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A Quasiorder-Based Perspective on Residual Automata

Authors Pierre Ganty , Elena Gutiérrez , Pedro Valero

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Author Details

Pierre Ganty
  • IMDEA Software Institute, Madrid, Spain
Elena Gutiérrez
  • IMDEA Software Institute, Madrid, Spain
  • Universidad Politécnica de Madrid, Spain
Pedro Valero
  • IMDEA Software Institute, Madrid, Spain
  • Universidad Politécnica de Madrid, Spain

Funding

All authors were partially supported by the Spanish project PGC2018-102210-B-I00 BOSCO
  • Ganty, Pierre: Partially supported by the Madrid regional project S2018/TCS-4339 BLOQUES and the Ramón y Cajal fellowship RYC-2016-20281.
  • Gutiérrez, Elena: Partially supported by BES-2016-077136 grant from the Spanish Ministry of Economy, Industry and Competitiveness.

Cite AsGet BibTex

Pierre Ganty, Elena Gutiérrez, and Pedro Valero. A Quasiorder-Based Perspective on Residual Automata. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 40:1-40:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.MFCS.2020.40

Abstract

In this work, we define a framework of automata constructions based on quasiorders over words to provide new insights on the class of residual automata. We present a new residualization operation and a generalized double-reversal method for building the canonical residual automaton for a given language. Finally, we use our framework to offer a quasiorder-based perspective on NL^*, an online learning algorithm for residual automata. We conclude that quasiorders are fundamental to residual automata as congruences are to deterministic automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Regular languages
Keywords
  • Residual Automata
  • Quasiorders
  • Double-Reversal Method
  • Canonical RFA
  • Regular Languages

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References

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