Related papers: Partially Observable Concurrent Kleene Algebra
Abstract interpretation offers a powerful toolset for static analysis, tackling precision, complexity and state-explosion issues. In the literature, state partitioning abstractions based on (bi)simulation and property-preserving state…
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…
Kleene algebra with tests (KAT) is an equational system for program verification, which is the combination of Boolean algebra (BA) and Kleene algebra (KA), the algebra of regular expressions. In particular, KAT subsumes the propositional…
We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras.…
For every partial combinatory algebra (pca), we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca's, i.e. the smallest ordinals where these relations become equal. We show that the…
Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational…
Partial combinatory algebras are algebraic structures that serve as generalized models of computation. In this paper, we study embeddings of pcas. In particular, we systematize the embeddings between relativizations of Kleene's models, of…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with tests, along the lines of the coalgebraic…
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…
Methods for causal inference from observational data are an alternative for scenarios where collecting counterfactual data or realizing a randomized experiment is not possible. Adopting a stacking approach, our proposed method ParKCA…
Weighted programs generalize probabilistic programs and offer a framework for specifying and encoding mathematical models by means of an algorithmic representation. Kleene algebra with tests is an algebraic formalism based on regular…
We study Kleene iteration in the categorical context. A celebrated completeness result by Kozen introduced Kleene algebra (with tests) as a ubiquitous tool for lightweight reasoning about program equivalence, and yet, numerous variants of…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
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…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
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).
We exhibit a way of "forcing a functional to be an effective operation" for arbitrary partial combinatory algebras (pcas). This gives a method of defining new pcas from old ones for some fixed functional, where the new partial functions can…
A number of extensions exist for Alternating-time Temporal Logic; some of these mix strategies and partial observability but, to the best of our knowledge, no work provides a unified framework for strategies, partial observability and…