
Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time
Guarded Kleene Algebra with Tests (GKAT) is a variation on Kleene Algebr...
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Completeness and Incompleteness of Synchronous Kleene Algebra
Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), w...
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Kleene Algebra Modulo Theories
Kleene algebras with tests (KATs) offer sound, complete, and decidable e...
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MatchKAT: An Algebraic Foundation For MatchAction
We present MatchKAT, an algebraic language for modeling matchaction pac...
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EquivalenceInvariant Algebraic Provenance for Hyperplane Update Queries
The algebraic approach for provenance tracking, originating in the semir...
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Axiomatising Infinitary Probabilistic Weak Bisimilarity of FiniteState Behaviours
In concurrency theory, weak bisimilarity is often used to relate process...
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Generalising KAT to verify weighted computations
Kleene algebra with tests (KAT) was introduced as an algebraic structure...
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Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness
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 socalled early termination axiom. We develop an operational (coalgebraic) and denotational (algebraic) semantics and show that they coincide. We then characterize the behaviors of GKAT expressions in this semantics, leading to a coequation that captures the covariety of automata corresponding to behaviors of GKAT expressions. Finally, we prove that the axioms of the reduced fragment are sound and complete w.r.t. the semantics, and then build on this result to recover a semantics that is sound and complete w.r.t. the full set of axioms.
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