NILE: Formalizing Natural-Language Descriptions of Formal Languages
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arXiv
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| Format: | Preprint |
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2026
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| author | Kneisel, Tristan Schmellenkamp, Marko Vehlken, Fabian Zeume, Thomas |
| author_facet | Kneisel, Tristan Schmellenkamp, Marko Vehlken, Fabian Zeume, Thomas |
| contents | This paper explores how natural-language descriptions of formal languages can be compared to their formal representations and how semantic differences can be explained. This is motivated from educational scenarios where learners describe a formal language (presented, e.g., by a finite state automaton, regular expression, pushdown automaton, context-free grammar or in set notation) in natural language, and an educational support system has to (1) judge whether the natural-language description accurately describes the formal language, and to (2) provide explanations why descriptions are not accurate.
To address this question, we introduce a representation language for formal languages, Nile, which is designed so that Nile expressions can mirror the syntactic structure of natural-language descriptions of formal languages. Nile is sufficiently expressive to cover a broad variety of formal languages, including all regular languages and fragments of context-free languages typically used in educational contexts. Generating Nile expressions that are syntactically close to natural-language descriptions then allows to provide explanations for inaccuracies in the descriptions algorithmically.
In experiments on an educational data set, we show that LLMs can translate natural-language descriptions into equivalent, syntactically close Nile expressions with high accuracy - allowing to algorithmically provide explanations for incorrect natural-language descriptions. Our experiments also show that while natural-language descriptions can also be translated into regular expressions (but not context-free grammars), the expressions are often not syntactically close and thus not suitable for providing explanations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_19743 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | NILE: Formalizing Natural-Language Descriptions of Formal Languages Kneisel, Tristan Schmellenkamp, Marko Vehlken, Fabian Zeume, Thomas Formal Languages and Automata Theory Computation and Language Logic in Computer Science This paper explores how natural-language descriptions of formal languages can be compared to their formal representations and how semantic differences can be explained. This is motivated from educational scenarios where learners describe a formal language (presented, e.g., by a finite state automaton, regular expression, pushdown automaton, context-free grammar or in set notation) in natural language, and an educational support system has to (1) judge whether the natural-language description accurately describes the formal language, and to (2) provide explanations why descriptions are not accurate. To address this question, we introduce a representation language for formal languages, Nile, which is designed so that Nile expressions can mirror the syntactic structure of natural-language descriptions of formal languages. Nile is sufficiently expressive to cover a broad variety of formal languages, including all regular languages and fragments of context-free languages typically used in educational contexts. Generating Nile expressions that are syntactically close to natural-language descriptions then allows to provide explanations for inaccuracies in the descriptions algorithmically. In experiments on an educational data set, we show that LLMs can translate natural-language descriptions into equivalent, syntactically close Nile expressions with high accuracy - allowing to algorithmically provide explanations for incorrect natural-language descriptions. Our experiments also show that while natural-language descriptions can also be translated into regular expressions (but not context-free grammars), the expressions are often not syntactically close and thus not suitable for providing explanations. |
| title | NILE: Formalizing Natural-Language Descriptions of Formal Languages |
| topic | Formal Languages and Automata Theory Computation and Language Logic in Computer Science |
| url | https://arxiv.org/abs/2602.19743 |