Synthesis of Geometry Proof Problems

Alvin, Chris; Gulwani, Sumit; Majumdar, Rupak; Mukhopadhyay, Supratik

doi:10.1609/aaai.v28i1.8745

Cited by 21 publications

(6 citation statements)

References 10 publications

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“…Nevins pointed out that the forward chaining method [nevins1975plane] can also be effective by efficiently representing the known conditions of the problem and limiting the typical application of those conditions. The development of geometry problem solving has led to the emergence of various downstream tasks, including geometry problem formalization [15,36],geometric knowledge extraction [38,37,51,20,59], geometric diagram parsing [40,55,45], geometric theorem proving [53,16,25], and geometry problem solving [41,58,1,2,39,52].…”

Section: Related Workmentioning

confidence: 99%

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

Zhuang

Huang

et al. 2019

Mathematical Biosciences and Engineering

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The crystallization kinetics and melting behavior of nylon 10,10 in neat nylon 10,10 and in nylon 10,10 -montmorillonite (MMT) nanocomposites were systematically investigated by differential scanning calorimetry. The crystallization kinetics results show that the addition of MMT facilitated the crystallization of nylon 10,10 as a heterophase nucleating agent; however, when the content of MMT was high, the physical hindrance of MMT layers to the motion of nylon 10,10 chains retarded the crystallization of nylon 10,10, which was also confirmed by polarized optical microscopy. However, both nylon 10,10 and nylon 10,10 -MMT nanocomposites exhibited multiple melting be-havior under isothermal and nonisothermal crystallization conditions. The temperature of the lower melting peak (peak I) was independent of MMT content and almost remained constant; however, the temperature of the highest melting peak (peak II) decreased with increasing MMT content due to the physical hindrance of MMT layers to the motion of nylon 10,10 chains.

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Section: Related Workmentioning

confidence: 99%

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

Zhuang

Huang

et al. 2019

Mathematical Biosciences and Engineering

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“…Nevins pointed out that the forward chaining method [10] can also be effective by efficiently representing the known conditions of the problem and limiting the typical application of those conditions. The development of geometry problem solving has led to the emergence of various downstream tasks, including geometry problem formalization [18,19], geometric knowledge extraction [20][21][22][23][24], geometric diagram parsing [25][26][27], geometric theorem proving [28][29][30], and geometry problem solving [31][32][33][34][35][36]. Such methods are essentially a search-based method, which requires humans to predefine the search space or provide the system with a priori knowledge, namely theorems.…”

Section: Related Workmentioning

confidence: 99%

FGeo-SSS: A Search-Based Symbolic Solver for Human-like Automated Geometric Reasoning

Zhang,

Zhu,

et al. 2024

Symmetry

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Geometric problem solving (GPS) has always been a long-standing challenge in the fields of automated reasoning. Its problem representation and solution process embody rich symmetry. This paper is the second in a series of our works. Based on the Geometry Formalization Theory and the FormalGeo geometric formal system, we have developed the Formal Geometric Problem Solver (FGPS) in Python 3.10, which can serve as an interactive assistant or as an automated problem solver. FGPS is capable of executing geometric predicate logic and performing relational reasoning and algebraic computation, ultimately achieving readable, traceable, and verifiable automated solutions for geometric problems. We observed that symmetry phenomena exist at various levels within FGPS and utilized these symmetries to further refine the system’s design. FGPS employs symbols to represent geometric shapes and transforms various geometric patterns into a set of symbolic operation rules. This maintains symmetry in basic transformations, shape constructions, and the application of theorems. Moreover, we also have annotated the formalgeo7k dataset, which contains 6981 geometry problems with detailed formal language descriptions and solutions. Experiments on formalgeo7k validate the correctness and utility of the FGPS. The forward search method with random strategy achieved a 39.71% problem-solving success rate.

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“…There are several challenges in synthesizing new visual programming tasks with the above mentioned features, including the following: (i) current techniques for synthesizing visual programming tasks do not adapt to student attempts [1]; (ii) the mapping from the space of visual tasks to their solution codes is highly discontinuous as shown in [1], and hence task mutation based techniques are ineffective [27,37]; (iii) the space of possible tasks and their solutions is potentially unbounded, and hence techniques that rely on exhaustive enumeration are intractable [2,4,37].…”

Section: Key Challenges and Our Contributionsmentioning

confidence: 99%

“…Since S quiz ∈ SUBSTRUCTS(S in,⋆ ) by the design of Stage 1, we begin by picking C seed from the set REDCODES(C in,⋆ | S quiz ). 4 The methodology of [1] provides us multiple code mutations of C seed . The extent to which these code mutations differ from C seed and C in,⋆ is controlled by the constraints imposed based on the values of the boolean variables, conditionals, and action blocks (move, turnLeft, turnRight, pickMarker, putMarker) of C seed , as well as constraints on the size of the obtained code.…”

Section: Stage 2: Synthesizingmentioning

confidence: 99%

Adaptive Scaffolding in Block-Based Programming via Synthesizing New Tasks as Pop Quizzes

Ghosh

Tschiatschek

Devlin

et al. 2022

Lecture Notes in Computer Science

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Block-based programming environments are increasingly used to introduce computing concepts to beginners. However, novice students often struggle in these environments, given the conceptual and open-ended nature of programming tasks. To effectively support a student struggling to solve a given task, it is important to provide adaptive scaffolding that guides the student towards a solution. We introduce a scaffolding framework based on pop quizzes presented as multi-choice programming tasks. To automatically generate these pop quizzes, we propose a novel algorithm, PQUIZSYN. More formally, given a reference task with a solution code and the student's current attempt, PQUIZSYN synthesizes new tasks for pop quizzes with the following features: (a) Adaptive (i.e., individualized to the student's current attempt), (b) Comprehensible (i.e., easy to comprehend and solve), and (c) Concealing (i.e., do not reveal the solution code). Our algorithm synthesizes these tasks using techniques based on symbolic reasoning and graphbased code representations. We show that our algorithm can generate hundreds of pop quizzes for different student attempts on reference tasks from Hour of Code: Maze Challenge [11] and Karel [9]. We assess the quality of these pop quizzes through expert ratings using an evaluation rubric. Further, we have built an online platform for practicing block-based programming tasks empowered via pop quiz based feedback, and report results from an initial user study.

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Synthesis of Geometry Proof Problems

Cited by 21 publications

References 10 publications

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

FGeo-SSS: A Search-Based Symbolic Solver for Human-like Automated Geometric Reasoning

Adaptive Scaffolding in Block-Based Programming via Synthesizing New Tasks as Pop Quizzes

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