Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness

@inproceedings{Schmid2021GuardedKA,
  title={Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness},
  author={Todd J. Schmid and Tobias Kapp'e and Dexter Kozen and Alexandra Silva},
  booktitle={ICALP},
  year={2021}
}
Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that can distinguish between unsuccessful programs performing different actions, by omitting the so-called early termination axiom. We develop an operational (coalgebraic) and denotational (algebraic) semantics and show that they coincide. We then characterize the… 
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