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Priority Downward Closures

Authors Ashwani Anand, Georg Zetzsche

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Author Details

Ashwani Anand
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany
Georg Zetzsche
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany

Funding

Funded by the European Union (ERC, FINABIS, 101077902). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.

Acknowledgements

The authors are grateful to Yousef Shakiba for discussions on the block downward closure of regular languages.

Cite As Get BibTex

Ashwani Anand and Georg Zetzsche. Priority Downward Closures. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 39:1-39:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CONCUR.2023.39

Abstract

When a system sends messages through a lossy channel, then the language encoding all sequences of messages can be abstracted by its downward closure, i.e. the set of all (not necessarily contiguous) subwords. This is useful because even if the system has infinitely many states, its downward closure is a regular language. However, if the channel has congestion control based on priorities assigned to the messages, then we need a finer abstraction: The downward closure with respect to the priority embedding. As for subword-based downward closures, one can also show that these priority downward closures are always regular.
While computing finite automata for the subword-based downward closure is well understood, nothing is known in the case of priorities. We initiate the study of this problem and provide algorithms to compute priority downward closures for regular languages, one-counter languages, and context-free languages.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • downward closure
  • priority order
  • pushdown automata
  • non-deterministic finite automata
  • abstraction
  • computability

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