Succinct Dictionary Matching With No Slowdown

The problem of dictionary matching is a classical problem in string matching: given a set S of d strings of total length n characters over an (not necessarily constant) alphabet of size sigma, build a data structure so that we can match in a any text T all occurrences of strings belonging to S. The classical solution for this problem is the Aho-Corasick automaton which finds all occ occurrences in a text T in time O(|T| + occ) using a data structure that occupies O(m log m) bits of space where m <= n + 1 is the number of states in the automaton. In this paper we show that the Aho-Corasick automaton can be represented in just m(log sigma + O(1)) + O(d log(n/d)) bits of space while still maintaining the ability to answer to queries in O(|T| + occ) time. To the best of our knowledge, the currently fastest succinct data structure for the dictionary matching problem uses space O(n log sigma) while answering queries in O(|T|log log n + occ) time. In this paper we also show how the space occupancy can be reduced to m(H0 + O(1)) + O(d log(n/d)) where H0 is the empirical entropy of the characters appearing in the trie representation of the set S, provided that sigma < m^epsilon for any constant 0 < epsilon < 1. The query time remains unchanged.Comment: Corrected typos and other minor error

Linear Parsing Expression Grammars

PEGs were formalized by Ford in 2004, and have several pragmatic operators (such as ordered choice and unlimited lookahead) for better expressing modern programming language syntax. Since these operators are not explicitly defined in the classic formal language theory, it is significant and still challenging to argue PEGs' expressiveness in the context of formal language theory.Since PEGs are relatively new, there are several unsolved problems.One of the problems is revealing a subclass of PEGs that is equivalent to DFAs. This allows application of some techniques from the theory of regular grammar to PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some patterns of recursive nonterminal in PEGs, and include the full set of ordered choice, unlimited lookahead, and greedy repetition, which are characteristic of PEGs. Although the conversion judgement of parsing expressions into DFAs is undecidable in general, the formalism of LPEGs allows for a syntactical judgement of parsing expressions.Comment: Parsing expression grammars, Boolean finite automata, Packrat parsin

Reasoning about embedded dependencies using inclusion dependencies

The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded dependencies that is based on the chase and uses inclusion dependencies and implicit existential quantification in the intermediate steps of deductions

Abstract Interpretation of Indexed Grammars.

Indexed grammars are a generalization of context-free grammars and recognize a proper subset of context-sensitive languages. The class of languages recognized by indexed grammars are called indexed languages and they correspond to the languages recognized by nested stack automata. For example indexed grammars can recognize the language {a^n b^n c^n | n &gt; = 1} which is not context-free, but they cannot recognize {(ab^n)^n) | n &gt;= 1} which is context-sensitive. Indexed grammars identify a set of languages that are more expressive than context-free languages, while having decidability results that lie in between the ones of context-free and context-sensitive languages. In this work we study indexed grammars in order to formalize the relation between indexed languages and the other classes of languages in the Chomsky hierarchy. To this end, we provide a fixpoint characterization of the languages recognized by an indexed grammar and we study possible ways to abstract, in the abstract interpretation sense, these languages and their grammars into context-free and regular languages

Pilot Assessment of the Repeatability of Indocyanine Green Fluorescence Imaging and Correlation with Traditional Foot Perfusion Assessments

Background: Ankle brachial index (ABI), toe pressures (TP), and transcutaneous oxygen pressure (TcPO2) are traditionally used in the assessment of critical limb ischemia (CLI). Indocyanine green (ICG) fluorescence imaging can be used to evaluate local circulation in the foot and to evaluate the severity of ischemia. This prospective study analyzed the suitability of a fluorescence imaging system (photodynamic eye [PDE]) in CLI. Material and methods: Forty-one patients with CLI were included. Of the patients, 66% had diabetes and there was an ischemic tissue lesion in 70% of the limbs. ABI, toe pressures, TcPO2 and ICG-fluorescence imaging (ICG-FI) were measured in each leg. To study the repeatability of the ICG-FI, each patient underwent the study twice. After the procedure, foot circulation was measured using a time-intensity curve, where T1/2 (the time needed to achieve half of the maximum fluorescence intensity) and PDE10 (increase of the intensity during the first 10 s) were determined. A time-intensity curve was plotted using the same areas as for the TcPO2 probes (n=123). Results: The mean ABI was 0.43, TP 21 mmHg, TcPO2 23 mmHg, T1/2 38 5, and PDE10 19 AU. Time-intensity curves were repeatable. In a Bland-Altman scatter plot, the 95% limits of agreement of PDE10 was 9.9 AU and the corresponding value of T1/2 was 14 s. Correlation between ABI and TP was significant (R=.73, p Conclusions: According to this pilot study, ICG-Fl with PDE can be used in the assessment of blood supply in the ischemic foot. (C) 2016 European Society for Vascular Surgery. Published by Elsevier Ltd. All rights reserved.Peer reviewe

Viral and Bacterial Pathogens in Bovine Respiratory Disease in Finland

Pathogens causing bovine respiratory tract disease in Finland were investigated. Eighteen cattle herds with bovine respiratory disease were included. Five diseased calves from each farm were chosen for closer examination and tracheobronchial lavage. Blood samples were taken from the calves at the time of the investigation and from 86 calves 3–4 weeks later. In addition, 6–10 blood samples from animals of different ages were collected from each herd, resulting in 169 samples. Serum samples were tested for antibodies to bovine parainfluenza virus-3 (PIV-3), bovine respiratory syncytial virus (BRSV), bovine coronavirus (BCV), bovine adenovirus-3 (BAV-3) and bovine adenovirus-7 (BAV-7). About one third of the samples were also tested for antibodies to bovine virus diarrhoea virus (BVDV) with negative results. Bacteria were cultured from lavage fluid and in vitro susceptibility to selected antimicrobials was tested. According to serological findings, PIV-3, BAV-7, BAV-3, BCV and BRSV are common pathogens in Finnish cattle with respiratory problems. A titre rise especially for BAV-7 and BAV-3, the dual growth of Mycoplasma dispar and Pasteurella multocida, were typical findings in diseased calves. Pasteurella sp. strains showed no resistance to tested antimicrobials. Mycoplasma bovis and Mannheimia haemolytica were not found

Interaction of quasilocal harmonic modes and boson peak in glasses

The direct proportionality relation between the boson peak maximum in glasses, $\omega_b$, and the Ioffe-Regel crossover frequency for phonons, $\omega_d$, is established. For several investigated materials $\omega_b = (1.5\pm 0.1)\omega_d$. At the frequency $\omega_d$ the mean free path of the phonons $l$ becomes equal to their wavelength because of strong resonant scattering on quasilocal harmonic oscillators. Above this frequency phonons cease to exist. We prove that the established correlation between $\omega_b$ and $\omega_d$ holds in the general case and is a direct consequence of bilinear coupling of quasilocal oscillators with the strain field.Comment: RevTex, 4 pages, 1 figur

Implementing Shor's algorithm on Josephson Charge Qubits

We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21. We consider both the physical and algorithmic requirements for an optimal implementation when only a small number of qubits is available. These aspects of quantum computation are usually the topics of separate research communities; we present a unifying discussion of both of these fundamental features bridging Shor's algorithm to its physical realization using Josephson junction qubits. In order to meet the stringent requirements set by a short decoherence time, we accelerate the algorithm by decomposing the quantum circuit into tailored two- and three-qubit gates and we find their physical realizations through numerical optimization.Comment: 12 pages, submitted to Phys. Rev.