4,616 research outputs found

    Decomposition of sequential and concurrent models

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    Le macchine a stati finiti (FSM), sistemi di transizioni (TS) e le reti di Petri (PN) sono importanti modelli formali per la progettazione di sistemi. Un problema fodamentale Ăš la conversione da un modello all'altro. Questa tesi esplora il mondo delle reti di Petri e della decomposizione di sistemi di transizioni. Per quanto riguarda la decomposizione dei sistemi di transizioni, la teoria delle regioni rappresenta la colonna portante dell'intero processo di decomposizione, mirato soprattutto a decomposizioni che utilizzano due sottoclassi delle reti di Petri: macchine a stati e reti di Petri a scelta libera. Nella tesi si dimostra che una proprietĂ  chiamata ``chiusura rispetto all'eccitazione" (excitation-closure) Ăš sufficiente per produrre un insieme di reti di Petri la cui sincronizzazione Ăš bisimile al sistema di transizioni (o rete di Petri di partenza, se la decomposizione parte da una rete di Petri), dimostrando costruttivamente l'esistenza di una bisimulazione. Inoltre, Ăš stato implementato un software che esegue la decomposizione dei sistemi di transizioni, per rafforzare i risultati teorici con dati sperimentali sistematici. Nella seconda parte della dissertazione si analizza un nuovo modello chiamato MSFSM, che rappresenta un insieme di FSM sincronizzate da due primitive specifiche (Wait State - Stato d'Attesa e Transition Barrier - Barriera di Transizione). Tale modello trova un utilizzo significativo nella sintesi di circuiti sincroni a partire da reti di Petri a scelta libera. In particolare vengono identificati degli errori nell'approccio originale, fornendo delle correzioni.Finite State Machines (FSMs), transition systems (TSs) and Petri nets (PNs) are important models of computation ubiquitous in formal methods for modeling systems. Important problems involve the transition from one model to another. This thesis explores Petri nets, transition systems and Finite State Machines decomposition and optimization. The first part addresses decomposition of transition systems and Petri nets, based on the theory of regions, representing them by means of restricted PNs, e.g., State Machines (SMs) and Free-choice Petri nets (FCPNs). We show that the property called ``excitation-closure" is sufficient to produce a set of synchronized Petri nets bisimilar to the original transition system or to the initial Petri net (if the decomposition starts from a PN), proving by construction the existence of a bisimulation. Furthermore, we implemented a software performing the decomposition of transition systems, and reported extensive experiments. The second part of the dissertation discusses Multiple Synchronized Finite State Machines (MSFSMs) specifying a set of FSMs synchronized by specific primitives: Wait State and Transition Barrier. It introduces a method for converting Petri nets into synchronous circuits using MSFSM, identifies errors in the initial approach, and provides corrections

    A Unifying Theory for Graph Transformation

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    The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Mirror symmetry for Dubrovin-Zhang Frobenius manifolds

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    Frobenius manifolds were formally defined by Boris Dubrovin in the early 1990s, and serve as a bridge between a priori very different fields of mathematics such as integrable systems theory, enumerative geometry, singularity theory, and mathematical physics. This thesis concerns, in particular, a specific class of Frobenius manifolds constructed on the orbit space of an extension of the affine Weyl group defined by Dubrovin together with Youjin Zhang. Here, we find Landau-Ginzburg superpotentials, or B-model mirrors, for these Frobenius structures by considering the characteristic equation for Lax operators of relativistic Toda chains as proposed by Andrea Brini. As a bonus, the results open up various applications in topology, integrable hierarchies, and Gromov-Witten theory, making interesting research questions in these areas more accessible. Some such applications are considered in this thesis. The form of the determinant of the Saito metric on discriminant strata is investigated, applications to the combinatorics of Lyashko-Looijenga maps are given, and investigations into the integrable systems theoretic and enumerative geometric applications are commenced

    Exploration autonome et efficiente de chantiers miniers souterrains inconnus avec un drone filaire

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    Abstract: Underground mining stopes are often mapped using a sensor located at the end of a pole that the operator introduces into the stope from a secure area. The sensor emits laser beams that provide the distance to a detected wall, thus creating a 3D map. This produces shadow zones and a low point density on the distant walls. To address these challenges, a research team from the UniversitĂ© de Sherbrooke is designing a tethered drone equipped with a rotating LiDAR for this mission, thus benefiting from several points of view. The wired transmission allows for unlimited flight time, shared computing, and real-time communication. For compatibility with the movement of the drone after tether entanglements, the excess length is integrated into an onboard spool, contributing to the drone payload. During manual piloting, the human factor causes problems in the perception and comprehension of a virtual 3D environment, as well as the execution of an optimal mission. This thesis focuses on autonomous navigation in two aspects: path planning and exploration. The system must compute a trajectory that maps the entire environment, minimizing the mission time and respecting the maximum onboard tether length. Path planning using a Rapidly-exploring Random Tree (RRT) quickly finds a feasible path, but the optimization is computationally expensive and the performance is variable and unpredictable. Exploration by the frontier method is representative of the space to be explored and the path can be optimized by solving a Traveling Salesman Problem (TSP) but existing techniques for a tethered drone only consider the 2D case and do not optimize the global path. To meet these challenges, this thesis presents two new algorithms. The first one, RRT-Rope, produces an equal or shorter path than existing algorithms in a significantly shorter computation time, up to 70% faster than the next best algorithm in a representative environment. A modified version of RRT-connect computes a feasible path, shortened with a deterministic technique that takes advantage of previously added intermediate nodes. The second algorithm, TAPE, is the first 3D cavity exploration method that focuses on minimizing mission time and unwound tether length. On average, the overall path is 4% longer than the method that solves the TSP, but the tether remains under the allowed length in 100% of the simulated cases, compared to 53% with the initial method. The approach uses a 2-level hierarchical architecture: global planning solves a TSP after frontier extraction, and local planning minimizes the path cost and tether length via a decision function. The integration of these two tools in the NetherDrone produces an intelligent system for autonomous exploration, with semi-autonomous features for operator interaction. This work opens the door to new navigation approaches in the field of inspection, mapping, and Search and Rescue missions.La cartographie des chantiers miniers souterrains est souvent rĂ©alisĂ©e Ă  l’aide d’un capteur situĂ© au bout d’une perche que l’opĂ©rateur introduit dans le chantier, depuis une zone sĂ©curisĂ©e. Le capteur Ă©met des faisceaux laser qui fournissent la distance Ă  un mur dĂ©tectĂ©, crĂ©ant ainsi une carte en 3D. Ceci produit des zones d’ombres et une faible densitĂ© de points sur les parois Ă©loignĂ©es. Pour relever ces dĂ©fis, une Ă©quipe de recherche de l’UniversitĂ© de Sherbrooke conçoit un drone filaire Ă©quipĂ© d’un LiDAR rotatif pour cette mission, bĂ©nĂ©ficiant ainsi de plusieurs points de vue. La transmission filaire permet un temps de vol illimitĂ©, un partage de calcul et une communication en temps rĂ©el. Pour une compatibilitĂ© avec le mouvement du drone lors des coincements du fil, la longueur excĂ©dante est intĂ©grĂ©e dans une bobine embarquĂ©e, qui contribue Ă  la charge utile du drone. Lors d’un pilotage manuel, le facteur humain entraĂźne des problĂšmes de perception et comprĂ©hension d’un environnement 3D virtuel, et d’exĂ©cution d’une mission optimale. Cette thĂšse se concentre sur la navigation autonome sous deux aspects : la planification de trajectoire et l’exploration. Le systĂšme doit calculer une trajectoire qui cartographie l’environnement complet, en minimisant le temps de mission et en respectant la longueur maximale de fil embarquĂ©e. La planification de trajectoire Ă  l’aide d’un Rapidly-exploring Random Tree (RRT) trouve rapidement un chemin rĂ©alisable, mais l’optimisation est coĂ»teuse en calcul et la performance est variable et imprĂ©visible. L’exploration par la mĂ©thode des frontiĂšres est reprĂ©sentative de l’espace Ă  explorer et le chemin peut ĂȘtre optimisĂ© en rĂ©solvant un Traveling Salesman Problem (TSP), mais les techniques existantes pour un drone filaire ne considĂšrent que le cas 2D et n’optimisent pas le chemin global. Pour relever ces dĂ©fis, cette thĂšse prĂ©sente deux nouveaux algorithmes. Le premier, RRT-Rope, produit un chemin Ă©gal ou plus court que les algorithmes existants en un temps de calcul jusqu’à 70% plus court que le deuxiĂšme meilleur algorithme dans un environnement reprĂ©sentatif. Une version modifiĂ©e de RRT-connect calcule un chemin rĂ©alisable, raccourci avec une technique dĂ©terministe qui tire profit des noeuds intermĂ©diaires prĂ©alablement ajoutĂ©s. Le deuxiĂšme algorithme, TAPE, est la premiĂšre mĂ©thode d’exploration de cavitĂ©s en 3D qui minimise le temps de mission et la longueur du fil dĂ©roulĂ©. En moyenne, le trajet global est 4% plus long que la mĂ©thode qui rĂ©sout le TSP, mais le fil reste sous la longueur autorisĂ©e dans 100% des cas simulĂ©s, contre 53% avec la mĂ©thode initiale. L’approche utilise une architecture hiĂ©rarchique Ă  2 niveaux : la planification globale rĂ©sout un TSP aprĂšs extraction des frontiĂšres, et la planification locale minimise le coĂ»t du chemin et la longueur de fil via une fonction de dĂ©cision. L’intĂ©gration de ces deux outils dans le NetherDrone produit un systĂšme intelligent pour l’exploration autonome, dotĂ© de fonctionnalitĂ©s semi-autonomes pour une interaction avec l’opĂ©rateur. Les travaux rĂ©alisĂ©s ouvrent la porte Ă  de nouvelles approches de navigation dans le domaine des missions d’inspection, de cartographie et de recherche et sauvetage

    Improved Approximation Algorithms for Steiner Connectivity Augmentation Problems

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    The Weighted Connectivity Augmentation Problem is the problem of augmenting the edge-connectivity of a given graph by adding links of minimum total cost. This work focuses on connectivity augmentation problems in the Steiner setting, where we are not interested in the connectivity between all nodes of the graph, but only the connectivity between a specified subset of terminals. We consider two related settings. In the Steiner Augmentation of a Graph problem (kk-SAG), we are given a kk-edge-connected subgraph HH of a graph GG. The goal is to augment HH by including links and nodes from GG of minimum cost so that the edge-connectivity between nodes of HH increases by 1. In the Steiner Connectivity Augmentation Problem (kk-SCAP), we are given a Steiner kk-edge-connected graph connecting terminals RR, and we seek to add links of minimum cost to create a Steiner (k+1)(k+1)-edge-connected graph for RR. Note that kk-SAG is a special case of kk-SCAP. All of the above problems can be approximated to within a factor of 2 using e.g. Jain's iterative rounding algorithm for Survivable Network Design. In this work, we leverage the framework of Traub and Zenklusen to give a (1+ln⁥2+Δ)(1 + \ln{2} +\varepsilon)-approximation for the Steiner Ring Augmentation Problem (SRAP): given a cycle H=(V(H),E)H = (V(H),E) embedded in a larger graph G=(V,EâˆȘL)G = (V, E \cup L) and a subset of terminals R⊆V(H)R \subseteq V(H), choose a subset of links S⊆LS \subseteq L of minimum cost so that (V,EâˆȘS)(V, E \cup S) has 3 pairwise edge-disjoint paths between every pair of terminals. We show this yields a polynomial time algorithm with approximation ratio (1+ln⁥2+Δ)(1 + \ln{2} + \varepsilon) for 22-SCAP. We obtain an improved approximation guarantee of (1.5+Δ)(1.5+\varepsilon) for SRAP in the case that R=V(H)R = V(H), which yields a (1.5+Δ)(1.5+\varepsilon)-approximation for kk-SAG for any kk
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