Kolmogorov complexity metrics in assessing L2 proficiency: An information-theoretic approachKolmogorov complexity metrics in assessing L2 proficiency: An information-theoretic approach

Abstract: Based on 774 argumentative writings produced by Chinese English as a foreign language (EFL) learners, this study examined the extent to which Kolmogorov complexity metrics can distinguish the proficiency levels of beginner, lower-intermediate, and upper-intermediate second language (L2) English learners. Kolmogorov complexity metric is a holistic information-theoretic approach, which measures three facets of linguistic complexity, i.e., overall, syntactic, and morphological complexity simultaneously. To assess its validity in distinguishing L2 proficiency, Kolmogorov complexity metric is compared with traditional syntactic and morphological complexity metrics as well as fine-grained syntactic complexity metrics. Results showed that Kolmogorov overall and syntactic complexity could significantly distinguish any adjacent pair of L2 levels, serving as the best separators explored in the present study. Neither Kolmogorov morphological complexity nor other complexity metrics at both the syntactic and morphological levels can distinguish between all pairs of adjacent levels. Results of correlation analysis showed that Kolmogorov syntactic complexity was not or weakly correlated with all the fine-grained syntactic complexity metrics, indicating that they may address distinct linguistic features and can complement each other to better predict different proficiency levels.

摘要： 本研究基于中国英语学习者撰写的 774 篇议论文，考察 Kolmogorov 复杂度指标能在多大程度上区分初级、中低级和中高级二语英语学习者的水平。Kolmogorov 复杂度是一种整体性的信息论方法，可同时测量语言复杂度的三个方面，即整体、句法和形态复杂度。为检验其区分二语水平的效度，我们将 Kolmogorov 复杂度与传统句法、形态复杂度指标以及细颗粒度句法复杂度指标进行了比较。结果显示，Kolmogorov 整体复杂度和句法复杂度能显著区分任意两个相邻水平，是本研究所考察指标中区分效果最好的。Kolmogorov 形态复杂度以及句法、形态层面的其他复杂度指标，都无法区分所有相邻水平组。相关分析表明，Kolmogorov 句法复杂度与各项细颗粒度句法复杂度指标均不相关或仅弱相关，说明二者可能反映不同的语言特征，可以互为补充，更好地预测学习者水平。