Arithmetic expression construction

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...

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Main Authors: Alcock, L (Author), Bosboom, J (Author), Chen, C (Author), Epstein, R (Author), Hirschfeld, L (Author), Lynch, J (Author), Zhang, L (Author), Asif, S (Author), Brunner, J (Author), Demaine, ED (Author), Hesterberg, A (Author), Hu, W (Author), Scheffler, S (Author)
Format: Article
Language:English
Published: 2022-07-22T14:19:40Z.
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Online Access:Get fulltext
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042 |a dc 
100 1 0 |a Alcock, L  |e author 
700 1 0 |a Bosboom, J  |e author 
700 1 0 |a Chen, C  |e author 
700 1 0 |a Epstein, R  |e author 
700 1 0 |a Hirschfeld, L  |e author 
700 1 0 |a Lynch, J  |e author 
700 1 0 |a Zhang, L  |e author 
700 1 0 |a Asif, S  |e author 
700 1 0 |a Brunner, J  |e author 
700 1 0 |a Demaine, ED  |e author 
700 1 0 |a Hesterberg, A  |e author 
700 1 0 |a Hu, W  |e author 
700 1 0 |a Scheffler, S  |e author 
245 0 0 |a Arithmetic expression construction 
260 |c 2022-07-22T14:19:40Z. 
856 |z Get fulltext  |u https://hdl.handle.net/1721.1/143959 
520 |a 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. 
546 |a en 
655 7 |a Article 
773 |t 10.4230/LIPIcs.ISAAC.2020.12 
773 |t Leibniz International Proceedings in Informatics, LIPIcs