Related papers: Indexing Finite-State Automata Using Forward-Stabl…
The compressed indexing problem is to preprocess a string $S$ of length $n$ into a compressed representation that supports pattern matching queries. That is, given a string $P$ of length $m$ report all occurrences of $P$ in $S$. We present…
The notion of containment and avoidance provides a natural partial ordering on set partitions. Work of Sagan and of Goyt has led to enumerative results in avoidance classes of set partitions, which were refined by Dahlberg et al. through…
Every partial applicative structure gives rise to an indexed binary relation, that is a contravariant functor from the category of sets to the category of sets endowed with binary relations and maps preserving them. In this paper we…
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…
Index is an important component in database systems. Learned indexes have been shown to outperform traditional tree-based index structures for fixed-sized integer or floating point keys. However, the application of the learned solution to…
Uniform preorders are a class of combinatory representations of Set-indexed preorders that generalize Pieter Hofstra's basic relational objects. An indexed preorder is representable by a uniform preorder if and only if it has as generic…
In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…
In the last few years, the amount of collected data, in various computer science applications, has grown considerably. These large volumes of data need to be analyzed in order to extract useful hidden knowledge. This work focuses on…
Marx (STOC~2010, J.~ACM 2013) introduced the notion of submodular width of a conjunctive query (CQ) and showed that for any class $\Phi$ of Boolean CQs of bounded submodular width, the model-checking problem for $\Phi$ on the class of all…
A goal of this paper is to introduce the new construction of an automaton with shortest synchronizing word of length $O(d^{\frac{n}{d}})$, where $d \in \mathbb{N}$ and $n$ is the number of states for that automaton. Additionally we…
A lattice is a set of all the integer linear combinations of certain linearly independent vectors. One of the most important concepts on lattice is the successive minima which is of vital importance from both theoretical and practical…
We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on…
Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine…
The bandwidth of timed automata characterizes the quantity of information produced/transmitted per time unit. We previously delimited 3 classes of TA according to the nature of their asymptotic bandwidth: meager, normal, and obese. In this…
Scalable persistent memory (PM) has opened up new opportunities for building indexes that operate and persist data directly on the memory bus, potentially enabling instant recovery, low latency and high throughput. When real PM hardware…
The rapid growth of symbolic data in areas like internet, biological, and financial data has increased the demand for efficient pattern matching and regular expression processing. Non-deterministic Finite Automata (NFA) are used for these…
Symbolic Finite Automata and Register Automata are two orthogonal extensions of finite automata motivated by real-world problems where data may have unbounded domains. These automata address a demand for a model over large or infinite…
This article describes an algorithm for reducing the intermediate alphabets in cascades of finite-state transducers (FSTs). Although the method modifies the component FSTs, there is no change in the overall relation described by the whole…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
Text indexing is a classical algorithmic problem that has been studied for over four decades: given a text $T$, pre-process it off-line so that, later, we can quickly count and locate the occurrences of any string (the query pattern) in $T$…