The Expressive Power of One Variable Used Once: The Chomsky Hierarchy and First-Order Monadic Constructor Rewriting

Author Jakob Grue Simonsen

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Jakob Grue Simonsen
  • Department of Computer Science, University of Copenhagen, Denmark


I wish to thank the anonymous referees for diligent comments that have helped improve the presentation of the paper.

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Jakob Grue Simonsen. The Expressive Power of One Variable Used Once: The Chomsky Hierarchy and First-Order Monadic Constructor Rewriting. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We study the implicit computational complexity of constructor term rewriting systems where every function and constructor symbol is unary or nullary. Surprisingly, adding simple and natural constraints to rule formation yields classes of systems that accept exactly the four classes of languages in the Chomsky hierarchy.

Subject Classification

ACM Subject Classification
  • Theory of computation → Grammars and context-free languages
  • Theory of computation → Equational logic and rewriting
  • Theory of computation → Computability
  • Constructor term rewriting
  • Chomsky Hierarchy
  • Implicit Complexity


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