Author image not provided
 Daniel Silva Graça

Authors:
Add personal information
  Affiliation history
Bibliometrics: publication history
Average citations per article4.15
Citation Count83
Publication count20
Publication years2003-2017
Available for download2
Average downloads per article72.00
Downloads (cumulative)144
Downloads (12 Months)95
Downloads (6 Weeks)26
SEARCH
ROLE
Arrow RightAuthor only


AUTHOR'S COLLEAGUES
See all colleagues of this author

SUBJECT AREAS
See all subject areas




BOOKMARK & SHARE


20 results found Export Results: bibtexendnoteacmrefcsv

Result 1 – 20 of 20
Result page: 1 2

Sort by:

1 published by ACM
October 2017 Journal of the ACM (JACM): Volume 64 Issue 6, November 2017
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 26,   Downloads (12 Months): 89,   Downloads (Overall): 89

Full text available: PDFPDF
The outcomes of this article are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class P of languages computable in polynomial time in terms of differential equations with polynomial right-hand side. This result gives a purely continuous ...
Keywords: computable analysis, continuous-time models of computation, Analog models of computation, computational complexity, ordinary differential equations, implicit complexity

2
October 2016 Journal of Complexity: Volume 36 Issue C, October 2016
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

In 1941, Claude Shannon introduced the General Purpose Analog Computer (GPAC) as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later on electronic) machines of that time.Following Shannon's arguments, functions generated by the GPAC must satisfy a polynomial differential algebraic ...
Keywords: General Purpose Analog Computer, Analog computation, Continuous-time computations, Real computations

3
May 2016 Theoretical Computer Science: Volume 626 Issue C, May 2016
Publisher: Elsevier Science Publishers Ltd.
Bibliometrics:
Citation Count: 0

In this paper we investigate the computational complexity of solving ordinary differential equations (ODEs) y ' = p ( y ) over unbounded time domains, where p is a vector of polynomials. Contrarily to the bounded (compact) time case, this problem has not been well-studied, apparently due to the "intuition" ...
Keywords: Adaptive Taylor algorithms, Computation with real numbers, Ordinary differential equations, Computational complexity

4
November 2015 MACIS 2015: Revised Selected Papers of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences - Volume 9582
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

In this abstract we present a rigorous numerical algorithm which solves initial-value problems IVPs defined with polynomial differential equations i.e.﾿IVPs of the type $$y'=pt,y$$, $$yt_0=y_0$$, where p is a vector of polynomials for any value of t. The inputs of the algorithm are the data defining the initial-value problem, the ...

5
August 2015 Theory of Computing Systems: Volume 57 Issue 2, August 2015
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

In many applications one is interested in finding the stability regions (basins of attraction) of some stationary states (attractors). In this paper we show that one cannot compute, in general, the basins of attraction of even very regular systems, namely analytic systems with hyperbolic asymptotically stable equilibrium points. To prove ...
Keywords: Basins of attractions, Computability with real numbers, Reachability problem, Asymptotically stable equilibrium points

6
August 2013 Journal of Computer and System Sciences: Volume 79 Issue 5, August, 2013
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 1

This paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust ...
Keywords: Reachability, Computational power, Dynamical systems, Robustness, Verification

7
October 2012 Theoretical Computer Science: Volume 457, October, 2012
Publisher: Elsevier Science Publishers Ltd.
Bibliometrics:
Citation Count: 1

As one of the seven open problems in the addendum to their 1989 book Computability in Analysis and Physics Pour-El and Richards (1989) [17], Pour-El and Richards asked, ''What is the connection between the computability of the original nonlinear operator and the linear operator which results from it?'' Yet at ...
Keywords: Computability, Linearization, Differential equations, Hartman-Grobman theorem

8 published by ACM
July 2012 ISSAC '12: Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 0,   Downloads (12 Months): 6,   Downloads (Overall): 55

Full text available: PDFPDF
In this paper we prove that computing the solution of an initial-value problem y = p ( y ) with initial condition y ( t 0 ) = y 0 ∈ R d at time t 0 + T with precision 2 −μ where p is a vector of polynomials ...

9
July 2012 Complexity: Volume 17 Issue 6, July 2012
Publisher: John Wiley & Sons, Inc.
Bibliometrics:
Citation Count: 1

One of the most significant achievements from theoretical computer science was to show that there are noncomputable problems, which cannot be solved through algorithms. Although the formulation of such problems is mathematical, they often can be interpreted as problems derived from other fields, like physics or computer science. However, no ...
Keywords: computability theory, computable analysis, valuation, finance

10
August 2011 MFCS'11: Proceedings of the 36th international conference on Mathematical foundations of computer science
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 2

In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains of R n and C n , under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of ...

11
August 2010 MFCS'10: Proceedings of the 35th international conference on Mathematical foundations of computer science
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 2

In this paper we discuss the computational power of Lipschitz dynamical systems which are robust to infinitesimal perturbations. Whereas the study in [1] was done only for not-so-natural systems from a classical mathematical point of view (discontinuous differential equation systems, discontinuous piecewise affine maps, or perturbed Turing machines), we prove ...
Keywords: verification, analog computations, computable analysis, model-checking

12
October 2009 Applied Mathematics and Computation: Volume 215 Issue 4, October, 2009
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 1

In this paper we study from a computational perspective some properties of the solutions of polynomial ordinary differential equations. We consider elementary (in the sense of Analysis) discrete-time dynamical systems satisfying certain criteria of robustness. We show that those systems can be simulated with elementary and robust continuous-time dynamical systems ...
Keywords: Computability, Dynamical systems, Turing machines, Differential equations

13
September 2009 UC '09: Proceedings of the 8th International Conference on Unconventional Computation
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 0

In this note we investigate the problem of computing the domain of attraction of a flow on *** 2 for a given attractor. We consider an operator that takes two inputs, the description of the flow and a cover of the attractors, and outputs the domain of attraction for the ...

14
December 2008 Electronic Notes in Theoretical Computer Science (ENTCS): Volume 221, December, 2008
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 6

In this note we consider the computability of the solution of the initial-value problem for ordinary differential equations with continuous right-hand side. We present algorithms for the computation of the solution using the ''thousand monkeys'' approach, in which we generate all possible solution tubes, and then check which are valid. ...
Keywords: differential inclusions, Lipschitz condition, Ordinary differential equations, computability

15
March 2008 Advances in Applied Mathematics: Volume 40 Issue 3, March, 2008
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 4

In this paper, we show that there are initial value problems defined with polynomial ordinary differential equations that can simulate universal Turing machines in the presence of bounded noise. The polynomial ODE defining the IVP is explicitly obtained and the simulation is performed in real time.

16
March 2008 Electronic Notes in Theoretical Computer Science (ENTCS): Volume 202, March, 2008
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 0

Consider the initial-value problem with computable parameters{dxdt=p(t,x)x(t"0)=x"0, where p:R^n^+^1->R^n is a vector of polynomials and (t"0,x"0)@?R^n^+^1. We show that the problem of determining whether the maximal interval of definition of this initial-value problem is bounded or not is in general undecidable.
Keywords: Ordinary differential equations, maximal interval, decidability, initial-value problems

17
June 2007 Journal of Complexity: Volume 23 Issue 3, June, 2007
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 15

In the last decade, there have been several attempts to understand the relations between the many models of analog computation. Unfortunately, most models are not equivalent. Euler's Gamma function, which is computable according to computable analysis, but that cannot be generated by Shannon's General Purpose Analog Computer (GPAC), has often ...
Keywords: Differential equations, General Purpose Analog Computer, Analog computation, Church--Turing thesis, Computable analysis

18
May 2006 TAMC'06: Proceedings of the Third international conference on Theory and Applications of Models of Computation
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 4

In this paper we revisit one of the first models of analog computation, Shannon’s General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPAC-computability in a natural way, we compute ...

19
June 2005 CiE'05: Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 11

In this paper, we show that closed-form analytic maps and flows can simulate Turing machines in an error-robust manner. The maps and ODEs defining the flows are explicitly obtained and the simulation is performed in real time.

20
October 2003 Journal of Complexity: Volume 19 Issue 5, October 2003
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 32

In this paper we show that Shannon's general purpose analog computer (GPAC) is equivalent to a particular class of recursive functions over the reals with the flavour of Kleene's classical recursive function theory.We first consider the GPAC and several of its extensions to show that all these models have drawbacks ...
Keywords: analog circuits, Shannon's general purpose analog computer, recursive functions over the reals, differentially algebraic functions



The ACM Digital Library is published by the Association for Computing Machinery. Copyright © 2018 ACM, Inc.
Terms of Usage   Privacy Policy   Code of Ethics   Contact Us