The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
The notion of redundancies in texts, regarded as sequences of symbols, appear under various concepts in the literature of Combinatorics on words and of Algorithms on strings: repetitions, repeats, runs, covers, seeds, and palindromes, for example. We explore some of the newest aspects of these redundancies.
It is well known that the minimization problem of deterministic finite automata (DFAs) is related to the indistinguishability notion of states (cf. [HMU00]). Indeed, a well known technique to minimize a DFA, essentially, consists in finding pairs of states that are equivalent (or indistinguishable), namely pairs of states (p,q) such that it is impossible to assert the difference between p and q only...
The aim of this paper is to give a short survey of the area formed by the intersection of two popular lines of investigation in formal language theory. The first line, originated by Thue in 1906, concerns about repetition-free words and languages. The second line is the study of growth functions for words and languages; it can be traced back to the classical papers by Morse and Hedlund on symbolic...
Regular expressions [4] and tools to handle them, especially tools for regular expression matching—an early one is described in the seminal paper [5] by Ken Thompson—, are one of the major achievements of formal language and automata theory. Google counts 303,000 results for “regular expressions matching” (May 4, 2011); there are numerous command line tools for working with regular expressions such...
A number of basic questions concerning the state complexity research are discussed, which include why many basic problems weren’t studied earlier, whether there is a general algorithm for state complexity, and whether there is a new approach in this area of research. The new concept of state complexity approximation is also discussed. We show that this new concept can be used to obtain good results...
A binary matrix satisfies the consecutive ones property (C1P) if its columns can be permuted such that the 1s in each row of the resulting matrix are consecutive. Equivalently, a family of setsF = {Q1,...,Qm}, where Qi ⊆ R for some universe R, satisfies the C1P if the symbols in R can be permuted such that...
We study abelian repetitions in partial words, or sequences that may contain some unknown positions or holes. First, we look at the avoidance of abelian pth powers in infinite partial words, where p > 2, extending recent results regarding the case where p = 2. We investigate, for a given p, the smallest alphabet size needed to construct an infinite partial word with finitely or infinitely many...
In spite of wide investigations of finite splicing systems in formal language theory, basic questions, such as their characterization, remain unsolved. In search for understanding the class of finite splicing systems, it has been conjectured that a necessary condition for a regular language L to be a splicing language is that L must have a constant in the Schützenberger’s sense. We prove this longstanding...
In this paper, the relation between the Glushkov automaton ( ) and the partial derivative automaton ( ) of a given regular expression, in terms of transition complexity, is studied. The average transition complexity of was proved by Nicaud to be linear in the size of the corresponding expression. This result...
We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call “átomaton”, whose states are the “atoms” of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing the átomaton, and prove that it is isomorphic to the normal automaton of Sengoku, and to an automaton...
The state complexity of a regular language is the number of states in the minimal deterministic automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the worst-case syntactic complexity taken as a function of the state complexity n of languages in that class. We...
Brüggemann-Klein and Wood have introduced a new family of regular languages, the one-unambiguous regular languages, a very important notion in XML DTDs. A regular language L is one-unambiguous if and only if there exists a regular expression E over the operators of sum, catenation and Kleene star such that L(E) = L and the position automaton of E is deterministic. It implies that for a one-unambiguous...
We study the notion of simulation over a class of automata which recognize 2D languages (languages of arrays of letters). This class of two-dimensional On-line Tessellation Automata (2OTA) accepts the same class of languages as the class of tiling systems, considered as the natural extension of classical regular word languages to the 2D case. We prove that simulation over 2OTA implies language inclusion...
Δ-clearing restarting automata represent a new restricted model of restarting automata which, based on a limited context, can either delete a substring of the current content of its tape or replace a substring by a special auxiliary symbol Δ, which cannot be overwritten anymore, but it can be deleted later. The main result of this paper consists in proving that besides their limited operations, Δ-clearing...
We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We...
Infinite games are studied in a format where two players, called Player 1 and Player 2, generate a play by building up an ω-word as they choose letters in turn. A game is specified by the ω-language which contains the plays won by Player 2. We analyze ω-languages generated from certain classes of regular languages of finite words (called *-languages), using natural transformations of...
Non-Archimedean words have been introduced as a new type of infinite words which can be investigated through classical methods in combinatorics on words due to a length function. The length function, however, takes values in the additive group of polynomials ℤ[t] (and not, as traditionally, in ℕ), which yields various new properties. Non-Archimedean words allow to solve a number of algorithmic problems...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.