相关论文: Fast synchronization of inhomogenous random automa…

The \v{C}ern\'y conjecture states that every $n$-state synchronizing automaton has a reset word of length at most $(n-1)^2$. We study the hardness of finding short reset words. It is known that the exact version of the problem, i.e.,…

We present a new series of examples of binary slowly synchronizing automata with sink state. The reset threshold of the $n$-state automaton in this series is $\frac{n^2}{4}+2n-9$. This improves on the previously known lower bound for the…

The repetition threshold for words on $n$ letters, denoted $\mbox{RT}(n)$, is the infimum of the set of all $r$ such that there are arbitrarily long $r$-free words over $n$ letters. A repetition threshold for circular words on $n$ letters…

Following (Kolpakov et al., 2013; Gawrychowski and Manea, 2015), we continue the study of {\em $\alpha$-gapped repeats} in strings, defined as factors $uvu$ with $|uv|\leq \alpha |u|$. Our main result is the $O(\alpha n)$ bound on the…

We present several series of synchronizing automata with multiple parameters, generalizing previously known results. Let p and q be two arbitrary co-prime positive integers, q > p. We describe reset thresholds of the colorings of primitive…

We consider the randomized decision tree complexity of the recursive 3-majority function. We prove a lower bound of $(1/2-\delta) \cdot 2.57143^h$ for the two-sided-error randomized decision tree complexity of evaluating height $h$ formulae…

In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite…

In this paper we prove that a uniformly distributed random circular automaton $\mathcal{A}_n$ of order $n$ synchronizes with high probability (whp). More precisely, we prove that $$ \mathbb{P}\left[\mathcal{A}_n \text{ synchronizes}\right]…

We study the problem of reaching agreement in a synchronous distributed system by $n$ autonomous parties, when the communication links from/to faulty parties can omit messages. The faulty parties are selected and controlled by an adaptive,…

We investigate the number of maximal independent set queries required to reconstruct the edges of a hidden graph. We show that randomised adaptive algorithms need at least $\Omega(\Delta^2 \log(n / \Delta) / \log \Delta)$ queries to…

Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…

This paper studies the online scheduling problem of minimizing total flow time for $n$ jobs on $m$ identical machines. A classical $\Omega(n)$ lower bound shows that no deterministic single-machine algorithm can beat the trivial greedy,…

We study a connection between synchronizing automata and its set $M$ of minimal reset words, i.e., such that no proper factor is a reset word. We first show that any synchronizing automaton having the set of minimal reset words whose set of…

This paper concerns {\em randomized} leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete $n$-node networks that runs in O(1) rounds and (with high probability) uses only…

We prove the exact asymptotic $1-\left({\frac{2\pi}{3}-\frac{827}{288\pi}}+o(1)\right)/{\sqrt{n}}$ for the probability that the underlying graph of a random mapping of $n$ elements possesses a unique highest tree. The property of having a…

In this paper we present a deterministic $O(\log\log n)$-round algorithm for the 2-ruling set problem in the Massively Parallel Computation model with $\tilde{O}(n)$ memory; this algorithm also runs in $O(\log\log n)$ rounds in the…

In this work we construct an automaton for the commutative closure of a given regular group language. The number of states of the resulting automaton is bounded by the number of states of the original automaton, raised to the power of the…

A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state deterministic automaton has a synchronizing word, then…

In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far…

Consider the finite regular language L_n = {w0 : w \in {0,1}^*, |w| \le n}. It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum…