Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Độ khó và tính không xấp xỉ của việc tối thiểu hóa các chuỗi phân biệt thích ứng
Tóm tắt
Một chuỗi phân biệt thích ứng (ADS) có thể được sử dụng để xác định trạng thái ban đầu chưa biết của một máy trạng thái hữu hạn (FSM). Từ lâu, người ta đã biết rằng kiểm tra sự tồn tại của một ADS cho một FSM, và tìm một ADS cho một FSM khi tồn tại, có thể được thực hiện trong thời gian đa thức. Tuy nhiên, vấn đề tìm một ADS tối thiểu vẫn chưa được nghiên cứu cho đến nay. Việc tạo ra một ADS tối thiểu đặc biệt có động lực khi một ADS như vậy được sử dụng nhiều lần, chẳng hạn như để xây dựng một chuỗi thử nghiệm. Chúng tôi giới thiệu một số tiêu chí để định nghĩa một ADS tối thiểu và cho thấy rằng vấn đề tạo ra một ADS tối thiểu theo những tiêu chí này là NP-đầy đủ. Ngoài ra, chúng tôi cung cấp các kết quả không xấp xỉ cho những vấn đề khó khăn này và chỉ ra rằng không chỉ việc quyết định mà còn việc xấp xỉ một ADS tối thiểu như vậy là một vấn đề khó khăn. Chúng tôi đã sửa đổi thuật toán tạo ADS tồn tại duy nhất trong thời gian đa thức và cho thấy thí nghiệm rằng những sửa đổi này tạo ra các ADS giảm thiểu. Chúng tôi cũng xác thực động lực của việc tối thiểu hóa ADS bằng cách trình bày kết quả thí nghiệm về tác động của việc sử dụng các ADS giảm thiểu để tạo ra các chuỗi thử nghiệm.
Từ khóa
#chuỗi phân biệt thích ứng #máy trạng thái hữu hạn #ADS tối thiểu #NP-đầy đủ #thuật toán tạo ADSTài liệu tham khảo
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