147 research outputs found
On the Multi-Interval Ulam-R\'enyi Game: for 3 lies 4 intervals suffice
We study the problem of identifying an initially unknown -bit number by
using yes-no questions when up to a fixed number of the answers can be
erroneous. In the variant we consider here questions are restricted to be the
union of up to a fixed number of intervals. For any let be the
minimum such that for all sufficiently large , there exists a strategy
matching the information theoretic lower bound and only using -interval
questions. It is known that . However, it has been conjectured
that the This linearity conjecture is supported by the known
results for small values of . For we have We extend
these results to the case . We show improving upon the
previously known bound Comment: 31 pages, 5 figures, extension of the result to non-asymptotic
strategie
Bubble-Flip---A New Generation Algorithm for Prefix Normal Words
We present a new recursive generation algorithm for prefix normal words.
These are binary strings with the property that no substring has more 1s than
the prefix of the same length. The new algorithm uses two operations on binary
strings, which exploit certain properties of prefix normal words in a smart
way. We introduce infinite prefix normal words and show that one of the
operations used by the algorithm, if applied repeatedly to extend the string,
produces an ultimately periodic infinite word, which is prefix normal.
Moreover, based on the original finite word, we can predict both the length and
the density of an ultimate period of this infinite word.Comment: 30 pages, 3 figures, accepted in Theoret. Comp. Sc.. This is the
journal version of the paper with the same title at LATA 2018 (12th
International Conference on Language and Automata Theory and Applications,
Tel Aviv, April 9-11, 2018
On Constrained Intersection Representations of Graphs and Digraphs
We study the problem of determining minimal directed intersection representations of DAGs in a model introduced by [Kostochka, Liu, Machado, and Milenkovic, ISIT2019]: vertices are assigned color sets, two vertices are connected by an arc if and only if they share at least one color and the tail vertex has a strictly smaller color set than the head, and the goal is to minimize the total number of colors. We show that the problem is polynomially solvable in the class of triangle-free and Hamiltonian DAGs and also disclose the relationship of this problem with several other models of intersection representations of graphs and digraphs
On Infinite Prefix Normal Words
Prefix normal words are binary words that have no factor with more s than
the prefix of the same length. Finite prefix normal words were introduced in
[Fici and Lipt\'ak, DLT 2011]. In this paper, we study infinite prefix normal
words and explore their relationship to some known classes of infinite binary
words. In particular, we establish a connection between prefix normal words and
Sturmian words, between prefix normal words and abelian complexity, and between
prefix normality and lexicographic order.Comment: 20 pages, 4 figures, accepted at SOFSEM 2019 (45th International
Conference on Current Trends in Theory and Practice of Computer Science,
Nov\'y Smokovec, Slovakia, January 27-30, 2019
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