Academic dishonesty is met with zero tolerance in higher education, yet plagiarism has become increasingly prevalent in the era of online teaching and learning. Automatic Question Generation (AQG) presents a potential solution to mitigate copying by creating unique questions for each student. Additionally, AQG can provide a vast array of practice questions. Our AQG focuses on generating logical equivalence questions for Discrete Mathematics, a foundational course for first-year computer science students. A literature review reveals that existing AQGs for this type of question generate all propositions that meet user-defined constraints, resulting in inefficiencies and a lack of uniform question difficulty. To address this, we propose a new approach that defines logical equivalence questions using a formal language, translates this language into two sets of generation rules, and develops a linear-time algorithm for question generation. We evaluated our AQG through two experiments. The first involved a group of students completing questions generated by our system. Statistical analysis shows that the accuracy of these questions is comparable to that of textbook questions. The second experiment assessed the number of steps required to solve our generated questions, textbook questions, and those generated by multiple large language models. The results indicated that the difficulty of our questions was similar to that of textbook questions, confirming the quality of our AQG.

The increase in academic dishonesty cases among college students has raised concern, particularly due to the shift towards online learning caused by the pandemic. We aim to develop and implement a method capable of generating tailored questions for each student. The use of Automatic Question Generation (AQG) is a possible solution. Previous studies have investigated AQG frameworks in education, which include validity, user-defined difficulty, and personalized problem generation. Our new AQG approach produces logical equivalence problems for Discrete Mathematics, which is a core course for year-one computer science students. This approach utilizes a syntactic grammar and a semantic attribute system through top-down parsing and syntax tree transformations. Our experiments show that the difficulty level of questions generated by our AQG approach is similar to the questions presented to students in the textbook [1]. These results confirm the practicality of our AQG approach for automated question generation in education, with the potential to significantly enhance learning experiences.