Filters








105,934 Hits in 3.4 sec

UNAVOIDABLE SETS OF CONSTANT LENGTH

JEAN-MARC CHAMPARNAUD, GEORGES HANSEL, DOMINIQUE PERRIN
2004 International journal of algebra and computation  
For k, q ≥ 1, let c(k, q) be the number of conjugacy classes of words of length k on q letters. An unavoidable set of words of length k on q symbols has at least c(k, q) elements.  ...  We show that for any k, q ≥ 1 there exists an unavoidable set of words of length k on q symbols having c(k, q) elements.  ...  It is easy to see that an unavoidable set of words of constant length k on some alphabet A has to contain at least one word of each conjugacy class of words of length k on this alphabet.  ... 
doi:10.1142/s0218196704001700 fatcat:do7ozqsadbcojh46f3limxwl2m

Number of holes in unavoidable sets of partial words II

F. Blanchet-Sadri, Steven Ji, Elizabeth Reiland
2012 Journal of Discrete Algorithms  
Towards this, we investigate the minimum size of unavoidable sets of partial words with a fixed number of holes.  ...  Additionally, we analyze the complexity of variations on the decision problem when placing restrictions on the number of holes and length of the words.  ...  words in a set and returns bounds on the minimum cardinality of an unavoidable set with those parameters.  ... 
doi:10.1016/j.jda.2011.12.002 fatcat:cwk24hdtr5e5zkjyejt4e4jgie

Unavoidable sets

Peter M. Higgins, Christopher J. Saker
2006 Theoretical Computer Science  
We obtain new results on minimum lengths of words in an unavoidable set of words of cardinality n before introducing the notion of aperiodic unavoidable sets, a natural extension of unavoidable sets.  ...  Let X be an unavoidable set of non-empty words all of length m + 1. Then for some v ∈ A m we have {va 1 , va 2 , . . . , va k } ⊆ X. Proof.  ...  Acknowledgement The authors would like to thank the referee for finding the error in Section 3 of the original draft and essentially devising Examples 22 and 23.  ... 
doi:10.1016/j.tcs.2006.03.024 fatcat:v5uzfmcybnacvhxchb6alspw5u

Page 814 of Mathematical Reviews Vol. , Issue 86b [page]

1986 Mathematical Reviews  
The language L(p) is the set of all words over the alphabet of constant symbols generated from p by substituting some nonempty words for the variables in p.  ...  A grammar G = (5, V, P) is said to be D-algebraic if V is a finite set of nonterminals and if P = {(a > m):a€V,me€(ZUV)’} is such that the length of m is bounded.  ... 

On the complexity of deciding avoidability of sets of partial words

Brandon Blakeley, F. Blanchet-Sadri, Josh Gunter, Narad Rampersad
2010 Theoretical Computer Science  
We give a polynomial bound on the period of an infinite avoiding word, in the case of sets of full words, in terms of two parameters: the length and the number of words in the set.  ...  The same algorithm also decides if the number of words of length n avoiding a given finite set of partial words grows polynomially or exponentially with n.  ...  When we consider constant length sets of partial words, we implicitly require that neither the first or last position in any of the words be a hole. Proof.  ... 
doi:10.1016/j.tcs.2010.09.006 fatcat:bwvs6vekt5a45lwze2xpxbs5ka

On the Complexity of Deciding Avoidability of Sets of Partial Words [chapter]

Brandon Blakeley, Francine Blanchet-Sadri, Josh Gunter, Narad Rampersad
2009 Lecture Notes in Computer Science  
We give a polynomial bound on the period of an infinite avoiding word, in the case of sets of full words, in terms of two parameters: the length and the number of words in the set.  ...  The same algorithm also decides if the number of words of length n avoiding a given finite set of partial words grows polynomially or exponentially with n.  ...  When we consider constant length sets of partial words, we implicitly require that neither the first or last position in any of the words be a hole. Proof.  ... 
doi:10.1007/978-3-642-02737-6_9 fatcat:agy5mp2yyjgvhb6yenw6yguj7a

Optimal Packings of 22 and 33 Unit Squares in a Square [article]

Wolfram Bentz
2016 arXiv   pre-print
To achieve our results, we modify the well-known method of sets of unavoidable points by replacing them with continuously varying families of such sets.  ...  Let s(n) be the side length of the smallest square into which n non-overlapping unit squares can be packed. In 2010, the author showed that s(13)=4 and s(46)=7.  ...  By the same basic argument as applied to Figure 2 we can show that both the set of red points and the set of blue points form unavoidable sets.  ... 
arXiv:1606.03746v1 fatcat:altddffd3fhcvbm2orj5gvhxju

Page 789 of Mathematical Reviews Vol. 49, Issue 2 [page]

1975 Mathematical Reviews  
] of ‘class-determin- ing measured sets’.  ...  The following notation is used: N denotes the set of positive integers, X° denotes the set of all infinite binary sequences, x(n) denotes the nth member of the binary sequence 2, x" denotes the initial  ... 

Complexity of Sequential Pattern Matching Algorithms [chapter]

Mireille Régnier, Wojciech Szpankowski
1998 Lecture Notes in Computer Science  
Namely, we prove the exlstence of "unavoidable positions" where the algorithm must stop to compare.  ...  Our results hold for any given pattern and text and for stationary ergodic pattern and text providing the length of the pattern is order of magnitude smaller than the square root of the text length.  ...  The uniform bound [15] on the linearity constant, allows to define Ep(Et(cr,n))' when p ranges over a random (possibly infinite) set of patterns.  ... 
doi:10.1007/3-540-49543-6_16 fatcat:muwhtmqe5ng6fbjnhog2nvpmci

Some characterizations of a class of unavoidable compact sets in the game of Banach and Mazur

Haim Hanani, Marian Reichaw-Reichbach
1961 Pacific Journal of Mathematics  
Steinhaus, an unavoidable perfect set of measure 0 with the game-constant k -1 was constructed.  ...  Finally (p 3 ) A set S is said to have the property (p 3 ) if it is unavoidable (for the game constant k).  ...  PUBLISHED BY PACIFIC JOURNAL OF MATHEMATICS, A NON-PROFIT CORPORATION The Supporting Institutions listed above contribute to the cost of publication of this Journal, but they are not owners or publishers  ... 
doi:10.2140/pjm.1961.11.945 fatcat:4zbappmlmbdajonglhg43xwqtm

Isosystolic inequalities for optical hypersurfaces [article]

Juan-Carlos Alvarez Paiva, Florent Balacheff, Kroum Tzanev
2016 arXiv   pre-print
This result is deduced from an interesting dual version of Minkowski's lattice-point theorem: if the origin is the unique integer point in the interior of a planar convex body, the area of its dual body  ...  We explore a natural generalization of systolic geometry to Finsler metrics and optical hypersurfaces with special emphasis on its relation to the Mahler conjecture and the geometry of numbers.  ...  The set of unavoidable convex bodies in R n whose volume is bounded above by some constant c > 0 is compact modulo unimodular transformations.  ... 
arXiv:1308.5522v2 fatcat:zrbyxoqiczajfhx7ieqsq6zgc4

Strict Bounds for Pattern Avoidance [chapter]

Francine Blanchet-Sadri, Brent Woodhouse
2013 Lecture Notes in Computer Science  
Cassaigne conjectured in 1994 that any pattern with m distinct variables of length at least 3(2 m−1 ) is avoidable over a binary alphabet, and any pattern with m distinct variables of length at least 2  ...  Building upon the work of Rampersad and the power series techniques of Bell and Goh, we obtain both of these suggested strict bounds.  ...  By Lemma 1, the number of words of length n in S is at most [x n ]C(x), where By hypothesis, d i ⩾2 for 1⩽i⩽m. In order to use Theorem 1 on Σ , define and set the constant λ=k−0.08.  ... 
doi:10.1007/978-3-642-38771-5_11 fatcat:cclt6tzmzzhm5a6yem6k5pzwy4

Strict bounds for pattern avoidance

F. Blanchet-Sadri, Brent Woodhouse
2013 Theoretical Computer Science  
Cassaigne conjectured in 1994 that any pattern with m distinct variables of length at least 3(2 m−1 ) is avoidable over a binary alphabet, and any pattern with m distinct variables of length at least 2  ...  Building upon the work of Rampersad and the power series techniques of Bell and Goh, we obtain both of these suggested strict bounds.  ...  By Lemma 1, the number of words of length n in S is at most [x n ]C(x), where By hypothesis, d i ⩾2 for 1⩽i⩽m. In order to use Theorem 1 on Σ , define and set the constant λ=k−0.08.  ... 
doi:10.1016/j.tcs.2013.08.010 fatcat:qi6eqc6xs5cn5bie5ewur7ozx4

The Complexity of Unavoidable Word Patterns [article]

Paul Sauer
2019 arXiv   pre-print
We present various complexity-related properties of unavoidable words. For words that are unavoidable, we provide an upper bound to the lengths of words that avoid them.  ...  A natural subsequent question is how many unavoidable words there are. We show that the fraction of words that are unavoidable drops exponentially fast in the length of the word.  ...  For n ∈ N we symbolize the set of words of length n over A by A n .  ... 
arXiv:1901.07431v4 fatcat:xdj6hyrz35fbzkdenaatcs7lxi

Page 6292 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
We restrict a set of distributions that a learning algorithm may use for its statistical queries to be a set of product distributions with each bit being | with probability p, 1/2 or 1—p for a constant  ...  (French summary) |Unavoidable sets] Sém. Lothar. Combin. 47 (2001/02), Article B47e, 16 pp. (electronic).  ... 
« Previous Showing results 1 — 15 out of 105,934 results