an:07076873
Zbl 1415.68124
Das, Anupam; Doumane, Amina; Pous, Damien
Left-handed completeness for Kleene algebra, via cyclic proofs
EN
Barthe, Gilles (ed.) et al., LPAR-22. 22nd international conference on logic for programming, artificial intelligence and reasoning, Awassa, Ethiopia, November 17--21, 2018. Selected papers. Manchester: EasyChair. EPiC Ser. Comput. 57, 271-289 (2018).
2018
a
68Q45 03B70
automata; axiomatisation; cyclic proofs; induction; Kleene algebra; regular languages
Summary: 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 \textit{M. Boffa} (which relies on Krob's completeness result) [RAIRO, Inform. Th??or. Appl. 29, No. 6, 515--518 (1995; Zbl 0881.68071)], and the more recent proof of \textit{D. Kozen} and \textit{A. Silva} [Lect. Notes Comput. Sci. 7560, 162--178 (2012; Zbl 1364.68268)]. Our proof builds on a recent non-well-founded sequent calculus which makes it possible to explicitly compute the invariants required for left-handed Kleene algebra.
For the entire collection see [Zbl 1407.68021].
Zbl 0881.68071; Zbl 1364.68268