Phase Space Invertible Asynchronous Cellular Automata
Simon Wacker (Karlsruhe Institute of Technology, Germany), Thomas, Worsch (Karlsruhe Institute of Technology, Germany)
TL;DR
This paper explores phase space invertibility in asynchronous cellular automata, demonstrating their ability to simulate Turing machines and establishing the decidability of their invertibility in various dimensions.
Contribution
It introduces the concept of phase space invertible asynchronous cellular automata and proves their computational universality and the decidability of invertibility.
Findings
Each Turing machine can be simulated by such an automaton
Invertibility is decidable in higher dimensions
The paper clarifies reversibility notions for asynchronous automata
Abstract
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call phase space invertible asynchronous cellular automata in more detail. We will show that for each Turing machine there is such a cellular automaton simulating it, and that it is decidable whether an asynchronous cellular automaton has this property or not, even in higher dimensions.
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