Search results for " Formal"
showing 10 items of 273 documents
Automata and Quantum Computing
2015
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers. Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity
Quantum Computation With Devices Whose Contents Are Never Read
2010
In classical computation, a "write-only memory" (WOM) is little more than an oxymoron, and the addition of WOM to a (deterministic or probabilistic) classical computer brings no advantage. We prove that quantum computers that are augmented with WOM can solve problems that neither a classical computer with WOM nor a quantum computer without WOM can solve, when all other resource bounds are equal. We focus on realtime quantum finite automata, and examine the increase in their power effected by the addition of WOMs with different access modes and capacities. Some problems that are unsolvable by two-way probabilistic Turing machines using sublogarithmic amounts of read/write memory are shown to…
Open and Closed Prefixes of Sturmian Words
2013
A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We deal with the sequence of open and closed prefixes of Sturmian words and prove that this sequence characterizes every finite or infinite Sturmian word up to isomorphisms of the alphabet. We then characterize the combinatorial structure of the sequence of open and closed prefixes of standard Sturmian words. We prove that every standard Sturmian word, after swapping its first letter, can be written as an infinite product of squares of reversed standard words.
Minimal forbidden factors of circular words
2017
Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist algorithms for computing the minimal forbidden factors of a word, as well as of a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an algorithm that, given the trie recognizing a finite antifactorial language $M$, computes a DFA recognizing the language whose set of minimal forbidden factors is $M$. In the same paper, they showed that the obtained DFA is minimal if the input trie recognizes the minimal forbidden factors of a single word.…
String attractors and combinatorics on words
2019
The notion of \emph{string attractor} has recently been introduced in [Prezza, 2017] and studied in [Kempa and Prezza, 2018] to provide a unifying framework for known dictionary-based compressors. A string attractor for a word $w=w[1]w[2]\cdots w[n]$ is a subset $\Gamma$ of the positions $\{1,\ldots,n\}$, such that all distinct factors of $w$ have an occurrence crossing at least one of the elements of $\Gamma$. While finding the smallest string attractor for a word is a NP-complete problem, it has been proved in [Kempa and Prezza, 2018] that dictionary compressors can be interpreted as algorithms approximating the smallest string attractor for a given word. In this paper we explore the noti…
Exact affine counter automata
2017
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las Vegas affine finite automata. Lastly, we show that how a counter helps for affine finite automata by showing that the language MANYTWINS, which is conjectured not to be recognized by affin…
Finite automata with advice tapes
2013
We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, demonstrate an infinite hierarchy of language classes recognized by automata with increasing advice lengths, and establish the relationships between this and the previously studied ways of providing advice to finite automata.
Is R&D Enough to Take Advantage From External Knowledge?: Focusing on Coordination Mechanisms
2014
The purpose of this paper is to analyze the role of research and development (R&D) and coordination mechanisms (such as decentralization in decision-making and formalization of organizational processes) in the transformation of external knowledge into innovation results. We use survey data for performing standard ordinary least squares regressions in a representative sample of firms from the Spanish Ceramic Tile Industry. The results suggest that R&D is an important moderator influencing the relationship between acquiring external knowledge and innovation outcomes. Second, formalization tends to have a detrimental effect in the transformation of external knowledge into innovation outputs. T…
Agreement on the Choice of Non-applicable Law or Law not in Accordance with Article 22(1) of the Twin Regulations: what Consequences for the Couple’s…
2021
Los Reglamentos (UE) 2016/1103 y 2016/1104 del Consejo autorizan a las parejas transfronterizas a elegir la ley aplicable a sus relaciones patrimoniales sobre la base de uno de los criterios enumerados en el artículo 22.1. Sin embargo, el acuerdo de elección de la ley puede tener un contenido diferente al señalado en la redacción del artículo 22 de los ?Reglamentos Gemelos?. El objetivo del análisis es ilustrar que sería incorrecto sostener que tales acuerdos son, a priori, inválidos o no permiten la autonomía de la voluntad. Esta cuestión requiere una evaluación de la finalidad concreta del acuerdo de las partes y debería, al menos, estar abierta al examen del tribunal competente.
The Intersection of $3$-Maximal Submonids
2020
Very little is known about the structure of the intersection of two $k$-generated monoids of words, even for $k=3$. Here we investigate the case of $k$-maximal monoids, that is, monoids whose basis of cardinality $k$ cannot be non-trivially decomposed into at most $k$ words. We characterize the intersection in the case of two $3$-maximal monoids.