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Do there exists reversible gate sets of intermediate growth?

Suppose that $f_{1},...,f_{k}:\{0,1\}^{r}\rightarrow\{0,1\}^{r}$ are bijective functions. For all $n\geq r$, let $G_{f_{1},...,f_{k};r}=\subseteq S(\{0,1\}^{n})$ be the subgroup generated by i. the ...
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1answer
45 views

Counting reversibly using few FullAdders and little work space

Given N bits on a reversible computer, I want to compute their Hamming weight (into a binary register) while using a minimal number of FullAdder circuits (takes 3 bits, outputs their sum as 2 bits) ...
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40 views

What is reversible automaton and how it works? [closed]

I have not understood how reversibility works in case of an automaton. Kindly explain.
4
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1answer
317 views

Why don't the critters ever age?

So the two-dimensional reversible cellular automaton Critters (which you can simulate online at https://dmishin.github.io/js-revca/index.html#) on the Torus does not seem to follow the second law of ...
2
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48 views

Which invertible linear transformations can be computed reversibly without ancilla/garbage bits just as easily as they can be computed irreversibly?

Suppose that $L:F_{2}^{n}\rightarrow F_{2}^{n}$ is an invertible linear transformation. Then define $w(L)$ to be the gate count of the smallest reversible circuit on $n$ bits without ancilla/garbage ...
10
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1answer
175 views

Program inversion algorithms for higher-order programs

The term program inversion has multiple shades of meaning, but probably got started with J. McCarthy's 1956 work The Inversion of Functions Defined by Turing Machines in the context of AI. By now ...
13
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1answer
291 views

Parallel Pebble Game on a Line

In the pebble game on a line there are N+1 nodes labelled 0 through N. The game starts with a pebble on node 0. If there is a pebble on node i, you can add or remove a pebble from node i+1. The goal ...