Complexity trade-off in agglutinative languages
Wenchao Li (Zhejiang University) †膠着型言語における複雑さのトレードオフ
李文超 (浙江大学)

Abstract
This study utilised 25 treebanks of 16 agglutinative languages across nine language families,
exploring the correlation between morphological richness and word order flexibility.
Morphological richness was measured at moving-average morphological richness and movingaverage mean size of paradigm. Cosine similarity and entropy were employed to capture wordorder flexibility. Statistical analysis revealed that the richer the morphology, the more flexible
the word order. A fairly strong correlation between morphology and syntax was confirmed,
supporting the complexity trade-off hypothesis. Among nine language families, Austronesian,Afroasiatic, Dravidian languages were found morphologically and syntactically less diverse
than Altaic, Indo-Aryan, and Uralic languages. Turkish, Uyghur, Basque, and North Samishowed the most balanced proportions of S, V, O combinations. Further, there are separations
within the same language family, i.e. the Uralic Finnic branch was found more flexible thanFinno-Ugric; the Altaic Mongolic branch was found more rigid than the Turkic branch.
Keywords: morphological richness, word order flexibility, natural language processing,mathematical linguistics
1. Introduction
Human language is a complex, dynamic, and hierarchically organised but regular system(Fenk-Oczlon and Pilz 2021). One such regularity is complex trade-off, i.e. if one component(e.g. phonology, morphology, syntax, semantics) in a language is sophistic, then anothercomponent is likely to be simplified, allowing languages to manifest roughly the same degreeof complexity (Menzerath’s law 1954; Shosted 2006; Sinnemäki 2014; Fenk-Oczlon and Fenk
2014). Complexity trade-off hypothesis has been addressed from a variety of linguistic
components, i.e. phoneme-syllable-word (Coloma 2017), phonology-morphology (Shosted
2006), morphology-syntax (Sapir 1921; Jakobson 1936; McFadden 2003; Koplenig 2017; Yanand Liu 2021; Li, Liu and Xiong 2022). A crucial issue in the trade-off idea resides in: to what
extent that trade-off holds, i.e. is it a case of piece-meal or whole-meal? Among the numbersof correlations, which linguistic component is the key factor? Regarding the first issue, moststudies deemed that trade-off is some-participate, e.g. the more syllable per word, the fewer
phonemes per syllable; the more phonemes per syllable, the fewer morpholo gical cases, themore morphological cases, the more free of word order (Fenk-Oczlon and Fenk 1999; Shosted
2006; Sinnemäki 2008, 2014; Miestamo 2009; Koplenig et al. 2017). In terms of the second
issue, after examining parallel data of translation, Fenk-Oczlon and Pilz (2021) contend thatsyllable complexity is a key factor in the correlations between phoneme inventory size, syllablesize, length of words, length of clauses and population size.
This study targets 16 agglutinative languages, i.e. Basque, North Sami, Estonian, Finnish,† widelia@zju.edu.cn

Hungarian, Japanese, Marathi, Tamil, Telugu, Turkish, Uyghur, Kazakh, Buryat, Wolof,
Indonesian and Coptic. 23 annotated corpora from Universal Dependencies (of spoken, written
and different genres) were analysed. By combining natural language processing technologythat helps tokenisation, lemmatisation, POS and morphological features tagging, dependency
parsing, this study aims to draw an insight of the associations between morphological diversity
and word order flexibility of natural languages. Morphological richness is measured via two
metrics: moving-average morphological richness (MAMR: Čech and Kubát 2018) and moving average mean size of paradigm (MAMSP: Xanthos and Gillis 2010). Cosine similarity (COS )and entropy (ENTR: Shannon 1948, Chen et al. 2016, Bentz et al. 2017, Yan and Liu 2021, Li
et al. 2022) are employed to capture word-order flexibility. Spearman’s rank correlation
coefficient is applied to search for the interactions of the linguistic components.
2. Methodology
2.1 Dataset
25 treebanks were adopted, which involves: a). four Uralic languages: Estonian (twotreebanks), Finnish (two treebanks), North Sami (one treebank), Hungarian (one treebank); b).
four Altaic languages: Buryat (one treebank), Kazakh (one treebank), Turkish (two treebanks),
Uyghur (one treebank); c). two Dravidian languages: Tamil (two treebanks), Telugu (onetreebank); d). one Indo-Aryan language Marathi (one treebank); e). one Afroasiatic Egyptian
language Coptic (one treebank); f). one Niger-Congo Atlantic language Wolof (one treebank);g). one Basque language (one treebank); h). one Austronesian language: Indonesi an (three treebanks); i). Japanese (three treebanks). Table 1 provides the details on the treebanks.

Table 1. Dataset
Treebanks

Text types

Words

Sentences

Treebanks

Text types

Words

Sentences

Basque-BDTNews

121,443

8993

Marathi-UFAL

Wiki, fiction

3,847

466

Buryat-BDT

Fiction, grammar-examples, news

10,185927

Indonesian-PUD

News, wiki

19,446

1,000

Japanese-BCCWJ

Fiction,1,253,903

57,109Indonesian-GSD

Blog, news

122,019

5,598

blog, news

150,243

8,100

Wolof-WTB

bible, wiki

44,2582,107Japanese-PUD

news, wiki

28,7881,000

Uyghur_UDT

Fiction

40236

3,456

Tamil-TTB

News

9,581

600

Indonesian-CSUINews, nonfiction

28,263

1,030

Tamil-MWTT

News

2,584

534

Wolof-WTB

Bible, wiki

44,2582,107

Telugu-MTG

Grammar examples

6,465

1,328

Coptic-Scriptorium

Bible, fiction, nonfiction

55,8582,163

Buryat-BDT

Grammar examples, news, fiction

10,185927

Estonian-EDT

Fiction,news,

438,245

30,968blog,

202,453

15,136

news,

blog,

conference,

nonfiction
JapaneseGSDLUW

academic,

nonfiction
Kazakh-KTB

News, fiction, wiki

10,536

1,078

Finnish-TDT

Fiction,legal,

news,

grammar-examples,

Turkish-Kenet

News, nonfiction

183,555

16,396

Finnish-TDT

Poetry, medical, social, web

19,382

2,122

Turkish-Boun

News, nonfiction

125,212

9,761

North Sami-GiellaNews, nonfiction

26,845

3,122

Hungarian-Szeged

News

42,0321,800

2.2 Metrics
Morphological richness is measured via two metrics: moving-average morphological richness andmoving-average mean size of paradigm. Cosine similarity and entropy were used to capture wordorder flexibility.
2.2.1 Morphological richness
To minimise the influence of the corpus size, this study measured the morphological diversity of eachlanguage text by repeatedly calculating the type-token ratio (TTR) index for a subset of the text andthe average. It further employs Covington and McFall’s (2010) moving average TTR (MATTR) to
calculate the word forms and lemma vocabulary richness. MATTR (W)word form was obtained using
the following formula:
MATTR (W)word form =∑N−W+1Fi
I=1W (N − W + 1)

N is the size of the text, and W is the size of a randomly chosen window. Fi is a number in theextended form for a given window size. Regarding agglutinative languages such as Japanese, Turkish,there are two types of word forms. One is the agglutination of word root (sabishii.PRESENT TENSE ‘lonely’→ sabishikatta.PAST TENSE ‘lonely) and the other is derivation (sabishii ‘lonely → sabishimi‘loneliness’). In terms of inflectional languages, word forms can be inflectional (kind → kinder) and
derivational (kind→kindness). The window size of this study is 500 words. MATTR (W)word form is
the TTR for each window obtained through conjugation. The TTR for each window was obtained bya lemma using a similar formula:
MATTR (W)word lemma =∑N−W+1Li
I=1
W (N − W + 1)

N is the size of the text, and W is the size of a randomly chosen window. Li is the number in theextended form for a constant window size. MATTR (W)word lemma is the TTR for each window by
conjugation. MAMR refers to the differences between word form diversity and lemma diversity. It is
obtained via:
MAMR (W) = MATTR (W)word form − MATTR (W)word lemma
The higher the MAMR (W), the richer the language′s morphology. Another measure for
capturing lexical diversity was the mean size of paradigm (MSP, Xanthos and Gillis 2010). It is
obtained via two steps. First, divide the number of different inflections by the number of lemmas asfollows.
F
MSP = L
Obtain MAMSP as:𝐹𝑖∑N−W+1
I=1

𝐿𝑖
MAMSP = W (N−W+1)

The higher the MAMP and MAMSP values, the richer the morphology of the language.
2.2.2 Word order freedom
There are about 19 linguistic components involving word order (Tsunoda 2009 [1991]). This study
narrowed down the components to the order of S, O, V. Six possible word-order patterning werecounted: SVO, OVS, VSO, VOS, SOV, OSV. Assuming t is the expected value and s is the observed
value, the COS was obtained using the following formula:
COS (s, t) = ∑n∑ni=1 𝑠𝑖 𝑡𝑖

i=1 𝑠𝑖2 ・ ∑n 𝑡 2
i=1 𝑖

The higher the COS (s, t), the greater the degree of flexibility in the word order of the sample. ENTR
was obtained via:
ENTR = − ∑𝑛𝑖=1 𝑡𝑖 × ln 𝑡𝑖
The higher the entropy of a particular language, the higher the word order freedom. This study
examined both main sentences and sub sentences that consists of S, O, V.
3. Results
3.1 The reliability of the measures
To answer the research question 1, after obtaining the four metric values from 25 treebanks,
Spearman’s rank correlation coefficient analysis was performed. Figure 1 (left side) shows the scatterplot of MAMR vs. MAMSP values. The relationship between the metrics fits the regression line.

Figure 1. Scatter plot and regression line with MAMR, MAMSP; COS, ENTR
Further, Spearman’s rank correlation coefficient between MAMR and MAMSP was ρ = 0.909 and p= 0.000. This indicates that the two metrics (MAMR and MAMSP) are capable of capturingmorphological diversity. The Spearman’s rank correlation coefficient between COS and ENTR was
positive and strong, with ρ = 0.747 and p = 0.000. The regression line in Figure 3 (right side) fit the
scatter plots of the correlation. This indicates COS and ENTR are capable to convey word order
flexibility. Research question 1 is answered.
Table 2 provides a closer picture of values on morphological and word order diversity in eachlanguage. As indicated, the Turkic languages, i.e. Uyghur, Kazakh, Turkish present the highest valueof MAMR and MAMSP, indicating that the three languages are morphologically most rich in all
agglutinative languages in target. Then come the Indo-Aryan Marathi, an Indian language, belonging
to the Indo-Aryan branch. Marathi is the only agglutinative language in the Indo-Aryan branch and it
kept three grammatical genders: masculine, feminine and neuter. Other languages such as Urdu, Hindi
are fusional and gender-less. A calculation of MAMR, MAMSP of Urdu and Hindi revealed Marathi
presented the highest value of both morphology and syntax among the Indo-Aryan language. This
inspired us to deduce that agglutinative language is morphologically richer and syntactically morecomplex than fusional languages. The Uralic language family has seen variations, i.e. the Finnic
language (Estonian and Finnish) presented higher MAMR, MAMSP value than Finno-Ugric language(North Sami and Hungarian). Dravidian languages Telugu and Tamil showed medium degree ofmorphological variety. The Atlantic language Wolof, Malayo-Polynesian language Indonesian,Egyptian language Coptic ranked at the end of MAMR and MAMSP values. Japanese was seen tobear the lowest degree of morphological richness.
Table 2. MAMR, MAMSP, COS and ENTR value of each language (total treebanks)
Language family

BranchLanguages

MAMR

MAMSP

COS

ENTR

AltaicTurkicUyghur0.24181.47850.60390.8570

AltaicTurkicKazakh

0.1942

1.33410.58770.8106

AltaicTurkicTurkish0.17891.36000.57560.9074

Indo-European

Indo-Aryan

Marathi0.16781.43440.57040.7434

UralicFinnicEstonian

0.16771.28030.5512

0.6312

UralicFinnicFinnish0.1673

1.29850.55000.8567

AltaicMongolic

Buryat0.16681.27000.55080.7694BasqueBasqueBasque0.15691.24160.54700.7575

UralicFinno-Ugric

North Sami

0.13031.22800.54620.7085

UralicFinno-Ugric

Hungarian

0.12991.21940.51570.6731

DravidianDravidianTelugu0.10581.20000.53320.7074

DravidianDravidianTamil

0.1046

1.2474

0.53120.6890

Niger-Congo

Atlantic

Wolof

0.09771.25450.50970.6016Austronesian

Malayo-PolynesianIndonesian

0.05091.08290.54180.6318AfroasiaticEgyptian

Coptic0.0446

1.14130.53240.6898JapaneseJapaneseJapanese

0.0253

1.04880.55870.7130Turning to word order flexibility, the Indo-Aryan language Marathi, Altaic Turkish were seen mostflexible in word order, with ENTR ranging from 0.7434 to 0.9074. Afroasiatic Coptic, AustronesianIndonesian, Niger-Congo Wolof, Dravidian languages Tamil and Telugu were seen most rigid, cf.
ENTR ranging from 0.6016 to 0.7074. Table 3 presents the distribution of word order patterns. The
Turkic language Turkish and Uyghur, Basque, Finno-Ugric North Sami showed the most balanced
proportions of S, V, O combinations.
Table 3. The distribution of word order patterns in agglutinative languages
LanguageBasqueBuryatCopticEstonian
FinnishHungarianIndonesian
Japanese
Kazakh

SVO
58.84%
68.95%
72.58%
73.29%
79.71%
68.69%
68.53%
64.60%
69.97%

SOV
30.39%
28.77%
24.60%
20.43%
16.48%
22.43%
31.33%
34.13%
25.74%

VSO
0.34%
0.23%
0.40%
0.00%
0.16%
0.47%
0.14%
0.48%
0.99%

VOS
1.70%
0.00%
0.00%
0.08%
0.00%
0.00%
0.00%
0.00%
0.00%

OVS
3.97%
0.00%
0.00%
3.30%
1.11%
2.80%
0.00%
0.00%
0.00%

OSV
4.76%
2.05%
2.42%
2.90%
2.54%
5.61%
0.00%
0.79%
3.30%

KoreanMarathiNorth Sami
Tamil
TeluguTurkishUyghurWolof

87.17%
52.63%
80.75%
67.24%
67.61%
53.89%
72.32%
77.34%

12.57%
42.11%
16.07%
18.97%
26.15%
43.80%
25.11%
20.70%

0.00%
0.00%
0.79%
0.00%
0.15%
0.86%
0.86%
0.00%

0.00%
0.00%
0.20%
0.00%
0.00%
0.86%
0.21%
0.00%

0.00%
0.00%
0.99%
1.72%
0.00%
0.29%
0.43%
0.00%

0.26%
5.26%
1.19%
12.07%
6.09%
0.29%
1.07%
1.95%

3.2 Interactions between word form diversity, word order flexibility
The previous section has confirmed the validity of the four metrics for capturing morphological andsyntactic complexity, i.e. MAMR, MAMSP, COS and ENTR. This section proceeds to pursue thesecond research question, i.e. whether morphologically richer languages are likely to be syntacticallymore free? The Spearman’s rank correlation coefficient analysis was carried out between themorphological metrics vs. word order metrics. A positive and fairly strong correlation was confirmed,
i.e. MAMR vs. COS: ρ = 0.735 and p = 0.001; MAMR vs. ENTR: ρ = 0.656 and p = 0.006; MAMSP
vs. COS: ρ = 0.624 and p = 0.010; MAMSP vs. ENTR: ρ = 0.565 and p = 0.023. we plotted thescatterplot matrix of the four metrics in Figure 2.

Figure 2. Spearman’s rank correlation coefficient between MAMR, MAMSP, COS, ENTR
Figure 2 indicates a positive correlation between the four values, i.e. when the morphological richnessof languages increases, the word order flexibility ascends. This finding is consistent with the‘complexity trade-off’ hypothesis, as in Slavic languages (Yan and Liu 2021), written Japanese (Li etal. 2022).
Figure 3 and 4 showed the clustering of the agglutinative languages of nine language families
based on morphological and syntactic diversity. A separation of Finnic, and Finno-Ugric branches of
Uralic language family; Mongolic and Turkic branches of Altaic language family is seen. Specially,
the Turkic branch is morphologically richer and syntactically more flexible than the Mongolic branch.
Japanese is morphologically less rich compared with the rest 15 agglutinative languages but its word
order freedom are in medium degree.

Figure 3. A clustering of the agglutinative languages based on morphological richness

Figure 4. A clustering of the agglutinative languages based on word order flexibility
4. Summary
This study explored the correlation between morphological richness and word order flexibility by
utilizing 25 treebanks of 16 agglutinative languages across nine language families. The metrics,
MAMR and MAMSP; COS and ENTR were found to be valid to capture the morphological andsyntactic diversity. Statistical analysis revealed that the richer the morphology, the more flexible theword order. A fairly strong correlation between morphology and syntax was confirmed in all
agglutinative languages, which supports the complexity trade-off hypothesis. Among the ninelanguage families, Austronesian, Afroasiatic, Dravidian languages were found morphologically andsyntactically the least diverse. The languages of high morphological and syntactic diverse go to the
Altaic Turkic branch, the In-European Indo-Aryan branch, Uralic Finnic branch. Turkish, Uyghur,
Basque, and North Sami showed the most balanced proportions of S, V, O combinations. A separationof Finnic, and Finno-Ugric branch of Uralic language family; Mongolic and Turkic branch of Altaic
language family was confirmed. The Finnic was found more flexible than Finno-Ugric; the Mongolic
was found more rigid than the Turkic.

Acknowledgement
This paper is based on work that was supported by the National Foundation of Social Sciences ofChina (22BYY186).
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