One Approach to Decoding Monotone Logical Function

• Published in: Automation and remote control Vol. 83; no. 10; pp. 1600 - 1607
• Main Authors: Dragunov, N. A., Djukova, E. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.10.2022; Springer Nature B.V
• Subjects: Algorithms; Asymptotic properties; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Computer-Aided Engineering (CAD; Control; Mathematics; Mathematics and Statistics; Mechanical Engineering; Mechatronics; Robotics; Systems Theory; Thematic Issue; dualization over the product of k-valued chains; Shannon-optimal decoding algorithm; asymptotically optimal decoding algorithm; lower unit of a monotone logical function; maximal frequent element; minimal infrequent element; upper zero of monotone logical function
• ISSN: 0005-1179; 1608-3032
• DOI: 10.1134/S00051179220100125

We consider the problem of decoding a two-valued monotone function defined on a -valued -dimensional cube. The traditional approach to solving this problem is to construct a Shannon-optimal algorithm. The Shannon-optimal decoding algorithm has minimal “worst-case” complexity (efficient for the most difficult case). The authors propose and study an approach to the decoding problem based on the application of an asymptotically optimal dualization algorithm over the product of -valued chains. The asymptotically optimal decoding of the function is aimed at the “typical case” (typical version of the problem). The conditions for the applicability of the traditional and new approaches are experimentally revealed.