相关论文: On the Hopcroft's minimization algorithm

For a text given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering…

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem…

In this paper we study the approximate minimization problem for language modelling. We assume we are given some language model as a black box. The objective is to obtain a weighted finite automaton (WFA) that fits within a given size…

We study the recently introduced idea of worst-case sensitivity for monotone submodular maximization with cardinality constraint $k$, which captures the degree to which the output argument changes on deletion of an element in the input. We…

We study the sweep complexity of DFA in one-way jumping mode answering several questions posed earlier. This measure is the number of times in the worst case that such machines have to return to the beginning of their input after having…

The symbolic complexity of an infinite word $W$ is the function $p_W(l)$ counting the number of different subwords in $W$ of length $l$. In this paper our main purpose is to study the complexity for a class of topological dynamical systems,…

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…

Neural language models typically tokenise input text into sub-word units to achieve an open vocabulary. The standard approach is to use a single canonical tokenisation at both train and test time. We suggest that this approach is…

We study minimization problems for deterministic $\omega$-automata in the presence of don't care words. We prove that the number of priorities in deterministic parity automata can be efficiently minimized under an arbitrary set of don't…

In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…

We introduce the notion of de Bruijn entropy of an Eulerian quiver and show how the corresponding relative entropy can be applied to practical string similarity problems. This approach explicitly links the combinatorial and…

We show that the smoothed complexity of the FLIP algorithm for local Max-Cut is at most $\smash{\phi n^{O(\sqrt{\log n})}}$, where $n$ is the number of nodes in the graph and $\phi$ is a parameter that measures the magnitude of…

We study the computational and descriptional complexity of the following transformation: Given a one-counter automaton (OCA) A, construct a nondeterministic finite automaton (NFA) B that recognizes an abstraction of the language L(A): its…

The design of online algorithms has tended to focus on algorithms with worst-case guarantees, e.g., bounds on the competitive ratio. However, it is well-known that such algorithms are often overly pessimistic, performing sub-optimally on…

We consider the problem of maximizing a monotone submodular function subject to a knapsack constraint. Our main contribution is an algorithm that achieves a nearly-optimal, $1 - 1/e - \epsilon$ approximation, using…

We continue the study of restricted Monte Carlo algorithms in a general setting. Here we show a lower bound for minimal errors in the setting with finite restriction in terms of deterministic minimal errors. This generalizes a result of…

This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a…

Zipf's law of abbreviation, namely the tendency of more frequent words to be shorter, has been viewed as a manifestation of compression, i.e. the minimization of the length of forms -- a universal principle of natural communication.…

We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$…

This dissertation proves lower bounds on the inherent difficulty of deciding flow analysis problems in higher-order programming languages. We give exact characterizations of the computational complexity of 0CFA, the $k$CFA hierarchy, and…