2,737 research outputs found

    The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

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    Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page

    Representing Graph Families with Edge Grammars

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    An edge grammar is a formal mechanism for representing families of related graphs (binary trees, hypercubes, meshes, etc.). Given an edge grammar, larger graphs in the family are derived from simple basis graphs using edge rewriting rules. A drawback to many graph grammars is that they cannot represent some important, highly regular graph families such as the family of shuffie-exchange graphs. Edge grammars, however, exist for all "computable " graph families, and simple edge gramma.rs exist for most regular graph families. In this paper, we define and illuskate edge grammars and analyze them in the context of formal language theory. Our results include hierarchy and decidability properties. Since this work originally was motivated by a need to represent graph families found in parallel computation, the application of edge grammars in this context is also discussed

    Quantitative imaging of the complexity in liquid bubbles' evolution reveals the dynamics of film retraction

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    The dynamics and stability of thin liquid films have fascinated scientists over many decades. Thin film flows are central to numerous areas of engineering, geophysics, and biophysics and occur over a wide range of length, velocity, and liquid properties scales. In spite of many significant developments in this area, we still lack appropriate quantitative experimental tools with the spatial and temporal resolution necessary for a comprehensive study of film evolution. We propose tackling this problem with a holographic technique that combines quantitative phase imaging with a custom setup designed to form and manipulate bubbles. The results, gathered on a model aqueous polymeric solution, provide an unparalleled insight into bubble dynamics through the combination of full-field thickness estimation, three-dimensional imaging, and fast acquisition time. The unprecedented level of detail offered by the proposed methodology will promote a deeper understanding of the underlying physics of thin film dynamics

    An Approach to Regular Separability in Vector Addition Systems

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    We study the problem of regular separability of languages of vector addition systems with states (VASS). It asks whether for two given VASS languages K and L, there exists a regular language R that includes K and is disjoint from L. While decidability of the problem in full generality remains an open question, there are several subclasses for which decidability has been shown: It is decidable for (i) one-dimensional VASS, (ii) VASS coverability languages, (iii) languages of integer VASS, and (iv) commutative VASS languages. We propose a general approach to deciding regular separability. We use it to decide regular separability of an arbitrary VASS language from any language in the classes (i), (ii), and (iii). This generalizes all previous results, including (iv)

    Automata theory and formal languages

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    These lecture notes present some basic notions and results on Automata Theory, Formal Languages Theory, Computability Theory, and Parsing Theory. I prepared these notes for a course on Automata, Languages, and Translators which I am teaching at the University of Roma Tor Vergata. More material on these topics and on parsing techniques for context-free languages can be found in standard textbooks such as [1, 8, 9]. The reader is encouraged to look at those books. A theorem denoted by the triple k.m.n is in Chapter k and Section m, and within that section it is identified by the number n. Analogous numbering system is used for algorithms, corollaries, definitions, examples, exercises, figures, and remarks. We use ‘iff’ to mean ‘if and only if’. Many thanks to my colleagues of the Department of Informatics, Systems, and Production of the University of Roma Tor Vergata. I am also grateful to my stu- dents and co-workers and, in particular, to Lorenzo Clemente, Corrado Di Pietro, Fulvio Forni, Fabio Lecca, Maurizio Proietti, and Valerio Senni for their help and encouragement. Finally, I am grateful to Francesca Di Benedetto, Alessandro Colombo, Donato Corvaglia, Gioacchino Onorati, and Leonardo Rinaldi of the Aracne Publishing Com- pany for their kind cooperation

    Repetitive subwords

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    The central notionof thisthesisis repetitionsin words. We studyproblemsrelated to contiguous repetitions. More specifically we will consider repeating scattered subwords of non-primitive words, i.e. words which are complete repetitions of other words. We will present inequalities concerning these occurrences as well as giving apartial solutionto an openproblemposedby Salomaaet al. We will characterize languages, whichare closed under the operation ofduplication, thatis repeating any factor of a word. We alsogive newbounds onthe number of occurrencesof certain types of repetitions of words. We give a solution to an open problem posed by Calbrix and Nivat concerning regular languages consisting of non-primitive words. We alsopresentsomeresultsregarding theduplication closureoflanguages,among which a new proof to a problem of Bovet and Varricchio

    High-resolution 3D analysis of mouse small-intestinal stroma.

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    Here we detail a protocol for whole-mount immunostaining of mouse small-intestinal villi that can be used to generate high-resolution 3D images of all gut cell types, including blood and lymphatic vessel cells, neurons, smooth muscle cells, fibroblasts and immune cells. The procedure describes perfusion, fixation, dissection, immunostaining, mounting, clearing, confocal imaging and quantification, using intestinal vasculature as an example. As intestinal epithelial cells prevent visualization with some antibodies, we also provide an optional protocol to remove these cells before fixation. In contrast to alternative current techniques, our protocol enables the entire villus to be visualized with increased spatial resolution of cell location, morphology and cell-cell interactions, thus allowing for easy quantification of phenotypes. The technique, which takes 7 d from mouse dissection to microscopic examination, will be useful for researchers who are interested in most aspects of intestinal biology, including mucosal immunology, infection, nutrition, cancer biology and intestinal microbiota
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