Left-Handed Completeness for Kleene algebra, via Cyclic Proofs

19 pages•Published: October 23, 2018

Anupam Das, Amina Doumane and Damien Pous

Abstract

We give a new proof that the axioms of left-handed Kleene algebra are complete with respect to language containments. This proof is significantly simpler than both the proof of Boffa (which relies on Krob’s completeness result), and the more recent proof of Kozen and Silva. Our proof builds on a recent non-wellfounded sequent calculus which makes it possible to explicitly compute the invariants required for left-handed Kleene algebra.

Keyphrases: automata, axiomatisation, cyclic proofs, induction, kleene algebra, regular languages

In: Gilles Barthe, Geoff Sutcliffe and Margus Veanes (editors). LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 57, pages 271-289.

Links:	https://easychair.org/publications/paper/SDqf
	https://doi.org/10.29007/hzq3

BibTeX entry

@inproceedings{LPAR-22:Left_Handed_Completeness_Kleene,
  author    = {Anupam Das and Amina Doumane and Damien Pous},
  title     = {Left-Handed Completeness for Kleene algebra, via Cyclic Proofs},
  booktitle = {LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Gilles Barthe and Geoff Sutcliffe and Margus Veanes},
  series    = {EPiC Series in Computing},
  volume    = {57},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/SDqf},
  doi       = {10.29007/hzq3},
  pages     = {271-289},
  year      = {2018}}

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