Related papers: An Efficient Algorithm for the Equation Tree Autom…
The arithmetic complexity counts the number of algebraically independent entries in the periodic continued fraction $\theta=[b_1,\dots, b_N, \overline{a_1,\dots,a_k}]$. If $\mathscr{A}_{\theta}$ is a noncommutative torus corresponding to…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
k-means is a widely used clustering algorithm, but for $k$ clusters and a dataset size of $N$, each iteration of Lloyd's algorithm costs $O(kN)$ time. Although there are existing techniques to accelerate single Lloyd iterations, none of…
We propose a new approach for calculating the Lempel-Ziv factorization of a string, based on run length encoding (RLE). We present a conceptually simple off-line algorithm based on a variant of suffix arrays, as well as an on-line algorithm…
We prove that, for any arbitrary finite alphabet and for the uniform distribution over deterministic and accessible automata with n states, the average complexity of Moore's state minimization algorithm is in O(n log n). Moreover this bound…
We present an algorithm for searching regular expression matches in compressed text. The algorithm reports the number of matching lines in the uncompressed text in time linear in the size of its compressed version. We define efficient data…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
We present an efficient algorithm for checking language equivalence of states in top-down deterministic finite tree automata (DFTAs). Unlike string automata, tree automata operate over hierarchical structures, posing unique challenges for…
Equality saturation is an emerging technique for program and query optimization developed in the programming language community. It performs term rewriting over an E-graph, a data structure that compactly represents a program space. Despite…
E-generalization computes common generalizations of given ground terms w.r.t. a given equational background theory E. In 2005 [arXiv:1403.8118], we had presented a computation approach based on standard regular tree grammar algorithms, and…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
We prove that a uniformly random automaton with $n$ states on a 2-letter alphabet has a synchronizing word of length $O(n^{1/2}\log n)$ with high probability (w.h.p.). That is to say, w.h.p. there exists a word $\omega$ of such length, and…
The Arnoux-Rauzy-Poincar\'e multidimensional continued fraction algorithm is obtained by combining the Arnoux-Rauzy and Poincar\'e algorithms. It is a generalized Euclidean algorithm. Its three-dimensional linear version consists in…
It is known that the Wadge reducibility of regular $\omega$-languages is efficiently decidable (Krishnan et al., 1995), (Wilke, Yoo, 1995). In this paper we study analogous problem for regular k-partitions of $\omega$-languages. In the…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
Data summarization that presents a small subset of a dataset to users has been widely applied in numerous applications and systems. Many datasets are coded with hierarchical terminologies, e.g., the international classification of…
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…
In this work, we introduce a fast numerical algorithm to solve the time-dependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies the treecode algorithm to reduce the computational complexity…
An automaton is synchronizing if there is a word that maps all states onto the same state. \v{C}ern\'{y}'s conjecture on the length of the shortest such word is probably the most famous open problem in automata theory. We consider the…
We study realizable continual linear regression under random task orderings, a common setting for developing continual learning theory. In this setup, the worst-case expected loss after $k$ learning iterations admits a lower bound of…