Measuring linguistic complexity in Chinese: An information-theoretic approach

Linguistic complexity, encompassing both structural components and cognitive difficulty, is a crucial area of study in linguistics. While research has focused on English and European languages, Chinese, with its unique logographic system and isolating nature, has received less attention. Existing complexity metrics for Chinese require improvement; many are laborious to apply, prone to subjectivity, or lack cross-linguistic applicability. This study addresses these shortcomings by introducing Kolmogorov complexity, an information-theoretic method. Kolmogorov complexity measures the shortest possible description of a string; shorter descriptions indicate less information and thus lower complexity. This approach offers objective, holistic measurement across micro- and macro-structural levels, requiring no a priori feature tagging. The study aims to examine the reliability and validity of Kolmogorov complexity in measuring Chinese linguistic complexity by comparing it to other established metrics and exploring its ability to reveal inherent language features.

Previous research on linguistic complexity has primarily focused on English and other European languages, employing various metrics at lexical and syntactic tiers. These metrics often measure quantity, length, or ratios of linguistic units. However, limited work exists on measuring Chinese complexity. Some studies have adapted metrics designed for other languages to Chinese, while others have attempted to create Chinese-specific metrics. Despite these efforts, several issues remain: the use of numerous potentially collinear metrics; the laborious and subjective nature of a priori feature tagging; and the limited cross-linguistic comparability of some metrics. This paper addresses these limitations by proposing a more generalizable, objective method.

This study used a corpus of 480 PhD theses (approximately 58.4 million Chinese characters) from various disciplines, cleaned to remove non-Chinese characters and punctuation (except full stops). Three Kolmogorov complexity metrics were calculated: Morphological Complexity Score (MCS), Syntactic Complexity Score (SCS), and Adjusted Overall Complexity Score (AOCS). MCS involved randomly deleting 10% of characters, compressing both original and distorted texts, and calculating the compression ratio. SCS followed a similar process but with word deletion. AOCS used linear regression to model the relationship between the original and compressed text sizes, with residuals representing complexity. For comparison, 18 additional metrics from previous studies were employed, covering character, lexical, syntactic, and collocation levels. Spearman's rank correlation and Mann-Whitney U tests were used to analyze the data, due to non-normal distribution of most metrics. The R programming language, along with specialized tools (GUN zip, L2C-Rater, CTAP for Chinese, and CLRA), was used for data processing and analysis.

The Mann-Whitney U tests showed no significant differences in Kolmogorov complexity metrics between two randomly divided subgroups, indicating internal consistency. Correlation analysis revealed strong correlations between the three Kolmogorov complexity metrics (MCS, SCS, and AOCS). MCS showed strong positive correlations with character and lexical diversity metrics but a weak negative correlation with lexical density. SCS exhibited positive correlations with length-based and depth-based syntactic metrics but no significant correlation with ratio-based ones. All collocation metrics showed strong negative correlations with SCS. These results indicate that Kolmogorov complexity aligns well with traditional metrics, capturing different aspects of Chinese linguistic complexity. Cross-linguistic comparisons with nine European languages revealed that Chinese had a significantly higher MCS (reflecting morphological richness) and lower SCS (reflecting syntactic flexibility), supporting the validity of the Kolmogorov metrics. Further comparisons between high and low proficiency Chinese L2 learners showed that Kolmogorov complexity could distinguish between proficiency levels.

The strong correlations between the Kolmogorov complexity metrics and traditional metrics demonstrate the reliability of the proposed approach. The trade-off between MCS and SCS aligns with the Principle of Least Effort, suggesting that simplification in one area (e.g., morphology) is often compensated for by increased complexity in another (e.g., syntax). The findings support the interpretation of MCS as a measure of character and lexical richness and SCS as a measure of syntactic complexity related to sentence length and structural depth. The cross-linguistic and L1/L2 comparisons validated the approach, showcasing its ability to capture unique features of Chinese and discriminate between language proficiency levels. These results suggest the potential of Kolmogorov complexity as a robust and objective method for measuring linguistic complexity in Chinese.

This study successfully demonstrated the reliability and validity of Kolmogorov complexity for measuring linguistic complexity in Chinese. The three metrics—MCS, SCS, and AOCS—provide a concise yet comprehensive assessment, capturing key aspects of Chinese linguistic structure. The findings offer a promising tool for future quantitative analysis of Chinese language use, second language acquisition research, and proficiency assessment. Future research could explore more fine-grained metrics, extend the Kolmogorov system to other linguistic tiers (semantic, pragmatic), and use different units for morphological distortion (e.g., character strokes) to refine the methodology.

The study's limitations include the use of Chinese characters as the basic unit in morphological distortion, potentially causing overlap between MCS and SCS. Additionally, fine-grained syntactic metrics were not included in the comparison. Finally, the validation utilized an existing system of morphological, syntactic, and overall complexity metrics, and future work could explore expansions to other tiers.