Show simple item record

dc.contributor.authorMoshkov, Mikhail
dc.date.accessioned2022-01-12T12:51:16Z
dc.date.available2022-01-12T12:51:16Z
dc.date.issued2022-01-04
dc.identifier.urihttp://hdl.handle.net/10754/674930
dc.description.abstractIn 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.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2201.01013.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectdeterministic decision trees
dc.subjectnondeterministic decision trees
dc.subjecttime complexity
dc.subjectspace complexity
dc.subjectcomplexity classes
dc.subjecttime-space trade-off
dc.titleTime and space complexity of deterministic and nondeterministic decision trees
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.identifier.arxivid2201.01013
kaust.personMoshkov, Mikhail
refterms.dateFOA2022-01-12T12:53:00Z


Files in this item

Thumbnail
Name:
Preprintfile1.pdf
Size:
261.5Kb
Format:
PDF
Description:
Pre-print

This item appears in the following Collection(s)

Show simple item record