A uniformly computable Implicit Function Theorem

Timothy H. McNicholl · Mathematical logic quarterly · 2008

Abstract We prove uniformly computable versions of the Implicit Function Theorem in its differentiable and non‐differentiable forms. We show that the resulting operators are not computable if information about some of the partial derivatives of the implicitly defining function is omitted. Finally, as a corollary, we obtain a uniformly computable Inverse Function Theorem, first proven by M. Ziegler (2006). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Cited by 12

When is a function securely computable?

Himanshu Tyagi, Prakash Narayan, Piyush Gupta · 2011

A subset of a set of terminals that observe correlated signals seek to compute a given function of the signals using public communication. It is required that the value of the function be kept secret from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the “aided secret key” capacity of an associated secrecy generation model, for which a single-letter characterization is provided.

Cited by 13

The Distance Function on a Computable Graph

Chubb, Jennifer C, Wesley Calvert, Russell Miller · USF Scholarship Repository (University of San Francisco) · 2013

We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove assorted theorems about the new reducibilities and about functions which have nonincreasing computable approximations. Finally, we show that the spectrum of the distance function can consist of an arbitrary single bttdegree which is approximable from above, or of all such btt-degrees at once, or of the bT-degrees of exactly those functions approximable from above in at most n steps.

Cited by 0Open access

P.: When is a function securely computable

Himanshu Tyagi, Prakash Narayan, Piyush Gupta · 2011

Abstract—A subset of a set of terminals that observe correlated signals seek to compute a function of the signals using public com-munication. It is required that the value of the function be con-cealed from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the capacity of a new secrecy generationmodel, for which a single-letter characterization is provided. Index Terms—Aided secret key, balanced coloring lemma, func-tion computation, maximum common function, omniscience, se-cret key capacity, secure computability. I.

Cited by 0

Computable Function Representations Using Effective Chebyshev Polynomial

Mohammed A. Abutheraa, David Lester · Zenodo (CERN European Organization for Nuclear Research) · 2007

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

Cited by 10Open access

The Distance Function on a Computable Graph

Wesley Calvert, Russell Miller, Jennifer Chubb Reimann · arXiv (Cornell University) · 2011

We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove assorted theorems about the new reducibilities and about functions which have nonincreasing computable approximations. Finally, we show that the spectrum of the distance function can consist of an arbitrary single btt-degree which is approximable from above, or of all such btt-degrees at once, or of the bT-degrees of exactly those functions approximable from above in at most n steps.

Cited by 0Open access

What is a POLYNOMIAL-TIME Computable L2-Function?

Aras Bacho, Svetlana Selivanova, Martin Ziegler · arXiv (Cornell University) · 2026

We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).

Cited by 0Open access

What is a POLYNOMIAL-TIME Computable L2-Function?

Aras Bacho, Svetlana Selivanova, Martin Ziegler · ArXiv.org · 2026

We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).

Cited by 0Open access

Collapsing a coevolutionary process into a computable function

Oliveira, Pedro P. B. · Biblioteca Digital da Memória Científica do INPE (National Institute for Space Research) · 1996

It is shown how the entire dynamics of a class of evolutionary systems can be used to perform a computation. The argument is constructive by presenting a Turing-machine-based set-up implemented in Enact, an artificial-life world embedded in a family of cellular automata; in this system, a population of agents move about in a two-dimensional space, interacting with their environment, reproducing and undergoing developmental and coevolutionary processes. As a byproduct, the paper also serves to characterise the main model of computation underlying Enact. This model is essentially parallel, and relies upon the machinery defined by the artificial-life processes. According to the model, a particular computation is considered to have been performed, if and only if, for some initial population and en-vironmental configuration, at least one agent has developed into a state configuration that is insensitive to any further environmental interactions; in this situation, if the computation involved is a function, this individual has the result. If the population ever vanishes, or if the environment becomes short of the resources needed for development, the cellular space has to be re-initialised, and the process iterated. The presentation relies on the implementation of a function that recognises a particular context-free language. Implications of the model of computation are then discussed, in particular the model of coupled computations suggested by it.

Cited by 0

Every Feasibly Computable Reals-to-Reals Function Is Feasibly Uniformly Continuous

Kosheleva, Olga, Kreinovich, Vladik · scholarworks - UTEP (The University of Texas at El Paso) · 2024

It is known that every computable function is continuous; moreover, it is computably continuous in the sense that for every ε > 0, we can compute δ > 0 such that δ-close inputs lead to ε-close outputs. It is also known that not all functions which are, in principle, computable, can actually be computed: indeed, the computation sometimes requires more time than the lifetime of the Universe. A natural question is thus: can the above known result about computable continuity of computable functions be extended to the case when we limit ourselves to feasible computations? In this paper, we prove that this extension is indeed possible.

Cited by 0

Computable error bounds for asymptotic approximations of the quadratic discriminant function

Yasunori Fujikoshi · Hiroshima Mathematical Journal · 2020

This paper is concerned with computable error bounds for asymptotic approximations of the expected probabilities of misclassification (EPMC) of the quadratic discriminant function $Q$. A location and scale mixture expression for $Q$ is given as a special case of a general discriminant function including the linear and quadratic discriminant functions. Using the result, we provide computable error bounds for asymptotic approximations of the EPMC of $Q$ when both the sample size and the dimensionality are large. The bounds are numerically explored. Similar results are given for a quadratic discriminant function $Q_0$ when the covariance matrix is known.

Cited by 1Open access