# Polynomial differential equations compute all real computable functions on computable compact intervals

@article{Bournez2007PolynomialDE, title={Polynomial differential equations compute all real computable functions on computable compact intervals}, author={O. Bournez and M. L. Campagnolo and D. Graça and Emmanuel Hainry}, journal={J. Complex.}, year={2007}, volume={23}, pages={317-335} }

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 been used to argue that the GPAC is less powerful than digital computation. However, when computability with GPACs is not restricted to real-time… CONTINUE READING

59 Citations

A characterization of computable analysis on unbounded domains using differential equations

- Mathematics, Computer Science
- Inf. Comput.
- 2011

- PDF

Characterizing Computable Analysis with Differential Equations

- Mathematics, Computer Science
- Electron. Notes Theor. Comput. Sci.
- 2008

4- PDF

Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length

- Mathematics, Computer Science
- J. ACM
- 2017

18- PDF

Computing with Polynomial Ordinary Differential Equations

- Mathematics, Computer Science
- J. Complex.
- 2016

5- PDF

Algebraic Characterizations of Complexity-Theoretic Classes of Real Functions

- Mathematics, Computer Science
- Int. J. Unconv. Comput.
- 2011

5- PDF

The elementary computable functions over the real numbers: applying two new techniques

- Computer Science
- Arch. Math. Log.
- 2008

12- PDF

Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length: The General Purpose Analog Computer and Computable Analysis Are Two Efficiently Equivalent Models of Computations

- Mathematics, Computer Science
- ICALP
- 2016

10- PDF

Turing Machines Can Be Efficiently Simulated by the General Purpose Analog Computer

- Computer Science
- TAMC
- 2013

5- PDF

#### References

SHOWING 1-10 OF 48 REFERENCES

Computational complexity of real valued recursive functions and analog circuits

- Computer Science
- 2001

22

Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)

- Mathematics
- 1974

163- PDF

Iteration, Inequalities, and Differentiability in Analog Computers

- Mathematics, Computer Science
- J. Complex.
- 2000

58- PDF

Some recent developments on Shannon's General Purpose Analog Computer

- Computer Science
- Math. Log. Q.
- 2004

59 Highly Influential- PDF

Analog computers and recursive functions over the reals

- Mathematics, Computer Science
- J. Complex.
- 2003

104- PDF

On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines

- Mathematics
- 1989

1,034- PDF

Recursion Theory on the Reals and Continuous-Time Computation

- Mathematics, Computer Science
- Theor. Comput. Sci.
- 1996

168- PDF

Recursive Analysis Characterized as a Class of Real Recursive Functions

- Mathematics, Computer Science
- Fundam. Informaticae
- 2006

31- PDF