ON omiga-Generators and Codes

摘要

let C be a class of codes. Given a rational language L, deciding whether L sup omiga has an omiga-generator in C is still an open problem except if C denotes the set of prefix codes [9]. Here, we restict our investigations to omiga-languages L sup omiga whose greatest omiga-generator is a free submonoid. For such omiga-languages, we porve that there exists an omiga-generator in the sets of pure codes, circular codes, suffix codes or finite omiga-codes if and only if the root of the greatest omiga-generator is itself one. Furthemore, in the very precise case where the rot of the greatest omiga-generator is a three-element code, using a characteristic property of them [5,6], we characterize the case where W sup omiga=L sup omiga some omiga-code W-finite or infinite.