Work

Arithmetic Expression Construction

Year: 2020

Type: preprint

Abstract: When can $n$ given numbers be combined using arithmetic operators from a given subset of $\{+, -, \times, ÷\}$ 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 $\{+,-,\times,÷\}$, 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.

Source: arXiv (Cornell University)

DOI: 10.4230/lipics.isaac.2020.12

Authors: Alcock, Leo, Asif, Sualeh, Bosboom, Jeffrey, Brunner, Josh, Chen, Charlotte, Demaine, Erik D., Epstein, Rogers, Hesterberg, Adam, Hirschfeld, Lior, Hu, William, Lynch, Jayson, Scheffler, Sarah, Zhang, Lillian

Institutions: Harvard University, Massachusetts Institute of Technology, MIT Computer Science and Artificial Intelligence Laboratory, Boston University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: JST-Mirai Program

OpenAlex ID: W3114936134

Cites: 12

Cited by: 1

Related to: 10