Time Complexity of Tape Reduction for Reversible Turing Machines
Studies of reversible Turing machines (RTMs) often differ in their use of static resources such as the number of tapes, symbols and internal states. However, the interplay between such resources and computational complexity is not well-established for RTMs. In particular, many foundational results in reversible computing theory are about multitape machines with two or more tapes, but it is non-obvious what these results imply for reversible complexity theory.
Here, we study how the time complexity of multitape RTMs behaves under reductions to one and two tapes. For deterministic Turing machines, it is known that the reduction from k tapes to 1 tape in general leads to a quadratic increase in time. For k to 2 tapes, a celebrated result shows that the time overhead can be reduced to a logarithmic factor. We show that identical results hold for multitape RTMs.
This establishes that the structure of reversible time complexity classes mirrors that of irreversible complexity theory, with a similar hierarchy.
KeywordsTime Complexity Turing Machine Stick State Tape Head Reversible Complexity
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