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On the Height of Towers of Subsequences and Prefixes [article]

Štěpán Holub, Tomáš Masopust, Michaël Thomazo
2017 arXiv   pre-print
We study upper and lower bounds on the height of maximal finite towers with respect to the size of the NFA (the DFA) representation of the languages.  ...  A tower is a sequence of words alternating between two languages in such a way that every word is a subsequence of the following word. The height of the tower is the number of words in the sequence.  ...  bound on the height of towers of prefixes.  ... 
arXiv:1705.02813v1 fatcat:crfldvntrzba3bacmy52oqqmz4

On the height of towers of subsequences and prefixes

Štěpán Holub, Tomáš Masopust, Michaël Thomazo
2019 Information and Computation  
A tower is a sequence of words alternating between two languages in such a way that every word is a subsequence of the following word. The height of the tower is the number of words in the sequence.  ...  We study upper and lower bounds on the height of maximal finite towers between two regular languages with respect to the size of the NFA (respectively the DFA) representation.  ...  We are grateful to anonymous referees for their suggestions that allowed to improve and simplify the exposition.  ... 
doi:10.1016/j.ic.2019.01.004 fatcat:cis3qcln6rfrdpnc4przjccnqq

Alternating Towers and Piecewise Testable Separators [article]

Štěpán Holub and Tomáš Masopust and Michaël Thomazo
2015 arXiv   pre-print
We show that it is closely related to the height of maximal finite towers, and provide the upper and lower bounds with respect to the size of the given nondeterministic automata.  ...  Since these towers mostly turn out to be sequences of prefixes, we also provide a comparison with towers of prefixes.  ...  Acknowledgements The authors would like to thank Stefan Borgwardt, Wojciech Czerwiński, Galina Jirásková, Markus Krötzsch, and Wim Martens for valuable discussions on various parts of the paper.  ... 
arXiv:1409.3943v2 fatcat:qm7gkbvw5rahtod7uvkzro6sva

Page 332 of The University Magazine Vol. 35, Issue 207 [page]

1850 The University Magazine  
, by Pagan hands and for Some Remarks on the Origin of the Round Towers.  ...  once congregated, and whence they were subsequently scattered over the face of the whole earth.  ... 

On Upper and Lower Bounds on the Length of Alternating Towers [article]

Štěpán Holub, Galina Jirásková, Tomáš Masopust
2014 arXiv   pre-print
A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each  ...  We investigate upper and lower bounds on the length of finite towers between two regular languages with respect to the size of the automata representing the languages in the case there is no infinite tower  ...  Although every tower of prefixes is also a tower of subsequences, the condition that there are no infinite towers is weaker for prefixes.  ... 
arXiv:1404.4495v2 fatcat:lvksqohfjnfrlor5ygwg22chie

On Upper and Lower Bounds on the Length of Alternating Towers [chapter]

Štěpán Holub, Galina Jirásková, Tomáš Masopust
2014 Lecture Notes in Computer Science  
A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each  ...  We investigate upper and lower bounds on the length of finite towers between two regular languages with respect to the size of the automata representing the languages in the case there is no infinite tower  ...  Although every tower of prefixes is also a tower of subsequences, the condition that there are no infinite towers is weaker for prefixes.  ... 
doi:10.1007/978-3-662-44522-8_27 fatcat:gnjmoz4x6rcnpijbymxxhac44m

Page 165 of The Journal of Sacred Literature Vol. 3, Issue 5 [page]

1856 The Journal of Sacred Literature  
The tsukku (R. po sepsit) were, I presume, walls on each side of the canal, between which and it were “the walks,” subsequently mentioned. The entire is stated to have been dedicated to Marduk.  ...  In the 30th and 31st lines of the inscription on the cylinders which Col.  ... 

Page 296 of The Gentleman's Magazine Vol. 23, Issue [page]

1845 The Gentleman's Magazine  
The chancel and nave, being of equal breadth and height, are externally distinguished only by the juxtaposition of two of the roof-corbels.  ...  The tower is square, and, from certain marks on its north and south sides, is probably older than the nave ; but it pos- sesses nothing of Saxon character except, as at Barton and Barnack, the absence  ... 

Page 496 of Notes and Queries Vol. 6, Issue 160 [page]

1852 Notes and Queries  
The name in the first line yet adheres to us; the prefix in the second is no longer applicable ; nor is the last line now true, for in 1815 the tower of the church, which was then only about the height  ...  of that town, and subsequently a receiver of the customs within its harbour.  ... 

Page 362 of The Mirror, Monthly Magazine Vol. 30, Issue 866 [page]

1837 The Mirror, Monthly Magazine  
The tower, 154 feet high; its length, 30 feet by 32: the height of the body, from the paving to the vaulting, 109 feet: the whole supported by eight arches, surmounted by as many large windows on each  ...  The eras of the subsequent additions are not particularly re- corded ; yet the uniformity of style which ap- pears in the upper parts of the church and tower, imply, that it was completed in a short time  ... 

Page 201 of Monthly Chronicle of North Country Lore and Legend Vol. 1, Issue 5 [page]

1887 Monthly Chronicle of North Country Lore and Legend  
It was anciently the summer residence of the priors of Tynemouth, who had a chapel there, and subsequently it became the seat of the Shafto family.  ...  His son by the countess had a place in the Navy, and died in his father’s lifetime. A portrait of Bowes is prefixed to the memoirs of his life, written by Jesse Foote, his surgeon and friend.  ... 

Page 233 of Leisure Hour, an Illustrated Magazine for Home Reading Vol. 13, Issue 641 [page]

1864 Leisure Hour, an Illustrated Magazine for Home Reading  
Francis Gastrall must have been, I greatly fear, a pitiful creature; and the clerical prefix in no degree improves the name. The quiet street gets still quieter as one approaches the church.  ...  dense a mass of foliage, that of the church, which towers so high in the distance, we can discern no part save the door.  ... 

Modern geodetic techniques in the monitoring of historic buildings

Gabriela Kuczyńska, Magdalena Stawska, Anna Walicka, A. Volkov, A. Pustovgar, T. Sultanov, A. Adamtsevich
2019 E3S Web of Conferences  
The second building is the XX-century water tower, for which detailed architectural documentation of external walls was prepared on the basis of terrestrial laser scanning.  ...  The first one is the XIII-century cathedral, for which a network for testing vertical displacements was established and an initial measurement was performed.  ...  Networks Point numer Height of the point Height mean error Point numer Coordinate X (prefix: 5664000 m) X mean error Coordinate Y (prefix: 6433000 m) Y mean error [m] [mm  ... 
doi:10.1051/e3sconf/20199704043 fatcat:ubfwkk7aqbgszcscl4ceqwsp5a

Complexity analysis of a unifying algorithm for model checking Interval Temporal Logic

Laura Bozzelli, Angelo Montanari, Adriano Peron
2020 Information and Computation  
We analyze the time complexity of the algorithm and give, by non-trivial arguments, tight bounds on the length of certificates.  ...  This last result addresses a question left open in some papers regarding the possibility of fixing an elementary upper bound on the size of the descriptors for full HS.  ...  For all n, h ∈ N, Tower(n, h) denotes a tower of exponentials of height h and argument n: Tower(n, 0) = n and Tower(n, h + 1) = 2 Tower(n,h) . Let Σ be a finite alphabet.  ... 
doi:10.1016/j.ic.2020.104640 fatcat:alp76uf7ureqnpcfa6kmgc3ue4

Coboundaries and eigenvalues of finitary S-adic systems [article]

Valérie Berthé and Paulina Cecchi Bernales and Reem Yassawi
2022 arXiv   pre-print
A finitary S-adic dynamical system is one where the directive sequence consists of morphisms selected from a finite set.  ...  To do this we identify the notions of straightness and essential words, and use them to define a coboundary, which allows us to express necessary and sufficient conditions that a complex number must satisfy  ...  Thus if the heights of the towers T n (a) and T n (b) are comparable in an exact finite rank system, then so is the µ-mass of their bases.  ... 
arXiv:2202.07270v1 fatcat:dlvvntx3wfg4tkipvsb6i5g6im
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