Related papers: On Indexing and Compressing Finite Automata
In many real-world database systems, a large fraction of the data is represented by strings: sequences of letters over some alphabet. This is because strings can easily encode data arising from different sources. It is often crucial to…
We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset…
In this work, we study the problems of counting and sampling Mazurkiewicz traces that a regular language touches. Fix an alphabet $\Sigma$ and an independence relation $\mathbb{I} \subseteq \Sigma \times \Sigma$. The input consists of a…
Term pattern matching is the problem of finding all pattern matches in a subject term, given a set of patterns. Finding efficient algorithms for this problem is an important direction for research [19]. We present a new set automaton…
Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed…
This paper deals with the two fundamental problems concerning the handling of large n-gram language models: indexing, that is compressing the n-gram strings and associated satellite data without compromising their retrieval speed; and…
The suffix tree is arguably the most fundamental data structure on strings: introduced by Weiner (SWAT 1973) and McCreight (JACM 1976), it allows solving a myriad of computational problems on strings in linear time. Motivated by its large…
Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…
We present an algorithm for regular expression parsing and submatch extraction based on tagged deterministic finite automata. The algorithm works with different disambiguation policies. We give detailed pseudocode for the algorithm,…
In this paper, we show that every D3-directing CNFA can be mapped uniquely to a DFA with the same synchronizing word length. This implies that \v{C}ern\'y's conjecture generalizes to CNFAs and that the general upper bound for the length of…
We propose a query learning algorithm for residual symbolic finite automata (RSFAs). Symbolic finite automata (SFAs) are finite automata whose transitions are labeled by predicates over a Boolean algebra, in which a big collection of…
A data language is a set of finite words defined on an infinite alphabet. Data languages are used to express properties associated with data values (domain defined over a countably infinite set). In this paper, we introduce set augmented…
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 $T$…
Text indexing is a fundamental and well-studied problem. Classic solutions either replace the original text with a compressed representation, e.g., the FM-index and its variants, or keep it uncompressed but attach some redundancy - an index…
Regular expressions (res), because of their succinctness and clear syntax, are the common choice to represent regular languages. However, efficient pattern matching or word recognition depend on the size of the equivalent nondeterministic…
We revisit the problem of deciding whether a given string is uniquely decodable from its bigram counts by means of a finite automaton. An efficient algorithm for constructing a polynomial-size nondeterministic finite automaton that decides…
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.
Given a member A of the class of non-deterministic timed automata with silent transitions (eNTA), we effectively compute its timestamp: the set of all pairs (time value, action) of all observable timed traces of A, a generalization of the…
We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "\'atomaton", whose states are the "atoms" of the language, that is, non-empty intersections of complemented or uncomplemented left…
We study the fundamental question of how efficiently suffix array entries can be accessed when the array cannot be stored explicitly. The suffix array $SA_T[1..n]$ of a text $T$ of length $n$ encodes the lexicographic order of its suffixes…