Search results for "Formal language"
showing 10 items of 357 documents
Graph Connectivity, Monadic NP and built-in relations of moderate degree
1995
It has been conjectured [FSV93] that an existential secondoder formula, in which the second-order quantification is restricted to unary relations (i.e. a Monadic NP formula), cannot express Graph Connectivity even in the presence of arbitrary built-in relations.
Theory of tailor automata
2019
Abstract In the paper, a fragment of the new theory of tailor automata is presented, within which a deterministic finite automaton was defined. The proposed automaton provides a theoretical model of an informally characterized biomolecular automaton. The idea of working of which is founded on the concept of alternating cut of some double-stranded fragments of DNA, with the use of a restriction enzyme and ligations of some double-stranded fragments of DNA, with the use of the ligase enzyme.
Informal language in English L2 writing: What are pupils taught from textbooks?
2019
AbstractStudies show that intermediate and advanced learners of English overuse informal features in their academic writing, and researchers recommend that instructional material is developed to raise learners’ awareness of this overuse. In Norway, little research has been done on younger learners’ writing, and no previous study exists of how instructional material such as textbooks deal with informality. The present article investigates how all English textbooks published for lower secondary school under the current curriculum deal with informality in writing. The findings show that eight out of nine textbooks include instruction on informality. The most frequently mentioned informal featu…
Inducing the Lyndon Array
2019
In this paper we propose a variant of the induced suffix sorting algorithm by Nong (TOIS, 2013) that computes simultaneously the Lyndon array and the suffix array of a text in $O(n)$ time using $\sigma + O(1)$ words of working space, where $n$ is the length of the text and $\sigma$ is the alphabet size. Our result improves the previous best space requirement for linear time computation of the Lyndon array. In fact, all the known linear algorithms for Lyndon array computation use suffix sorting as a preprocessing step and use $O(n)$ words of working space in addition to the Lyndon array and suffix array. Experimental results with real and synthetic datasets show that our algorithm is not onl…
Novel Results on the Number of Runs of the Burrows-Wheeler-Transform
2021
The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms for sequence data, such as webpages, genomic and other biological sequences, or indeed any textual data. The BWT lends itself well to compression because its number of equal-letter-runs (usually referred to as $r$) is often considerably lower than that of the original string; in particular, it is well suited for strings with many repeated factors. In fact, much attention has been paid to the $r$ parameter as measure of repetitiveness, especially to evalua…
Popularity of patterns over $d$-equivalence classes of words and permutations
2020
Abstract Two same length words are d-equivalent if they have same descent set and same underlying alphabet. In particular, two same length permutations are d-equivalent if they have same descent set. The popularity of a pattern in a set of words is the overall number of copies of the pattern within the words of the set. We show the far-from-trivial fact that two patterns are d-equivalent if and only if they are equipopular over any d-equivalence class, and this equipopularity does not follow obviously from a trivial equidistribution.
On the Number of Closed Factors in a Word
2015
A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special. We investigate the structure of closed factors of words. We show that a word of length $n$ contains at least $n+1$ distinct closed factors, and characterize those words having exactly $n+1$ closed factors. Furthermore, we show that a word of length $n$ can contain $\Theta(n^{2})$ many distinct closed factors.
Alternating, private alternating, and quantum alternating realtime automata
2014
We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we present two equivalent definitions of realtime private alternating finite automata (PAFAs). We show that the emptiness problem is undecidable for PAFAs. Furthermore, PAFAs can recognize some nonregular unary languages, including the unary squares language, which seems to be difficult even for some classical counter automata with two-way input. Regarding quantum finite automata (QFAs), we show that the emptiness problem is undecidable both for universal QFAs o…
Probabilistic verification of all languages
2018
We present three protocols for verifying all languages: (i) For any unary (binary) language, there is a log-space (linear-space) interactive proof system (IPS); (ii) for any language, there is a constant-space weak-IPS (the non-members may not be rejected with high probability); and, (iii) for any language, there is a constant-space IPS with two provers where the verifier reads the input once. Additionally, we show that uncountably many binary (unary) languages can be verified in constant space and in linear (quadratic) expected time.
Inkdots as advice for finite automata
2015
We examine inkdots placed on the input string as a way of providing advice to finite automata, and establish the relations between this model and the previously studied models of advised finite automata. The existence of an infinite hierarchy of classes of languages that can be recognized with the help of increasing numbers of inkdots as advice is shown. The effects of different forms of advice on the succinctness of the advised machines are examined. We also study randomly placed inkdots as advice to probabilistic finite automata, and demonstrate the superiority of this model over its deterministic version. Even very slowly growing amounts of space can become a resource of meaningful use i…