From Reactive Systems to Cyber-Physical Systems pp 205-224 | Cite as

# Topological Interpretation of Interactive Computation

## Abstract

It is a great pleasure to write this tribute in honor of Scott A. Smolka on his 65th birthday. We revisit Goldin, Smolka hypothesis that *persistent Turing machine* (PTM) can capture the intuitive notion of *sequential interaction computation*. We propose a topological setting to model the abstract concept of *environment*. We use it to define a notion of a *topological Turing machine* (TTM) as a universal model for interactive computation and possible model for concurrent computation.

## Keywords

Persistent Turing machine Topological environment Topological Turing machine## Notes

### Acknowledgements

E. M. thanks Mario Rasetti for bringing her to conceive a new way of thinking about computer science and for numerous and lively discussions on topics related to this article; and Samson Abramsky with his group for insightful conversations on the topological interpretation of contextuality and contextual semantics. E. M. and A. W. thank the anonymous referees for suggesting many significant improvements.

### *Funding statements*

We acknowledge the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme (FP7) for Research of the European Commission, under the FP7 FET-Proactive Call 8 - DyMCS, Grant Agreement TOPDRIM, number FP7-ICT-318121.

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