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Concurrent Kleene Algebra (CKA) is a formalism to study concurrent programs. Like previous Kleene Algebra extensions, developing a correspondence between denotational and operational perspectives is important, for both foundations and…
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of…
Concurrent Kleene Algebra (CKA) is a recently proposed algebraic structure by Hoare and collaborators that unifies the laws of concurrent programming. The unifying power of CKA rests largely on the so-called exchange law that describes how…
We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with control structures, such as conditionals and loops. POCKA enables reasoning about programs that can access…
Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and Wehrman in 2009 as a framework to reason about concurrent programs. We prove that the axioms for CKA with bounded parallelism are complete for the semantics…
Concurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition operator, which enables reasoning about concurrent programs. However, CKA fundamentally misses tests, which are needed to model standard programming…
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not straightforward, because axioms native to KAT in conjunction…
In the literature on Kleene algebra (KA), a number of variants have been proposed such as Kleene algebra with tests, commutative KA, bi-KA, and concurrent KA. The equational theories of some of these structures have then been studied in the…
Kleene algebras (KA) and Kleene algebras with tests (KAT) provide an algebraic framework to capture the behavior of conventional programming constructs. This paper explores a broader understanding of these structures, in order to enable the…
We introduce Concurrent NetKAT (CNetKAT), an extension of NetKAT with operators for specifying and reasoning about concurrency in scenarios where multiple packets interact through state. We provide a model of the language based on…
We investigate the algebraic reasoning of quantum programs inspired by the success of classical program analysis based on Kleene algebra. One prominent example of such is the famous Kleene Algebra with Tests (KAT), which has furnished both…
Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…
Kleene algebra with tests (KAT) was introduced as an algebraic structure to model and reason about classic imperative programs, i.e. sequences of discrete transitions guarded by Boolean tests. This paper introduces two generalisations of…
We propose a generalisation of concurrent Kleene algebra \cite{Hoa09} that can take account of probabilistic effects in the presence of concurrency. The algebra is proved sound with respect to a model of automata modulo a variant of rooted…
Kleene algebra with tests (KAT) is a foundational equational framework for reasoning about programs, which has found applications in program transformations, networking and compiler optimizations, among many other areas. In his seminal…
Kleene algebra with tests, KAT, provides a simple two-sorted algebraic framework for verifying properties of propositional while programs. Kleene algebra with domain, KAD, is a one-sorted alternative to KAT. The equational theory of KAT…
We provide an extension of concurrent Kleene algebras to account for probabilistic properties. The algebra yields a unified framework containing nondeterminism, concurrency and probability and is sound with respect to the set of…
TopKAT is the algebraic theory of Kleene algebra with tests (KAT) extended with a top element. Compared to KAT, one pleasant feature of TopKAT is that, in relational models, the top element allows us to express the domain and codomain of a…
Guarded Kleene Algebra with Tests (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 GKAT…
Thirty years ago, I introduced a non-commutative variant of classical linear logic, called "pomset logic", issued from a particular categorical interpretation of linear logic known as coherence spaces. In addition to the usual commutative…