arXiv subjects

Marin Costes

Publications and source records attributed to Marin Costes.

4 recordsLinked to original sources

arXiv2025

Space-time reversible graph rewriting

In the mathematical tradition, reversibility requires that the evolution of a dynamical system be a bijective function. In the context of graph rewriting, however, the evolution is not even a function, because it is not even deterministic -- as the rewrite rules get applied at non-deterministically chosen locations. Physics, by contrast, suggests a more flexible understanding of reversibility in space-time, whereby any two closeby snapshots (aka `space-like cuts'), must mutually determine each other. We build upon the recently developed framework of space-time deterministic graph rewriting, in order to formalise this notion of space-time reversibility, and henceforth study reversible graph rewriting. We establish sufficient, local conditions on the rewrite rules so that they be space-time reversible. We provide an example featuring time dilation, in the spirit of general relativity.

cs.DM↗

arXiv2024

Space-time deterministic graph rewriting

We study non-terminating graph rewriting models, whose local rules are applied non-deterministically -- and yet enjoy a strong form of determinism, namely space-time determinism. Of course in the case of terminating computation it is well-known that the mess introduced by asynchronous rule applications may not matter to the end result, as confluence conspires to produce a unique normal form. In the context of non-terminating computation however, confluence is a very weak property, and (almost) synchronous rule applications is always preferred e.g. when it comes to simulating dynamical systems. Here we provide sufficient conditions so that asynchronous local rule applications conspire to produce well-determined events in the space-time unfolding of the graph, regardless of their application orders. Our first example is an asynchronous simulation of a dynamical system. Our second example features time dilation, in the spirit of general relativity.

cs.DM↗

arXiv2021

Addressable quantum gates

We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing indefinite causal orders and making their geometrical layout explicit: we express the quantum switch and the polarizing beam-splitter within the model. In this context, our main contribution is a full characterization of the anonymity constraints. Indeed, the names used as addresses should not matter beyond the wiring they describe, i.e. quantum evolutions should commute with "renamings". We show that these quantum evolutions can still act non-trivially upon the names. We specify the structure of "nameblind" matrices.

quant-ph↗

arXiv2021

Universal gauge-invariant cellular automata

Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter', and features a global symmetry. One then extends the theory so as make the global symmetry into a local one (a.k.a gauge-invariance). We formalise a discrete counterpart of this process, known as gauge extension, within the Computer Science framework of Cellular Automata (CA). We prove that the CA which admit a relative gauge extension are exactly the globally symmetric ones (a.k.a the colour-blind). We prove that any CA admits a non-relative gauge extension. Both constructions yield universal gauge-invariant CA, but the latter allows for a first example where the gauge extension mediates interactions within the initial CA.

nlin.CG↗