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Documents authored by Kim, Dohan

Document
DOI: 10.4230/LIPIcs.ITP.2025.10
An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems

Authors: Dohan Kim

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We present a formalized framework for semi-Thue and conditional semi-Thue systems for studying monoids and their word problem using the Isabelle/HOL proof assistant. We provide a formalized decision procedure for the word problem of monoids if they are finitely presented by complete semi-Thue systems. In particular, we present a new formalized method for checking confluence using (conditional) critical pairs for certain conditional semi-Thue systems. We propose and formalize an inference system for generating conditional equational theories and Thue congruences using conditional semi-Thue systems. Then we provide a new formalized decision procedure for the word problem of monoids which have finite complete (reductive) conditional presentations.
Cite as

Dohan Kim. An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kim:LIPIcs.ITP.2025.10,
  author =	{Kim, Dohan},
  title =	{{An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.10},
  URN =		{urn:nbn:de:0030-drops-246081},
  doi =		{10.4230/LIPIcs.ITP.2025.10},
  annote =	{Keywords: semi-Thue systems, conditional semi-Thue systems, conditional string rewriting, monoids, word problem}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.24
An Isabelle/HOL Formalization of Narrowing and Multiset Narrowing for E-Unifiability, Reachability and Infeasibility

Authors: Dohan Kim

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
We present an Isabelle/HOL formalization of narrowing for E-unifiability, reachability, and infeasibility. Given a semi-complete rewrite system ℛ and two terms s and t, we show a formalized proof that if narrowing terminates, then it provides a decision procedure for ℛ-unifiability for s and t, where ℛ is viewed as a set of equations. Furthermore, we present multiset narrowing and its formalization for multiset reachability and reachability analysis, providing decision procedures using certain restricted conditions on multiset reachability and reachability problems. Our multiset narrowing also provides a complete method for E-unifiability problems consisting of multiple goals if E can be represented by a complete rewrite system.
Cite as

Dohan Kim. An Isabelle/HOL Formalization of Narrowing and Multiset Narrowing for E-Unifiability, Reachability and Infeasibility. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kim:LIPIcs.ITP.2024.24,
  author =	{Kim, Dohan},
  title =	{{An Isabelle/HOL Formalization of Narrowing and Multiset Narrowing for E-Unifiability, Reachability and Infeasibility}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.24},
  URN =		{urn:nbn:de:0030-drops-207525},
  doi =		{10.4230/LIPIcs.ITP.2024.24},
  annote =	{Keywords: Narrowing, Multiset Narrowing, Unifiability, Reachability}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.19
An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems

Authors: Dohan Kim and Christopher Lynch

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
Rewriting modulo equations has been researched for several decades but due to the lack of suitable orderings, there are some limitations to rewriting modulo permutation equations. Given a finite set of permutation equations E, we present a new RPO-based ordering modulo E using (permutation) group actions and their associated orbits. It is an E-compatible reduction ordering on terms with the subterm property and is E-total on ground terms. We also present a completion and ground completion method for rewriting modulo a finite set of permutation equations E using our ordering modulo E. We show that our ground completion modulo E always admits a finite ground convergent (modulo E) rewrite system, which allows us to obtain the decidability of the word problem of ground theories modulo E.
Cite as

Dohan Kim and Christopher Lynch. An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kim_et_al:LIPIcs.FSCD.2021.19,
  author =	{Kim, Dohan and Lynch, Christopher},
  title =	{{An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.19},
  URN =		{urn:nbn:de:0030-drops-142572},
  doi =		{10.4230/LIPIcs.FSCD.2021.19},
  annote =	{Keywords: Recursive Path Ordering, Permutation Equation, Permutation Group, Rewrite System, Completion, Ground Completion}
}
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