arXiv subjects

Marc de Visme

Publications and source records attributed to Marc de Visme.

10 recordsLinked to original sources

arXiv2025

The Tensor-Plus Calculus

We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure or the additive structure is implicit and determined contextually rather than explicitly through tapes, world annotations, or other techniques, as is usually the case in the literature. The diagrams are used as parameter elements of a commutative semiring, whose choice is determined by the kind of computation we want to model, such as non-deterministic, probabilistic, or quantum. Given such a semiring, we provide a categorical semantics of diagrams and show the language as universal for it. We also provide an equational theory to identify diagrams that share the same semantics and show that the theory is sound and complete and captures semantical equivalence. In categorical terms, we design an internal language for semiadditive categories (C,+,0) with a symmetric monoidal structure (C,x,1) distributive over it, and such that the homset C(1,1) is isomorphic to a given commutative semiring, e.g., the semiring of non-negative real numbers for the probabilistic case.

cs.LO↗

arXiv2025

Quantum Petri Nets with Event Structure semantics

Classical Petri nets provide a canonical model of concurrency, with unfolding semantics linking nets, occurrence nets, and event structures. No comparable framework exists for quantum concurrency: existing ''quantum Petri nets'' lack rigorous concurrent and sound quantum semantics, analysis tools, and unfolding theory. We introduce Quantum Petri Nets (QPNs), Petri nets equipped with a quantum valuation compatible with the quantum event structure semantics of Clairambault, De Visme, and Winskel (2019). Our contributions are: (i) a local definition of Quantum Occurrence Nets (LQONs) compatible with quantum event structures, (ii) a construction of QPNs with a well-defined unfolding semantics, (iii) a compositional framework for QPNs. This establishes a semantically well grounded model of quantum concurrency, bridging Petri net theory and quantum programming.

cs.LO↗

arXiv2025

Quantum Petri Nets with Event Structures semantics

cs.LO↗

arXiv2025

Complete Compositional Syntax for Finite Transducers on Finite and Bi-Infinite Words

Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states non-deterministic transducer as a lingua franca for automata theory, transition systems, and sofic subshifts. We introduce a compositional diagrammatical syntax for transducers in form of string diagrams interpreted as relations. This syntax comes with sound rewriting rules allowing diagrammatical reasoning. Our main result is the completeness of our equational theory, ensuring that language-equivalence, trace-equivalence, or subshift equivalence can always be proved using our rewriting rules.

cs.LO↗

arXiv2024

Non-deterministic, probabilistic, and quantum effects through the lens of event structures (Technical report)

In this paper, we consider event structures and their probabilistic and quantum extensions as originally defined by Winskel. If these structures have already been part of sophisticated computational models, they have rarely been directly studied as an immediate model of execution traces of programs. This paper offers such an analysis. We propose a simple imperative operational framework and show how to derive soundness and adequacy results with event structures considered as a semantics. We show how event structures naturally handle non-deterministic, probabilistic and quantum effects.

cs.LO↗

arXiv2024

Minimality in Finite-Dimensional ZW-Calculi

The ZW-calculus is a graphical language capable of representing 2-dimensional quantum systems (qubit) through its diagrams, and manipulating them through its equational theory. We extend the formalism to accommodate finite dimensional Hilbert spaces beyond qubit systems. First we define a qu$d$it version of the language, where all systems have the same arbitrary finite dimension $d$, and show that the provided equational theory is both complete -- i.e. semantical equivalence is entirely captured by the equations -- and minimal -- i.e. none of the equations are consequences of the others. We then extend the graphical language further to allow for mixed-dimensional systems. We again show the completeness and minimality of the provided equational theory.

quant-ph↗

arXiv2023

Causal Unfoldings and Disjunctive Causes

In the simplest form of event structure, a prime event structure, an event is associated with a unique causal history, its prime cause. However, it is quite common for an event to have disjunctive causes in that it can be enabled by any one of multiple sets of causes. Sometimes the sets of causes may be mutually exclusive, inconsistent one with another, and sometimes not, in which case they coexist consistently and constitute parallel causes of the event. The established model of general event structures can model parallel causes. On occasion however such a model abstracts too far away from the precise causal histories of events to be directly useful. For example, sometimes one needs to associate probabilities with different, possibly coexisting, causal histories of a common event. Ideally, the causal histories of a general event structure would correspond to the configurations of its causal unfolding to a prime event structure; and the causal unfolding would arise as a right adjoint to the embedding of prime in general event structures. But there is no such adjunction. However, a slight extension of prime event structures remedies this defect and provides a causal unfolding as a universal construction. Prime event structures are extended with an equivalence relation in order to dissociate the two roles, that of an event and its enabling; in effect, prime causes are labelled by a disjunctive event, an equivalence class of its prime causes. With this enrichment a suitable causal unfolding appears as a pseudo right adjoint. The adjunction relies critically on the central and subtle notion of extremal causal realisation as an embodiment of causal history. Finally, we explore subcategories which support parallel causes as well the key operations needed in developing probabilistic distributed strategies with parallel causes.

cs.LO↗

arXiv2022

The Many-Worlds Calculus

In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We propose a colored PROP to model computation in this framework, where the choice is parameterized by an algebraic side effect: the model can support regular tests, probabilistic and non-deterministic branching, as well as quantum branching, i.e. superposition. The graphical language comes equipped with a denotational semantics based on linear applications, and an equational theory. We prove the language to be universal, and the equational theory to be complete with respect to this semantics.

cs.LO↗

arXiv2021

Graphical Language with Delayed Trace: Picturing Quantum Computing with Finite Memory

Graphical languages, like quantum circuits or ZX-calculus, have been successfully designed to represent (memoryless) quantum computations acting on a finite number of qubits. Meanwhile, delayed traces have been used as a graphical way to represent finite-memory computations on streams, in a classical setting (cartesian data types). We merge those two approaches and describe a general construction that extends any graphical language, equipped with a notion of discarding, to a graphical language of finite memory computations. In order to handle cases like the ZX-calculus, which is complete for post-selected quantum mechanics, we extend the delayed trace formalism beyond the causal case, refining the notion of causality for stream transformers. We design a stream semantics based on stateful morphism sequences and, under some assumptions, show universality and completeness results. Finally, we investigate the links of our framework with previous works on cartesian data types, signal flow graphs, and quantum channels with memories.

quant-ph↗

arXiv2016

Strategies with Parallel Causes

In a distributed game we imagine a team Player engaging a team Opponent in a distributed fashion. Such games and their strategies have been formalised in concurrent games based on event structures. However there are limitations in founding strategies on traditional event structures. Sometimes a probabilistic distributed strategy relies on certain benign races where, intuitively, several members of team Player may race each other to make a common move. Although there are event structures which support such parallel causes, in which an event is enabled in several compatible ways, they do not support an operation of hiding central to the composition of strategies; nor do they support probability adequately. An extension of traditional event structures is devised which supports parallel causes and hiding, as well as the mix of probability and nondeterminism needed to account for probabilistic distributed strategies. The extension is tested in the construction of a bicategory of probabilistic distributed strategies with parallel causes. The bicategory is rich in operations relevant to probabilistic as well as deterministic parallel programming.

cs.LO↗