Machine translation (MT) systems handle languages with complex grammatical rules by using a combination of linguistic rules, statistical models, and machine learning techniques. These systems aim to understand the syntactic structure, semantic meaning, and idiomatic expressions in a source language and then generate an accurate translation in the target language.

  Firstly, MT systems utilize linguistic rules to capture the grammar, syntax, and morphology of the languages. These rules are developed by linguists and language experts who analyze the structures and patterns of the languages. For languages with complex grammatical rules, such as case systems or verb conjugations, these rules help the MT system identify and generate appropriate structures in the target language.

  Secondly, statistical models play a crucial role in handling complex grammatical rules. These models are trained on large bilingual corpora, which provide examples of translations in different contexts. By analyzing these examples, the MT system learns patterns and probabilistic relationships between words and phrases in the source and target languages. This allows it to make intelligent decisions regarding word order, agreement, verb forms, and other complex grammatical aspects.

  Furthermore, machine learning techniques like neural networks have revolutionized machine translation. Neural machine translation (NMT) models can capture the syntactic and semantic meanings of phrases and sentences more accurately. NMT models, which are trained on vast amounts of bilingual data, can handle complex grammatical rules by capturing long-range dependencies and structural patterns in the languages.

  The performance of machine translation systems for languages with complex grammatical rules has significantly improved over the years. However, it is important to note that there are still limitations and challenges in accurately translating such languages. Ambiguities, idiomatic expressions, and language-specific nuances can pose difficulties for machine translation systems. Ongoing research and development efforts aim to address these challenges and improve the translation quality for languages with complex grammatical rules.