2,831 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 è 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 proprietà chiamata ``chiusura rispetto all'eccitazione" (excitation-closure) è sufficiente per produrre un insieme di reti di Petri la cui sincronizzazione è 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, è 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

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Posthuman Creative Styling can a creative writer’s style of writing be described as procedural?

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    This thesis is about creative styling — the styling a creative writer might use to make their writing unique. It addresses the question as to whether such styling can be described as procedural. Creative styling is part of the technique a creative writer uses when writing. It is how they make the text more ‘lively’ by use of tips and tricks they have either learned or discovered. In essence these are rules, ones the writer accrues over time by their practice. The thesis argues that the use and invention of these rules can be set as procedures. and so describe creative styling as procedural. The thesis follows from questioning why it is that machines or algorithms have, so far, been incapable of producing creative writing which has value. Machine-written novels do not abound on the bookshelves and writing styled by computers is, on the whole, dull in comparison to human-crafted literature. It came about by thinking how it would be possible to reach a point where writing by people and procedural writing are considered to have equal value. For this reason the thesis is set in a posthuman context, where the differences between machines and people are erased. The thesis uses practice to inform an original conceptual space model, based on quality dimensions and dynamic-inter operation of spaces. This model gives an example of the procedures which a posthuman creative writer uses when engaged in creative styling. It suggests an original formulation for the conceptual blending of conceptual spaces, based on the casting of qualities from one space to another. In support of and informing its arguments are ninety-nine examples of creative writing practice which show the procedures by which style has been applied, created and assessed. It provides a route forward for further joint research into both computational and human-coded creative writing

    On the use of senders for minimal Ramsey theory

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    This thesis investigates problems related to extremal and probabilistic graph theory. Our focus lies on the highly dynamic field of Ramsey theory. The foundational result of this field was proved in 1930 by Franck P. Ramsey. It implies that for every integer t and every sufficiently large complete graph Kn, every colouring of the edges of Kn with colours red and blue contains a red copy or a blue copy of Kt. Let q ⩾ 2 represent a number of colours, and let H1,..., Hq be graphs. A graph G is said to be q-Ramsey for the tuple (H1,...,Hq) if, for every colouring of the edges of G with colours {1, . . . , q}, there exists a colour i and a monochromatic copy of Hi in colour i. As we often want to understand the structural properties of the collection of graphs that are q-Ramsey for (H1,..., Hq), we restrict our attention to the graphs that are minimal for this property, with respect to subgraph inclusion. Such graphs are said to be q-Ramsey-minimal for (H1,..., Hq). In 1976, Burr, Erdős, and Lovász determined, for every s, t ⩾ 3, the smallest minimum degree of a graph G that is 2-Ramsey-minimal for (Ks, Kt). Significant efforts have been dedicated to generalising this result to a higher number of colours, q⩾3, starting with the ‘symmetric’ q-tuple (Kt,..., Kt). In this thesis, we improve on the best known bounds for this parameter, providing state-of-the-art bounds in different (q, t)-regimes. These improvements rely on constructions based on finite geometry, which are then used to prove the existence of extremal graphs with certain key properties. Another crucial ingredient in these proofs is the existence of gadget graphs, called signal senders, that were initially developed by Burr, Erdős, and Lovász in 1976 for pairs of complete graphs. Until now, these senders have been shown to exist only in the two-colour setting, when q = 2, or in the symmetric multicolour setting, when H1,..., Hq are pairwise isomorphic. In this thesis, we then construct similar gadgets for all tuples of complete graphs, providing the first known constructions of these tools in the multicolour asymmetric setting. We use these new senders to prove far-reaching generalisations of several classical results in the area

    Rainbow bases in matroids

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    Recently, it was proved by B\'erczi and Schwarcz that the problem of factorizing a matroid into rainbow bases with respect to a given partition of its ground set is algorithmically intractable. On the other hand, many special cases were left open. We first show that the problem remains hard if the matroid is graphic, answering a question of B\'erczi and Schwarcz. As another special case, we consider the problem of deciding whether a given digraph can be factorized into subgraphs which are spanning trees in the underlying sense and respect upper bounds on the indegree of every vertex. We prove that this problem is also hard. This answers a question of Frank. In the second part of the article, we deal with the relaxed problem of covering the ground set of a matroid by rainbow bases. Among other results, we show that there is a linear function ff such that every matroid that can be factorized into kk bases for some k≥3k \geq 3 can be covered by f(k)f(k) rainbow bases if every partition class contains at most 2 elements

    Thick Forests

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    We consider classes of graphs, which we call thick graphs, that have their vertices replaced by cliques and their edges replaced by bipartite graphs. In particular, we consider the case of thick forests, which are a subclass of perfect graphs. We show that this class can be recognised in polynomial time, and examine the complexity of counting independent sets and colourings for graphs in the class. We consider some extensions of our results to thick graphs beyond thick forests.Comment: 40 pages, 19 figure

    Canonical Decompositions in Monadically Stable and Bounded Shrubdepth Graph Classes

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    Single-Exponential FPT Algorithms for Enumerating Secluded F\mathcal{F}-Free Subgraphs and Deleting to Scattered Graph Classes

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    The celebrated notion of important separators bounds the number of small (S,T)(S,T)-separators in a graph which are 'farthest from SS' in a technical sense. In this paper, we introduce a generalization of this powerful algorithmic primitive that is phrased in terms of kk-secluded vertex sets: sets with an open neighborhood of size at most kk. In this terminology, the bound on important separators says that there are at most 4k4^k maximal kk-secluded connected vertex sets CC containing SS but disjoint from TT. We generalize this statement significantly: even when we demand that G[C]G[C] avoids a finite set F\mathcal{F} of forbidden induced subgraphs, the number of such maximal subgraphs is 2O(k)2^{O(k)} and they can be enumerated efficiently. This allows us to make significant improvements for two problems from the literature. Our first application concerns the 'Connected kk-Secluded F\mathcal{F}-free subgraph' problem, where F\mathcal{F} is a finite set of forbidden induced subgraphs. Given a graph in which each vertex has a positive integer weight, the problem asks to find a maximum-weight connected kk-secluded vertex set C⊆V(G)C \subseteq V(G) such that G[C]G[C] does not contain an induced subgraph isomorphic to any F∈FF \in \mathcal{F}. The parameterization by kk is known to be solvable in triple-exponential time via the technique of recursive understanding, which we improve to single-exponential. Our second application concerns the deletion problem to scattered graph classes. Here, the task is to find a vertex set of size at most kk whose removal yields a graph whose each connected component belongs to one of the prescribed graph classes Π1,…,Πd\Pi_1, \ldots, \Pi_d. We obtain a single-exponential algorithm whenever each class Πi\Pi_i is characterized by a finite number of forbidden induced subgraphs. This generalizes and improves upon earlier results in the literature.Comment: To appear at ISAAC'2

    Existence of a tricritical point for the Blume-Capel model on Zd\mathbb{Z}^d

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    We prove the existence of a tricritical point for the Blume-Capel model on Zd\mathbb{Z}^d for every d≥2d\geq 2. The proof in d≥3d\geq 3 relies on a novel combinatorial mapping to an Ising model on a larger graph, the techniques of Aizenman, Duminil-Copin, and Sidoravicious (Comm. Math. Phys, 2015), and the celebrated infrared bound. In d=2d=2, the proof relies on a quantitative analysis of crossing probabilities of the dilute random cluster representation of the Blume-Capel. In particular, we develop a quadrichotomy result in the spirit of Duminil-Copin and Tassion (Moscow Math. J., 2020), which allows us to obtain a fine picture of the phase diagram in d=2d=2, including asymptotic behaviour of correlations in all regions. Finally, we show that the techniques used to establish subcritical sharpness for the dilute random cluster model extend to any d≥2d\geq 2.Comment: 55 pages. 4 figures. v2 includes fixes of typos and clarification
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