2022/01/04 by Mikhail Moshkov, Moshkov, Mikhail
Computer Science · Mathematics · #Algorithm #Artificial intelligence #Binary decision diagram #Bounded function #Combinatorics #Computational Complexity (cs.CC) #Computer science #Decision problem #Decision tree #Decision tree model #Discrete mathematics #FOS: Computer and information sciences #Logarithm #Mathematics #NP #Nondeterministic algorithm #Rough Sets and Fuzzy Logic #Set (abstract data type) #Time complexity #Turing machine #cs.CC
paper · pdf · doi:10.48550/arxiv.2201.01013
published in arXiv (Cornell University) (Cornell University)
arxiv created 2022/01/04 · openalex publication_date 2022/01/04 · arxiv updated 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a problem over information system which is described by a finite number of attributes and a mapping corresponding a decision to each tuple of attribute values. As algorithms for problem solving, we use deterministic and nondeterministic decision trees. As time and space complexity, we study the depth and the number of nodes in the decision trees. In the worst case, with the growth of the number of attributes in the problem description, (i) the minimum depth of deterministic decision trees grows either almost as logarithm or linearly, (ii) the minimum depth of nondeterministic decision trees either is bounded from above by a constant or grows linearly, (iii) the minimum number of nodes in deterministic decision trees has either polynomial or exponential growth, and (iv) the minimum number of nodes in nondeterministic decision trees has either polynomial or exponential growth. Based on these results, we divide the set of all infinite binary information systems into five complexity classes, and study for each class issues related to time-space trade-off for decision trees.