Turing Tumble Is P(SPACE)-Complete

Turing Tumble is Turing-Complete

“…As mentioned, requiring a fixed, finite number of TT pieces results in a device no more powerful than a finite-state machine. However, if we allow a different finite number of pieces for each input size, as we do with circuits, then every finite-sized computer can be simulated as shown in Section 3, and as shown previously with interesting complexity results [5].…”

“…More recently, Johnson [5] investigates the complexity of TT itself, and shows that the TT decision problem (do any marbles ever reach a particular interceptor) is P-Complete via the Circuit Value Problem, and PSpace complete when an exponential number of marbles is allowed. Again, there is not an extension to universal computation, but instead to a larger finite board and piece supply.…”

“…This construction is extremely inefficient. Finite computation can be achieved from the much more efficient reduction of Johnson [5], showing that TT is P-complete via reduction from the Circuit Value Problem. The inefficient approach is presented here because the basic ideas of the read-branch-write loop are used in the next section.…”