Adaptive learning of compressible strings

Suppose an oracle knows a string S that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is s a substring of S?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm needs to ask the oracle Sigma n/4 - O(n) queries in order to be able to reconstruct the hidden string, where Sigma is the size of the alphabet of S and n its length, and gave an algorithm that spends (Sigma - 1)n + O(Sigma root n) queries to reconstruct S. The main contribution of our paper is to improve the above upper-bound in the context where the string is compressible. We first present a universal algorithm that, given a (computable) compressor that compresses the string to Tau bits, performs q = O(Tau) substring queries; this algorithm, however, runs in exponential time. For this reason, the second part of the paper focuses on more time-efficient algorithms whose number of queries is bounded by specific compressibility measures. We first show that any string of length n over an integer alphabet of size Sigma with rle runs can be reconstructed with q = O(rle(Sigma + log nrle)) substring queries in linear time and space. We then present an algorithm that spends q is an element of O (Sigma g log n) substring queries and runs in O (n(logn + log Sigma) + q) time using linear space, where g is the size of a smallest straight-line program generating the string. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Maximal Closed Substrings

A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a maximal closed substring (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least 2 are commonly called runs; those with exponent smaller than 2, instead, are particular cases of maximal gapped repeats. We show that a string of length n contains O(n1.5) MCSs. We also provide an output-sensitive algorithm that, given a string of length n over a constant-size alphabet, locates all m MCSs the string contains in O(nlog n+ m) time

A Characterization of Infinite LSP Words

G. Fici proved that a finite word has a minimal suffix automaton if and only if all its left special factors occur as prefixes. He called LSP all finite and infinite words having this latter property. We characterize here infinite LSP words in terms of $S$-adicity. More precisely we provide a finite set of morphisms $S$ and an automaton ${\cal A}$ such that an infinite word is LSP if and only if it is $S$-adic and all its directive words are recognizable by ${\cal A}$

Minimal Forbidden Factors of Circular Words

Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist algorithms for computing the minimal forbidden factors of a word, as well as of a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an algorithm that, given the trie recognizing a finite antifactorial language $M$, computes a DFA recognizing the language whose set of minimal forbidden factors is $M$. In the same paper, they showed that the obtained DFA is minimal if the input trie recognizes the minimal forbidden factors of a single word. We generalize this result to the case of a circular word. We discuss several combinatorial properties of the minimal forbidden factors of a circular word. As a byproduct, we obtain a formal definition of the factor automaton of a circular word. Finally, we investigate the case of minimal forbidden factors of the circular Fibonacci words.Comment: To appear in Theoretical Computer Scienc

POSTURE AND POSTUROLOGY, ANATOMICAL AND PHYSIOLOGICAL PROFILES: OVERVIEW AND CURRENT STATE OF ART

Background and aim of work: posture is the position of the body in the space, and is controlled by a set of anatomical structures. The maintenance and the control of posture are a set of interactions between muscle-skeletal, visual, vestibular, and skin system. Lately there are numerous studies that correlate the muscle-skeletal and the maintenance of posture. In particular, the correction of defects and obstruction of temporomandibular disorders, seem to have an impoact on posture. The aim of this work is to collect information in literature on posture and the influence of the stomatognatich system on postural system. Methods: Comparison of the literature on posture and posturology by consulting books and scientific sites. results: the results obtained from the comparison of the of the literature on posture and posturology by consulting books and scientific sites. Some studies support the correlation between stomatognatich system and posture, while others such a correlation. Conclusions: further studies are necessary to be able to confirm one or the other argument. (www.actabiomedica.it

Timing of Millisecond Pulsars in NGC 6752: Evidence for a High Mass-to-Light Ratio in the Cluster Core

Using pulse timing observations we have obtained precise parameters, including positions with about 20 mas accuracy, of five millisecond pulsars in NGC 6752. Three of them, located relatively close to the cluster center, have line-of-sight accelerations larger than the maximum value predicted by the central mass density derived from optical observation, providing dynamical evidence for a central mass-to-light ratio >~ 10, much higher than for any other globular cluster. It is likely that the other two millisecond pulsars have been ejected out of the core to their present locations at 1.4 and 3.3 half-mass radii, respectively, suggesting unusual non-thermal dynamics in the cluster core.Comment: Accepted by ApJ Letter. 5 pages, 2 figures, 1 tabl

A Characterization of Bispecial Sturmian Words

A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian words.Comment: Accepted to MFCS 201