Tim Boykett

Strongly Universal Reversible Gate Sets

It is well-known that the Toffoli gate and the negation gate together yield a universal gate set, in the sense that every permutation of

Rectangular groupoids and related structures

\{0,1\}^n

Units in Near-Rings

can be implemented as a composition of these gates. Since every bit operation that does not use all of the bits performs an even permutation, we need to use at least one auxiliary bit to perform every permutation, and it is known that one bit is indeed enough. Without auxiliary bits, all even permutations can be implemented. We generalize these results to non-binary logic: If

The Multiplicative Automorphisms of a Finite Nearfield, with an Application

A

DIFFERENCE METHODS AND FERRERO PAIRS

is a finite set of odd cardinality then a finite gate set can generate all permutations of

Finite generating sets for reversible gate sets under general conservation laws

A^n

ℐ2 RADICAL IN AUTOMATA NEARRINGS

for all

Seminearrings of Polynomials Over Semifields: A Note on Blackett’s Fredericton Paper

n

Efficient exhaustive listings of reversible one dimensional cellular automata

, without any auxiliary symbols. If the cardinality of

Conservation Laws in Rectangular CA.

A