1,296 research outputs found
Computational Complexity of Synchronization under Regular Commutative Constraints
Here we study the computational complexity of the constrained synchronization
problem for the class of regular commutative constraint languages. Utilizing a
vector representation of regular commutative constraint languages, we give a
full classification of the computational complexity of the constraint
synchronization problem. Depending on the constraint language, our problem
becomes PSPACE-complete, NP-complete or polynomial time solvable. In addition,
we derive a polynomial time decision procedure for the complexity of the
constraint synchronization problem, given some constraint automaton accepting a
commutative language as input.Comment: Published in COCOON 2020 (The 26th International Computing and
Combinatorics Conference); 2nd version is update of the published version and
1st version; both contain a minor error, the assumption of maximality in the
NP-c and PSPACE-c results (propositions 5 & 6) is missing, and of
incomparability of the vectors in main theorem; fixed in this version. See
(new) discussion after main theore
Computing Majority with Triple Queries
Consider a bin containing balls colored with two colors. In a -query,
balls are selected by a questioner and the oracle's reply is related
(depending on the computation model being considered) to the distribution of
colors of the balls in this -tuple; however, the oracle never reveals the
colors of the individual balls. Following a number of queries the questioner is
said to determine the majority color if it can output a ball of the majority
color if it exists, and can prove that there is no majority if it does not
exist. We investigate two computation models (depending on the type of replies
being allowed). We give algorithms to compute the minimum number of 3-queries
which are needed so that the questioner can determine the majority color and
provide tight and almost tight upper and lower bounds on the number of queries
needed in each case.Comment: 22 pages, 1 figure, conference version to appear in proceedings of
the 17th Annual International Computing and Combinatorics Conference (COCOON
2011
Streaming and Query Once Space Complexity of Longest Increasing Subsequence
Longest Increasing Subsequence (LIS) is a fundamental problem in
combinatorics and computer science. Previously, there have been numerous works
on both upper bounds and lower bounds of the time complexity of computing and
approximating LIS, yet only a few on the equally important space complexity.
In this paper, we further study the space complexity of computing and
approximating LIS in various models. Specifically, we prove non-trivial space
lower bounds in the following two models: (1) the adaptive query-once model or
read-once branching programs, and (2) the streaming model where the order of
streaming is different from the natural order.
As far as we know, there are no previous works on the space complexity of LIS
in these models. Besides the bounds, our work also leaves many intriguing open
problems.Comment: This paper has been accepted to COCOON 202
Combinatorics on words in information security: Unavoidable regularities in the construction of multicollision attacks on iterated hash functions
Classically in combinatorics on words one studies unavoidable regularities
that appear in sufficiently long strings of symbols over a fixed size alphabet.
In this paper we take another viewpoint and focus on combinatorial properties
of long words in which the number of occurrences of any symbol is restritced by
a fixed constant. We then demonstrate the connection of these properties to
constructing multicollision attacks on so called generalized iterated hash
functions.Comment: In Proceedings WORDS 2011, arXiv:1108.341
Approximating Weighted Duo-Preservation in Comparative Genomics
Motivated by comparative genomics, Chen et al. [9] introduced the Maximum
Duo-preservation String Mapping (MDSM) problem in which we are given two
strings and from the same alphabet and the goal is to find a
mapping between them so as to maximize the number of duos preserved. A
duo is any two consecutive characters in a string and it is preserved in the
mapping if its two consecutive characters in are mapped to same two
consecutive characters in . The MDSM problem is known to be NP-hard and
there are approximation algorithms for this problem [3, 5, 13], but all of them
consider only the "unweighted" version of the problem in the sense that a duo
from is preserved by mapping to any same duo in regardless of their
positions in the respective strings. However, it is well-desired in comparative
genomics to find mappings that consider preserving duos that are "closer" to
each other under some distance measure [19]. In this paper, we introduce a
generalized version of the problem, called the Maximum-Weight Duo-preservation
String Mapping (MWDSM) problem that captures both duos-preservation and
duos-distance measures in the sense that mapping a duo from to each
preserved duo in has a weight, indicating the "closeness" of the two
duos. The objective of the MWDSM problem is to find a mapping so as to maximize
the total weight of preserved duos. In this paper, we give a polynomial-time
6-approximation algorithm for this problem.Comment: Appeared in proceedings of the 23rd International Computing and
Combinatorics Conference (COCOON 2017
Sudo-Lyndon
Based on Lyndon words, a new Sudoku-like puzzle is presented and some
relative theoretical questions are proposed
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