128 research outputs found

    Almost Every Simply Typed Lambda-Term Has a Long Beta-Reduction Sequence

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    It is well known that the length of a beta-reduction sequence of a simply typed lambda-term of order k can be huge; it is as large as k-fold exponential in the size of the lambda-term in the worst case. We consider the following relevant question about quantitative properties, instead of the worst case: how many simply typed lambda-terms have very long reduction sequences? We provide a partial answer to this question, by showing that asymptotically almost every simply typed lambda-term of order k has a reduction sequence as long as (k-1)-fold exponential in the term size, under the assumption that the arity of functions and the number of variables that may occur in every subterm are bounded above by a constant. To prove it, we have extended the infinite monkey theorem for strings to a parametrized one for regular tree languages, which may be of independent interest. The work has been motivated by quantitative analysis of the complexity of higher-order model checking

    Pumping Lemma for Higher-order Languages

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    We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given language does not belong to the classes of regular/context-free/indexed languages. We prove a pumping lemma for word/tree languages of arbitrary orders, modulo a conjecture that a higher-order version of Kruskal\u27s tree theorem holds. We also show that the conjecture indeed holds for the order-2 case, which yields a pumping lemma for order-2 tree languages and order-3 word languages

    On Word and Frontier Languages of Unsafe Higher-Order Grammars

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    Higher-order grammars are an extension of regular and context-free grammars, where nonterminals may take parameters. They have been extensively studied in 1980\u27s, and restudied recently in the context of model checking and program verification. We show that the class of unsafe order-(n+1) word languages coincides with the class of frontier languages of unsafe order-n tree languages. We use intersection types for transforming an order-(n+1) word grammar to a corresponding order-n tree grammar. The result has been proved for safe languages by Damm in 1982, but it has been open for unsafe languages, to our knowledge. Various known results on higher-order grammars can be obtained as almost immediate corollaries of our result

    Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered

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    Asada and Kobayashi [ICALP 2017] conjectured a higher-order version of Kruskal\u27s tree theorem, and proved a pumping lemma for higher-order languages modulo the conjecture. The conjecture has been proved up to order-2, which implies that Asada and Kobayashi\u27s pumping lemma holds for order-2 tree languages, but remains open for order-3 or higher. In this paper, we prove a variation of the conjecture for order-3. This is sufficient for proving that a variation of the pumping lemma holds for order-3 tree languages (equivalently, for order-4 word languages)

    Size-Preserving Translations from Order-(n+1) Word Grammars to Order-n Tree Grammars

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    Higher-order grammars have recently been studied actively in the context of automated verification of higher-order programs. Asada and Kobayashi have previously shown that, for any order-(n+1) word grammar, there exists an order-n grammar whose frontier language coincides with the language generated by the word grammar. Their translation, however, blows up the size of the grammar, which inhibited complexity-preserving reductions from decision problems on word grammars to those on tree grammars. In this paper, we present a new translation from order-(n+1) word grammars to order-n tree grammars that is size-preserving in the sense that the size of the output tree grammar is polynomial in the size of an input tree grammar. The new translation and its correctness proof are arguably much simpler than the previous translation and proof

    On Average-Case Hardness of Higher-Order Model Checking

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    We study a mixture between the average case and worst case complexities of higher-order model checking, the problem of deciding whether the tree generated by a given ? Y-term (or equivalently, a higher-order recursion scheme) satisfies the property expressed by a given tree automaton. Higher-order model checking has recently been studied extensively in the context of higher-order program verification. Although the worst-case complexity of the problem is k-EXPTIME complete for order-k terms, various higher-order model checkers have been developed that run efficiently for typical inputs, and program verification tools have been constructed on top of them. One may, therefore, hope that higher-order model checking can be solved efficiently in the average case, despite the worst-case complexity. We provide a negative result, by showing that, under certain assumptions, for almost every term, the higher-order model checking problem specialized for the term is k-EXPTIME hard with respect to the size of automata. The proof is based on a novel intersection type system that characterizes terms that do not contain any useless subterms


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    Carbapenemase-producing Enterobacteriaceae represent a serious public health threat worldwide. Carbapenemase genes, harbored on a transferable plasmid, have been isolated globally with distinct geographical features. Klebsiella pneumoniae, included in Enterobacteriaceae, also produces carbapenemase and often shows hypervirulence. Overlapping carbapenem resistance and hypervirulence in K. pneumoniae have been reported, but such strains have not yet been found in Japan. Here, we screened 104 carbapenemase-producing K. pneumoniae isolates collected from 37 hospitals and outpatient clinics in Japan between September 2014 and July 2015. PCR and DNA sequencing demonstrated IMP-1 in 21 isolates and IMP-6 in 83 isolates, 77 of which coharbored CTX-M-2. Most of the isolates showed low MICs toward imipenem and meropenem but high MICs toward penicillin and cephalosporins. Conjugation experiments with an Escherichia coli J53 recipient showed that most of the plasmids in IMP-6 producers were transferable, whereas only one-half of the plasmids in IMP-1 producers were transferable. PCR-based replicon typing and multiplex PCR identified five isolates belonging to the CG258 non-tonB79 cluster and no isolate belonging to the CG258-tonB79 cluster or sequence type 307 (ST307). Four K1-ST23 isolates, 10 K2-ST65 isolates, and 7 K2-ST86 isolates were detected that harbored virulence genes. The resistance genes in 85 isolates were transferable, but the virulence genes were not transferred. These results demonstrate the acquisition of IMP-type carbapenemase genes and CTX-M-type genes among hypervirulence isolates in Japan, warranting further attention and countermeasures. In this study, we have determined the molecular characteristics and epidemiology of IMP-6 producers that coharbored various CTX-M genes in Japan.IMPORTANCE Carbapenems serve as a last resort for the clinical treatment of multidrug-resistant infections. Therefore, the rapid spread of carbapenemase-producing strains represents a serious public health threat, further limiting antibiotic choices. The current findings of hypervirulent carbapenemase-producing Klebsiella pneumoniae clinical isolates in Japan demonstrate the potential broad spread and transfer of these genes, necessitating close surveillance.博士(医学)・乙第1509号・令和3年3月15日Copyright © 2020 Yonekawa et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International license(https://creativecommons.org/licenses/by/4.0/)

    Hematopoietic stem cell-derived Tregs are essential for maintaining favorable B cell lymphopoiesis following posttransplant cyclophosphamide

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    Posttransplant cyclophosphamide (PTCy) is associated with a low incidence of chronic graft -versus-host disease (cGVHD) following hematopoietic stem cell (HSC) transplantation. Previous studies have shown the important roles of B cell immunity in cGVHD development. Here, we investigated the long-term reconstitution of B lymphopoiesis after PTCy using murine models. We first demonstrated that the immune homeostatic abnormality leading to cGVHD is characterized by an initial increase in effector T cells in the bone marrow and subsequent B and Treg cytopenia. PTCy, but not cyclosporine A or rapamycin, inhibits the initial alloreactive T cell response, which restores intra-bone marrow B lymphogenesis with a concomitant vigorous increase in Tregs. This leads to profound changes in posttransplant B cell homeostasis, including decreased B cell activating factors, increased transitional and regulatory B cells, and decreased germinal center B cells. To identify the cells responsible for PTCy-induced B cell tolerance, we selectively depleted Treg populations that were graft or HSC derived using DEREG mice. Deletion of either Treg population without PTCy resulted in critical B cytopenia. PTCy rescued B lymphopoiesis from graft-derived Treg deletion. In contrast, the negative effect of HSC-derived Treg deletion could not be overcome by PTCy, indicating that HSC-derived Tregs are essential for maintaining favorable B lymphopoiesis following PTCy. These findings define the mechanisms by which PTCy restores homeostasis of the B cell lineage and reestablishes immune tolerance

    Coincidence analysis to search for inspiraling compact binaries using TAMA300 and LISM data

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    Japanese laser interferometric gravitational wave detectors, TAMA300 and LISM, performed a coincident observation during 2001. We perform a coincidence analysis to search for inspiraling compact binaries. The length of data used for the coincidence analysis is 275 hours when both TAMA300 and LISM detectors are operated simultaneously. TAMA300 and LISM data are analyzed by matched filtering, and candidates for gravitational wave events are obtained. If there is a true gravitational wave signal, it should appear in both data of detectors with consistent waveforms characterized by masses of stars, amplitude of the signal, the coalescence time and so on. We introduce a set of coincidence conditions of the parameters, and search for coincident events. This procedure reduces the number of fake events considerably, by a factor 104\sim 10^{-4} compared with the number of fake events in single detector analysis. We find that the number of events after imposing the coincidence conditions is consistent with the number of accidental coincidences produced purely by noise. We thus find no evidence of gravitational wave signals. We obtain an upper limit of 0.046 /hours (CL =90= 90 %) to the Galactic event rate within 1kpc from the Earth. The method used in this paper can be applied straightforwardly to the case of coincidence observations with more than two detectors with arbitrary arm directions.Comment: 28 pages, 17 figures, Replaced with the version to be published in Physical Review