Weak Kleene Algebra is Sound and (Possibly) Complete for Simulation
Ernie Cohen
TL;DR
This paper proves that Weak Kleene Algebra axioms are sound and complete for regular expressions under simulation equivalence, contingent on their conjectured completeness for monodic trees.
Contribution
It establishes the soundness and completeness of WKA for simulation, linking it to monodic tree conjecture, advancing algebraic theory of regular expressions.
Findings
WKA axioms are sound for simulation equivalence
WKA axioms are complete assuming monodic tree conjecture
Connects algebraic properties to tree-based conjecture
Abstract
We show that the axioms of Weak Kleene Algebra (WKA) are sound and complete for the theory of regular expressions modulo simulation equivalence, assuming their completeness for monodic trees (as conjectured by Takai and Furusawa).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Logic, programming, and type systems · Formal Methods in Verification