Extension of codes and algorithms for alternative codes and codes of bounded words

Abstract

In this paper, we consider properties of +-unambiguous products, alternative codes and languages of bounded words (-languages). A new type of codes (-codes or codes of bounded words) is defined and an algorithm to determine whether a-recognizable language is a-code is established. This provides a new algorithm to verify for alternative codes whose complexity is smaller than the complexity of the previous one. A relationship between codes, alternative codes and-codes is considered. This shows that-codes is an extension of traditional codes and alternative codes. Tóm tắt. Bài báo xem xét một số tính chất của +-tích không nhập nhằng, mã luân phiên và ngôn ngữ của các từ định biên (-ngôn ngữ). Từ đó, xây dựng một hệ mã mới-mã của các từ định biên (-mã) cùng với thuật toán kiểm định một-ngôn ngữ đoán nhận được có là-mã hay không. Nhờ thuật toán kiểm định-mã, cho phép nhận được một thuật toán kiểm định mã luân phiên mới, làm giảm rõ rệt về độ phức tạp. Ngoài ra, bài báo còn đề xuất một sơ đồ phân lớp giữa ba lớp mã-mã, mã luân phiên và-mã, cho thấy-mã được xem như là sự mở rộng của mã và mã luân phiên.

B-Codes and their relationship with alternative codes

“…For more details of alternative codes, b-codes and their subclasses we refer to [5,6,7,8,9,10,17,18,19,20]. Now we formulate, in the form of lemmas, several facts which will be useful in the sequel.…”

“…Different modifications of such a product may lead to different extensions of the notion of codes. Such an approach has been proposed by P. T. Huy et al which deals with the so-called even alternative codes and codes of bounded words (or ♦-codes, for short) [5,6,7,10,17,18,19,20]. They demonstrated the importance characterizations as well as algorithms to test for these classes.…”

“…For simplicity, ♦-codes, weak left ♦-codes, weak right ♦-codes and strict ♦-codes in [17,18] are called simply respectively b-codes, left b-codes, right b-codes and strict b-codes instead. Recently, in [8,9,19,20], the authors proposed some classes of codes which concern alternative codes and b-codes. Several interesting characteristic properties and algorithms to test for such codes were established.…”

“…The final section discusses the problem investigations and presents a summary of the results obtained. Our work is motivated by the idea to define b-codes by equivalent factorizations on a b-language, and the way to solve the problem for b-codes as well as their well-known subclasses [6,17,18,19].…”

Characterizations for Several Classes of Alternative Codes

“…For simplicity, even alternative codes, weak left alternative codes, weak right alternative codes and alternative codes in [6,12] are called simply respectively alternative codes, left alternative codes, right alternative codes and strict alternative codes instead. Recently, in [4,11,12], the authors proposed some classes of codes which concern alternative codes. Several interesting characteristic properties and algorithms to test for such codes were established.…”