Author:
Rooduijn Jan,Kozen Dexter,Silva Alexandra
Abstract
AbstractGuarded Kleene Algebra with Tests ($$\texttt{GKAT}$$
GKAT
for short) is an efficient fragment of Kleene Algebra with Tests, suitable for reasoning about simple imperative while-programs. Following earlier work by Das and Pous on Kleene Algebra, we study $$\texttt{GKAT}$$
GKAT
from a proof-theoretical perspective. The deterministic nature of $$\texttt{GKAT}$$
GKAT
allows for a non-well-founded sequent system whose set of regular proofs is complete with respect to the guarded language model. This is unlike the situation with Kleene Algebra, where hypersequents are required. Moreover, the decision procedure induced by proof search runs in $$\textsf{NLOGSPACE}$$
NLOGSPACE
, whereas that of Kleene Algebra is in $$\textsf{PSPACE}$$
PSPACE
.
Publisher
Springer Nature Switzerland
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