Race Against the Teens – Benchmarking Mechanized Math on Pre-university Problems

Matsuzaki, Takashi; Iwane, Hidenao; Kobayashi, Munehiro; Zhan, Yiyang; Fukasaku, Ryoya; Kudo, Jumma; Anai, Hirokazu; Arai, Noriko

doi:10.1007/978-3-319-40229-1_15

Cited by 3 publications

(2 citation statements)

References 7 publications

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“…The problems are divided according to the source of the problems; IMO problems were taken from past International Mathematical Olympiads, Univ problems were from entrance exams of Japanese universities, and Chart problems were from a popular math practice book series. Please refer to another paper [16] on the ToroboMath benchmark for the details of the problems. The type reconstruction and formula simplification procedures presented in Sect.…”

Section: Methodsmentioning

confidence: 99%

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Formula Simplification via Invariance Detection by Algebraically Indexed Types

Matsuzaki

Fujita

2022

Automated Reasoning

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We describe a system that detects an invariance in a logical formula expressing a math problem and simplifies it by eliminating variables utilizing the invariance. Pre-defined function and predicate symbols in the problem representation language are associated with algebraically indexed types, which signify their invariance property. A Hindley-Milner style type reconstruction algorithm is derived for detecting the invariance of a problem. In the experiment, the invariance-based formula simplification significantly enhanced the performance of a problem solver based on quantifier-elimination for real-closed fields, especially on the problems taken from the International Mathematical Olympiads.

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Section: Methodsmentioning

confidence: 99%

“…This work is a part of the development of the Todai Robot Math Problem Solver (henceforth ToroboMath) [13][14][15][16]. Figure 2 presents an overview of the system.…”

Section: Todai Robot Math Solver and Problem Librarymentioning

confidence: 99%

Formula Simplification via Invariance Detection by Algebraically Indexed Types

Matsuzaki

Fujita

2022

Automated Reasoning

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Can an A.I. win a medal in the mathematical olympiad? – Benchmarking mechanized mathematics on pre-university problems1

Matsuzaki

Iwane

Kobayashi

et al. 2018

AIC

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Language Processing of Mathematical Problem Text

Matsuzaki¹

2017

Philosophy of Science

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This paper describes a computer system for solving pre-university mathematical problems written in Japanese. At the core of its language processing mechanism is a formal grammar, with which a semantic representation is derived from a sentence. The development process of the grammar is explained in detail. Finally, several observations are provided regarding the current research field of artificial intelligence and language processing.

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Race Against the Teens – Benchmarking Mechanized Math on Pre-university Problems

Cited by 3 publications

References 7 publications

Formula Simplification via Invariance Detection by Algebraically Indexed Types

Formula Simplification via Invariance Detection by Algebraically Indexed Types

Can an A.I. win a medal in the mathematical olympiad? – Benchmarking mechanized mathematics on pre-university problems1

Language Processing of Mathematical Problem Text

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