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- Tommaso Toffoli
- ICALP
- 1980

- Norman Margolus, Tommaso Toffoli
- Complex Systems
- 1987

T he advantages of an archite ct ure opt imized for cellular automata (CA) simula tions are so great that , for large-scale CA experiments , it becomes absurd to use any ot her kind of comput er .

- Tommaso Toffoli, Norman Margolus
- MIT Press series in scientific computation
- 1987

- Tommaso Toffoli
- J. Comput. Syst. Sci.
- 1977

- Tommaso Toffoli
- Mathematical systems theory
- 1981

We discuss and solve the problem of constructing a diffeomorphic componentwise extension for an arbitrary invertible combinatorial function. Interpreted in physical terms, our solution constitutes a proof of the physical realizability of general computing mechanisms based onreversible primitives.

- Tommaso Toffoli, Norman Margolus
- International Journal of High Speed Computing
- 1993

- Tommaso Toffoli
- IBM Journal of Research and Development
- 2004

Ordinary crystallography deals with regular, discrete, static arrangements in space. Of course, dynamic considerations— and thus the additional dimension of time—must be introduced when one studies the origin of crystals (since they are emergent structures) and their physical properties such as conductivity and compressibility. The space and time of the… (More)

where h is Planck’s constant and E is the quantum-mechanical average energy of the system. Expression (1) applies to the autonomous time evolution of a system, and it is not immediately applicable to changes in the system state caused by the interaction with another (external) system. This paper considers the question of what is the minimum time of… (More)

Based on extensive experience with concepts, theory, applications, and hardware and software implementations, we propose a canonical way to represent “programmable matter” structures such as cellular automata, lattice gases, and related fine-grained, uniform, massivelyparallel computational substrates. Our proposal is accompanied by an “exemplar” software… (More)

- Tommaso Toffoli
- IJUC
- 2004

Most work on computation deals with its structural aspects—what it is composed of, how the individual elements work in isolation and how they are connected to one another, how best they can be implemented by a physical systems, etc.—in sum, it concerns itself with a proximate account of computation’s mechanisms. We argue that, though that kind of work is of… (More)