Real number computation through Gray code embedding

Real number computation through Gray code embedding

Logic for Gray Code Computation

Gray code is a well-known binary number system such that neighboring values differ in one digit only. Tsuiki (2002) has introduced Gray code to the field of real number computation. He assigns to each number a unique 1⊥-sequence, i.e., a (possibly infinite) sequence of {−1, 1,⊥} such that at most one copy of ⊥ (meaning undefinedness) is contained in the sequence not as the last character. In th...

Gray code for permutations with a fixed number of cycles

We give the first Gray code for the set of n-length permutations with a given number of cycles. In this code, each permutation is transformed into its successor by a product with a cycle of length three, which is optimal. If we represent each permutation by its transposition array then the obtained list still remains a Gray code and this allows us to construct a constant amortized time (CAT) al...

Gray Code Representation of Exa t Real Numbers

Gray Code Compression

An n-bit (cyclic) Gray code is a (cyclic) sequence of all n-bit strings such that consecutive strings differ in a single bit. We describe an algorithm which for every positive integer n constructs an n-bit cyclic Gray code whose graph of transitions is the d-dimensional hypercube Qd if n = 2, or a subgraph of Qd if 2 d−1 < n < 2. This allows to compress sequences that follow this code so that o...