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  1. Free, publicly-accessible full text available January 1, 2025
  2. Free, publicly-accessible full text available January 1, 2024
  3. Large language models have shown a propensity for generating correct, multi-line programs from natural language prompts. Given past findings highlighting that bugs and patches can be distinguished by predictability according to simple language models, it is natural to ask if modern, large neural options lend themselves especially well to program repair without any calibration. We study this in the context of one-line bugs, providing a series of models of varying scales (from 160M to 12B parameters) with the context preceding a buggy line in 72 Java and Python programs and analyze the rank at which the correct patch (and original buggy line) is generated, if at all. Our results highlight a noticeable correlation of model size with test-passing accuracy and patch ranking quality, as well as several other findings related to the differences between the two languages and the propensity for especially the largest models to generate candidate patches that closely resemble (if not exactly match), the original developer patch. 
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  9. Satisfiability (SAT) solving has become an important technology in computer-aided mathematics with various successes in number and graph theory. In this paper we apply SAT solvers to color infinitely long strips in the plane with a given height and number of colors. The coloring is constrained as follows: two points that are exactly unit distance apart must be colored differently. To finitize the problem, we tile the strips and all points on a tile have the same color. We evaluated our approach using two different tile shapes: squares and hexagons. The visualization of bounded height strips using 3 to 6 colors reveal patterns that are similar to the best known lower bounds for infinite strips. Our method can be a useful tool for mathematicians to search for patterns that can be generalized to infinite strips and allowed us to increase the lower bound for the strip height with 5 colors to an improved height of 1.700084. 
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