arXiv subjects

Paul Brunet

Publications and source records attributed to Paul Brunet.

16 recordsLinked to original sources

arXiv2026

A new method to probe conducting filaments in MoS$_2$-based memristors

Two-dimensional (2D) transition metal dichalcogenides (TMDs), such as molybdenum disulfide (MoS$_2$), are emerging as promising materials for next-generation electronic devices. They have proved to be serious candidates for integration with memristors in non-volatile memory and radio frequency (RF) applications. However, the physical mechanisms behind their resistive switching, particularly the formation and resorption of conducting filaments, remain unclear. In this study, we present a novel mechanical exfoliation technique that selectively removes the top metallic electrode from MoS$_2$-based memristors by exploiting the weak van der Waals interaction between MoS$_2$ and the top electrode. This method enables direct and multi-scale characterization of the MoS$_2$ surface in different states (initial, ON and OFF) using Kelvin Probe Force Microscopy (KPFM) and Raman spectroscopy mapping. To complete this study, cross-sectional Transmission Electron Microscopy (TEM) was also performed in different conductive states. Our results reveal that the conducting filament is formed by metallic atom migration from the top electrode into the MoS$_2$ layer. Additionally, we demonstrate that the choice of metallic electrodes (gold vs. nickel) significantly impacts the switching behavior due to differences in adsorption and diffusion energies. This work not only clarifies the filament formation mechanism and introduces a reproducible approach for in-operando characterization but also represents a real progress in the understanding and optimization of 2D material-based memristors.

cond-mat.mtrl-sci↗

arXiv2026

A 2-adjunction between representations and preorder morphisms

The recently introduced model of representations has been defined and motivated somewhat ex-nihilo. In this document, I will show that representations are related to a more ''classical'' model through a 2-adjunction. The target model is that of preorder morphisms, i.e. maps between sets equipped with reflexive and transitive relation that satisfy some natural preservation property. The aim of this is two-fold: first, this provides in my opinion a further justification of representations, as an object in non-trivial yet tight connection to some natural constructs; and secondly it suggests some classical results about order preserving maps could have interesting consequences for representations. This work has been presented (but not published or peer-reviewed) at RAMiCS 2026.

cs.LO↗

arXiv2025

Representations

The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often, one particular property can prove frustrating to establish: completeness of the logic with respect to the semantics. In this paper, we try and make such developments easier, with a particular attention on completeness. Towards that aim, we propose a formal (meta-)model of software analysis systems (SAS), the eponymous Representations. This model requires few assumptions on the SAS being modelled, and as such is able to capture a large class of such systems. We then show how our approach can be fruitful, both to understand how existing completeness proofs can be structured, and to leverage this structure to build new systems and prove their completeness.

cs.LO↗

arXiv2025

Observation algebras: Heyting algebra over coherence spaces

In this report, we introduce observation algebras, constructed by considering the downclosed subsets of a coherence space ordered by reverse inclusion. These may be interpreted as specifications of sets of events via some predicates with some extra structure. We provide syntax for these algebras, as well as axiomatisations. We establish completeness of these axiomatisations in two cases: when the syntax is that of bounded distributive lattices (conjunction, disjunction, top, and bottom), and when the syntax also includes an implication operator (in the sense of Heyting algebra), but the underlying coherence space satisfies some tractability condition. We also provide a product construction to combine graphs and their axiomatisations, yielding a sound and complete composite system. This development has been fully formalised in Rocq.

cs.LO↗

arXiv2024

Development and optimization of large-scale integration of 2D material in memristors

Two-dimensional (2D) materials like transition metal dichalcogenides (TMD) have proved to be serious candidates to replace silicon in several technologies with enhanced performances. In this respect, the two remaining challenges are the wafer scale growth of TMDs and their integration into operational devices using clean room compatible processes. In this work, two different CMOS-compatible protocols are developed for the fabrication of MoS$_2$-based memristors, and the resulting performances are compared. The quality of MoS$_2$ at each stage of the process is characterized by Raman spectroscopy and x-ray photoemission spectroscopy. In the first protocol, the structure of MoS$_2$ is preserved during transfer and patterning processes. However, a polymer layer with a minimum thickness of 3 nm remains at the surface of MoS$_2$ limiting the electrical switching performances. In the second protocol, the contamination layer is completely removed resulting in improved electrical switching performances and reproducibility. Based on physico-chemical and electrical results, the switching mechanism is discussed in terms of conduction through grain boundaries.

physics.app-ph↗

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

Pomsets with Boxes: Protection, Separation, and Locality in Concurrent Kleene Algebra

Concurrent Kleene Algebra is an elegant tool for equational reasoning about concurrent programs. An important feature of concurrent programs that is missing from CKA is the ability to restrict legal interleavings. To remedy this we extend the standard model of CKA, namely pomsets, with a new feature, called boxes, which can specify that part of the system is protected from outside interference. We study the algebraic properties of this new model. Another drawback of CKA is that the language used for expressing properties of programs is the same as that which is used to express programs themselves. This is often too restrictive for practical purposes. We provide a logic, 'pomset logic', that is an assertion language for specifying such properties, and which is interpreted on pomsets with boxes. In contrast with other approaches, this logic is not state-based, but rather characterizes the runtime behaviour of a program. We develop the basic metatheory for the relationship between pomset logic and CKA, including frame rules to support local reasoning, and illustrate this relationship with simple examples.

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

A note on commutative Kleene algebra

In this paper we present a detailed proof of an important result of algebraic logic: namely that the free commutative Kleene algebra is the space of semilinear sets. The first proof of this result was proposed by Redko in 1964, and simplified and corrected by Pilling in his 1970 thesis. However, we feel that a new account of this proof is needed now. This result has acquired a particular importance in recent years, since it is a key component in the completeness proofs of several algebraic models of concurrent computations (bi-Kleene algebra, concurrent Kleene algebra...). To that effect, we present a new proof of this result.

cs.FL↗

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

A complete axiomatisation of reversible Kleene lattices

We consider algebras of languages over the signature of reversible Kleene lattices, that is the regular operations (empty and unit languages, union, concatenation and Kleene star) together with intersection and mirror image. We provide a complete set of axioms for the equational theory of these algebras. This proof was developed in the proof assistant Coq.

cs.LO↗

arXiv2018

On Series-Parallel Pomset Languages: Rationality, Context-Freeness and Automata

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 applications. This paper takes an important step towards such a correspondence, by precisely relating bi-Kleene Algebra (BKA), a fragment of CKA, to a novel type of automata, pomset automata (PAs). We show that PAs can implement the BKA semantics of series-parallel rational expressions, and that a class of PAs can be translated back to these expressions. We also characterise the behavior of general PAs in terms of context-free pomset grammars; consequently, universality, equivalence and series-parallel rationality of general PAs are undecidable.

cs.FL↗

arXiv2018

Equivalence checking for weak bi-Kleene algebra

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational expressions, i.e., rational expressions with an additional operator for bounded parallelism. As a consequence, we obtain a new proof that equivalence of series-rational expressions is decidable.

cs.FL↗

arXiv2018

Concurrent Kleene Algebra: Free Model and Completeness

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 proposed in the original paper; consequently, these semantics are the free model for this fragment. This result settles a conjecture of Hoare and collaborators. Moreover, the techniques developed along the way are reusable; in particular, they allow us to establish pomset automata as an operational model for CKA.

cs.FL↗

arXiv2017

Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages

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 the theory and potential applications. For CKA, this has been an open question for a few years and this paper makes an important step towards an answer. We present a new automaton model and a Kleene-like theorem that relates a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours.

cs.FL↗

arXiv2017

Petri Automata

Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary relations. We consider Kleene allegories, i.e., Kleene algebras with two additional operations and a constant which are natural in binary relation models: intersection, converse, and the full relation. While regular languages are closed under those operations, the above characterisation breaks. Putting together a few results from the literature, we give a characterisation in terms of languages of directed and labelled graphs. By taking inspiration from Petri nets, we design a finite automata model, Petri automata, allowing to recognise such graphs. We prove a Kleene theorem for this automata model: the sets of graphs recognisable by Petri automata are precisely the sets of graphs definable through the extended regular expressions we consider. Petri automata allow us to obtain decidability of identity-free relational Kleene lattices, i.e., the equational theory generated by binary relations on the signature of regular expressions with intersection, but where one forbids unit. This restriction is used to ensure that the corresponding graphs are acyclic. We actually show that this decision problem is EXPSPACE-complete.

cs.LO↗