Arithmetic expression construction
Name
LIPIcs-ISAAC-2020-12.pdf
Description
Published version
Size
584.38 KB
Format
Adobe PDF
Checksum (MD5)
d33ee04990d6b7f3731872b0d2473bf4
Author(s)
Alcock, L
Bosboom, J
Chen, C
Epstein, R
Hirschfeld, L
Lynch, J
Zhang, L
Asif, S
Brunner, J
Demaine, ED
Date Issued
December 1, 2020
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Citation
Alcock, L, Bosboom, J, Chen, C, Epstein, R, Hirschfeld, L et al. 2020. "Arithmetic expression construction." Leibniz International Proceedings in Informatics, LIPIcs, 181.
Version
Final published version
Abstract
When can n given numbers be combined using arithmetic operators from a given subset of {+,−,×,÷} to obtain a given target number? We study three variations of this problem of Arithmetic Expression Construction: when the expression (1) is unconstrained; (2) has a specified pattern of parentheses and operators (and only the numbers need to be assigned to blanks); or (3) must match a specified ordering of the numbers (but the operators and parenthesization are free). For each of these variants, and many of the subsets of {+,−,×,÷}, we prove the problem NP-complete, sometimes in the weak sense and sometimes in the strong sense. Most of these proofs make use of a rational function framework which proves equivalence of these problems for values in rational functions with values in positive integers.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 3.0 unported license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.ISAAC.2020.12
