arXiv subjects

Jana Wagemaker

Publications and source records attributed to Jana Wagemaker.

14 recordsLinked to original sources

arXiv2026

GKAT with Hoare Hypotheses

Guarded Kleene Algebra with Tests (GKAT) is a variant of Kleene algebra which allows for reasoning about simple imperative programs, and which features a decision procedure for program equivalence in nearly linear time. In the current paper, we address the challenge of reasoning under assumptions about these programs. In particular, we develop a form of Hoare hypotheses, which allow modelling basic domain knowledge on pre- and post-conditions of uninterpreted basic programs, and which are well-developed for classical Kleene algebra but not yet for GKAT. We show that the resulting axiomatisation is sound and complete. We then extend Hoare hypotheses to the more general form of word hypotheses. Based on an automata-theoretic approach, we show that equivalence of GKAT under word hypotheses is as efficiently decidable as for plain GKAT.

cs.LO↗

arXiv2026

Continuous Algebras with Hypotheses

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 presence of additional assumptions, called hypotheses. We propose a unifying framework encompassing all the previous structures, as well as regular tree languages. This is done by considering algebras ordered by complete lattices, where least fixpoints can be computed. We provide a canonical model consisting of closed languages, which we prove sound and complete with respect to all continuous models. Then we study quasi-equational axiomatisations. It is illusory to hope for a generic axiomatisation which would be sound and complete for all instances. Instead, we provide a generic axiomatisation which we prove sound and we setup tools that make it possible to get complete ones in a modular way, building on previous works from the literature. We showcase these tools by proving new completeness results for commutative KA, bi-KA, and regular tree languages, in each case extended with various hypotheses.

cs.LO↗

arXiv2026

NEST: Network Enforced Session Types (Technical Report)

This paper introduces NEST (Network-Enforced Session Types), a runtime verification framework that moves application-level protocol monitoring into the network fabric. Unlike prior work that instruments or wraps application code, we synthesize packet-level monitors that enforce protocols directly in the data plane. We develop algorithms to generate network-level monitors from session types and extend them to handle packet loss and reordering. We implement NEST in P4 and evaluate it on applications including microservice and network-function models, showing that network-level monitors can enforce realistic non-trivial protocols.

cs.PL↗

arXiv2025

Kleene Algebra

This booklet serves as an introduction to Kleene Algebra (KA), a set of laws that can be used to study general equivalences between programs. It discusses how general programs can be modeled using regular expressions, how those expressions correspond to automata, and how this correspondence can be exploited to obtain the central result of KA, namely that an equivalence of regular expressions is true if and only if it can be proved using the laws of KA. Each chapter closes with a set of exercises to further build intuition and understanding, and there is an optional chapter that develops automata theory through the lens of coalgebra.

cs.PL↗

arXiv2025

Generalised M\"obius Categories and Convolution Kleene Algebras

Convolution algebras on maps from structures such as monoids, groups or categories into semirings, rings or fields abound in mathematics and the sciences. Of special interest in computing are convolution algebras based on variants of Kleene algebras, which are additively idempotent semirings equipped with a Kleene star. Yet an obstacle to the construction of convolution Kleene algebras on a wide class of structures has so far been the definition of a suitable star. We show that a generalisation of M\"obius categories combined with a generalisation of a classical definition of a star for formal power series allow such a construction. We discuss several instances of this construction on generalised M\"obius categories: convolution Kleene algebras with tests, modal convolution Kleene algebras, concurrent convolution Kleene algebras and higher convolution Kleene algebras (e.g. on strict higher categories and higher relational monoids). These are relevant to the verification of weighted and probabilistic sequential and concurrent programs, using quantitative Hoare logics or predicate transformer algebras, as well as for algebraic reasoning in higher-dimensional rewriting. We also adapt the convolution Kleene algebra construction to Conway semirings, which is widely studied in the context of weighted automata. Finally, we compare the convolution Kleene algebra construction with a previous construction of convolution quantales and present concrete example structures in preparation for future applications.

cs.FL↗

arXiv2025

StacKAT: Infinite State Network Verification

We develop StacKAT, a network verification language featuring loops, finite state variables, nondeterminism, and - most importantly - access to a stack with accompanying push and pop operations. By viewing the variables and stack as the (parsed) headers and (to-be-parsed) contents of a network packet, StacKAT can express a wide range of network behaviors including parsing, source routing, and telemetry. These behaviors are difficult or impossible to model using existing languages like NetKAT. We develop a decision procedure for StacKAT program equivalence, based on finite automata. This decision procedure provides the theoretical basis for verifying network-wide properties and is able to provide counterexamples for inequivalent programs. Finally, we provide an axiomatization of StacKAT equivalence and establish its completeness.

cs.PL↗

arXiv2024

Centralized vs Decentralized Monitors for Hyperproperties

This paper focuses on the runtime verification of hyperproperties expressed in Hyper-recHML, an expressive yet simple logic for describing properties of sets of traces. To this end, we consider a simple language of monitors that observe sets of system executions and report verdicts w.r.t. a given Hyper-recHML formula. We first employ a unique omniscient monitor that centrally observes all system traces. Since centralised monitors are not ideal for distributed settings, we also provide a language for decentralized monitors, where each trace has a dedicated monitor; these monitors yield a unique verdict by communicating their observations to one another. For both the centralized and the decentralized settings, we provide a synthesis procedure that, given a formula, yields a monitor that is correct (i.e., sound and violation complete). A key step in proving the correctness of the synthesis for decentralized monitors is a result showing that, for each formula, the synthesized centralized monitor and its corresponding decentralized one are weakly bisimilar for a suitable notion of weak bisimulation.

cs.LO↗

arXiv2023

Completeness Theorems for Kleene algebra with tests and top

We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of Kleene algebra, this is no longer the case when we consider an additional constant ``top'' for the full element. Indeed, the full relation satisfies more laws than the full language, and we show that those additional laws can all be derived from a single additional axiom. We recover that the two equational theories coincide if we slightly generalise the notion of relational model, allowing sub-algebras of relations where top is a greatest element but not necessarily the full relation. We use models of closed languages and reductions in order to prove our completeness results, which are relative to any axiomatisation of the algebra of regular events. For one of our constructions, we extend the concept of finite monoid recognisability to guarded-string languages; this device makes it possible to obtain a PSpace algorithm for the equational theory of binary relations.

cs.FL↗

arXiv2022

On Tools for Completeness of Kleene Algebra with Hypotheses

In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure specified by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene algebra with observations (KAO), or make specific assumptions about certain constants, as for instance in NetKAT. Many of these variants fit within the unifying perspective offered by Kleene algebra with hypotheses, which comes with a canonical language model constructed from a given set of hypotheses. For the case of KAT, this model corresponds to the familiar interpretation of expressions as languages of guarded strings. A relevant question therefore is whether Kleene algebra together with a given set of hypotheses is complete with respect to its canonical language model. In this paper, we revisit, combine and extend existing results on this question to obtain tools for proving completeness in a modular way. We showcase these tools by giving new and modular proofs of completeness for KAT, KAO and NetKAT, and we prove completeness for new variants of KAT: KAT extended with a constant for the full relation, KAT extended with a converse operation, and a version of KAT where the collection of tests only forms a distributive lattice.

cs.LO↗

arXiv2022

Concurrent NetKAT: Modeling and analyzing stateful, concurrent networks

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 partially-ordered multisets (pomsets), which are a well-established mathematical structure for defining the denotational semantics of concurrent languages. We provide a sound and complete axiomatization of this model, and we illustrate the use of CNetKAT through examples. More generally, CNetKAT can be understood as an algebraic framework for reasoning about programs with both local state (in packets) and global state (in a global store).

cs.PL↗

arXiv2020

Partially Observable Concurrent Kleene Algebra

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 variables and values, which we illustrate through concrete examples. We prove that POCKA is a sound and complete axiomatisation of a model of partial observations, and show the semantics passes an important check for sequential consistency.

cs.LO↗

arXiv2020

Concurrent Kleene Algebra with Observations: from Hypotheses to Completeness

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 constructs such as conditionals and $\mathsf{while}$-loops. It turns out that integrating tests in CKA is subtle, due to their interaction with parallelism. In this paper we provide a solution in the form of Concurrent Kleene Algebra with Observations (CKAO). Our main contribution is a completeness theorem for CKAO. Our result resorts on a more general study of CKA "with hypotheses", of which CKAO turns out to be an instance: this analysis is of independent interest, as it can be applied to extensions of CKA other than CKAO.

cs.LO↗

arXiv2019

Kleene Algebra with Observations

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 with expected axioms for concurrency lead to an anomalous equation. In this paper, we propose Kleene algebra with observations (KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. We characterise the free model of KAO, and establish a decision procedure w.r.t. its equational theory.

cs.LO↗

arXiv2019

Completeness and Incompleteness of Synchronous Kleene Algebra

Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. We provide a countermodel witnessing that the axioms of SKA are incomplete w.r.t. its language semantics, by exploiting a lack of interaction between the synchronous product operator and the Kleene star. We then propose an alternative set of axioms for SKA, based on Salomaa's axiomatisation of regular languages, and show that these provide a sound and complete characterisation w.r.t. the original language semantics.

cs.LO↗