Loopless algorithms to generate maximum length gray cycles wrt. k-character substitutions.

Given a binary word relation τ onto A ⁎ and a finite language X ⊆ A ⁎ , a τ -Gray cycle over X consists in a permutation (w [ i ]) 0 ≤ i ≤ | X | − 1 of X such that each word w [ i ] is an image under τ of the previous word w [ i − 1 ]. We define the complexity measure λ A , τ (n) , equal to the largest cardinality of a language X having words of length at most n , and st. some τ -Gray cycle over X exists. The present paper is concerned with τ = σ k , the so-called k -character substitution, st. (u , v) ∈ σ k holds if, and only if, the Hamming distance of u and v is k. We present loopless (resp., constant amortized time) algorithms for computing specific maximum length σ k -Gray cycles. [ABSTRACT FROM AUTHOR]