Lower bounds for computations with the floor operation

Yishay Mansour, Baruch Schieber, Prasoon Tiwari

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


We prove an Ω(√log n) lower bound on the depth of any decision tree with operations {+, −, *, /, ⌊·⌋, <}, that decides whether an integer is a perfect square, for any n-bit integer. We then extend the arguments to obtain the same lower bound on the time complexity of any RAM program with operations {+, −, *, /, ⌊·⌋, <} that solves the problem. Our proof technique can be used to derive lower bounds for many other problems. Another related result is described in a companion paper ([IBM Research Report RC 14271], [Proceedings of the 29th FOCS]).

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 16th International Colloquium, Proceedings
EditorsMariangiola Dezani-Ciancaglini, Simonetta Ronchi Della Rocca, Giorgio Ausiello
PublisherSpringer Verlag
Number of pages15
ISBN (Print)9783540513711
StatePublished - 1989
Externally publishedYes
Event16th International Colloquium on Automata, Languages and Programming, 1989 - Stresa, Italy
Duration: Jul 11 1989Jul 15 1989

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume372 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Colloquium on Automata, Languages and Programming, 1989

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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