Related papers: Approximation algorithm for finding short synchron…
A word $w$ of letters on edges of underlying graph $\Gamma$ of deterministic finite automaton (DFA) is called synchronizing if $w$ sends all states of the automaton to a unique state. J. \v{C}erny discovered in 1964 a sequence of $n$-state…
Given an approximation algorithm $A$, we want to find the input with the worst approximation ratio, i.e., the input for which $A$'s output's objective value is the worst possible compared to the optimal solution's objective value. Such hard…
We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the…
We address the approximate minimization problem for weighted finite automata (WFAs) with weights in $\mathbb{R}$, over a one-letter alphabet: to compute the best possible approximation of a WFA given a bound on the number of states. This…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
The present paper uses spectral theory of linear operators to construct approximately minimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the SVD decomposition of infinite Hankel matrices based on…
Weighted pushdown automata (WPDAs) are at the core of many natural language processing tasks, like syntax-based statistical machine translation and transition-based dependency parsing. As most existing dynamic programming algorithms are…
String matching is the problem of finding all the substrings of a text which match a given pattern. It is one of the most investigated problems in computer science, mainly due to its very diverse applications in several fields. Recently,…
We present a fully dynamic algorithm for maintaining approximate maximum weight matching in general weighted graphs. The algorithm maintains a matching ${\cal M}$ whose weight is at least $1/8 M^{*}$ where $M^{*}$ is the weight of the…
In this paper we describe an algorithm for aligning sentences with their translations in a bilingual corpus using lexical information of the languages. Existing efficient algorithms ignore word identities and consider only the sentence…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
Since the seminal work by Angluin and the introduction of the L*-algorithm, active learning of automata by membership and equivalence queries has been extensively studied to learn various extensions of automata. For weighted automata,…
We study a variant of the synchronization game on finite deterministic automata. In this game, Alice chooses one input letter of an automaton $A$ on each of her moves while Bob may respond with an arbitrary finite word over the input…
In probabilistic programming, the inference problem asks to determine a program's posterior distribution conditioned on its "observe" instructions. Inference is challenging, especially when exact rather than approximate results are…
In this paper, we study the approximate minimization problem of weighted finite automata (WFAs): to compute the best possible approximation of a WFA given a bound on the number of states. By reformulating the problem in terms of Hankel…
For a finite state automaton, a synchronizing sequence is an input sequence that takes all the states to the same state. Checking the existence of a synchronizing sequence and finding a synchronizing sequence, if one exists, can be…
We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with…
This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text…
We engineer an algorithm to solve the approximate dictionary matching problem. Given a list of words $\mathcal{W}$, maximum distance $d$ fixed at preprocessing time and a query word $q$, we would like to retrieve all words from…
A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Cerny had found in 1964 a sequence of n-state complete DFA with…