Regular Languages Research Articles

The Properties of Semi-Simple Splicing System Over Alternating Group, A3

Splicing system was introduced by Head in 1987 in order to explore the recombinant behaviour of deoxyribonucleic acid (DNA) strands in the presence of restriction enzymes and ligases. Restriction enzymes cut the DNA strands into a left - pattern and right-pattern while the ligases recombine the left-pattern of the first string with the right-pattern of the second string and vice-versa. Semi-simple splicing system is a variant of splicing system where the splicing of DNA strands will be at two distinct sites. Splicing languages generated from the splicing system are classified based on their computational power, according to the Chomsky Hierarchy. Previous researchers found that the splicing system of finite set of strings and rules generates only regular languages which has the lowest computational power. Hence, some restriction has been introduced to increase the computational power of splicing languages generated. In this research, an element of alternating group of order three is associated with the initial strings of semi-simple splicing system to generate non-regular languages which has higher computational power. Some lemmas and theorems are proven to show that associating the alternating group to the initial strings could increase the computational power of the splicing languages.

L-Valued Multiset Automata and l-Valued Multiset Languages

The reason for this work is to present and study deterministic multiset automata, multiset automata and their languages with membership values in complete residuated lattice without zero divisors. We build up the comparability of deterministic [Formula: see text]-valued multiset finite automaton and [Formula: see text]-valued multiset finite automaton in sense of recognizability of a [Formula: see text]-valued multiset language. Then, we relate multiset regular languages to a given [Formula: see text]-valued multiset regular languages and vice versa. At last, we present the concept of pumping lemma for [Formula: see text]-valued multiset automata theory, which we utilize to give a necessary and sufficient condition for a [Formula: see text]-valued multiset language to be non-constant.

ОБУЧЕНИЕ СТУДЕНТОВ НЕЛИНГВИСТИЧЕСКИХ ВУЗОВ РАБОТЕ С ПРОФЕССИОНАЛЬНО-ОРИЕНТИРОВАННЫМ ИНОЯЗЫЧНЫМ ТЕКСТОМ

Objective of the article is to substantiate the necessity and possibility of implementing foreign language training for students of non-linguistic universities with an additional goal-the formation and development of skills to work with a professionally-oriented foreign language text. This goal should not require additional time or financial resources, but should be implemented in the process of regular foreign language training. Applied methods : goal setting; researching advanced pedagogical practices and modern approaches to foreign language training, current educational technologies and techniques, diagnostic tools to monitor the effectiveness of development of skills to work with a text; adaptation of diagnostic instruments for a specific purpose and other psycho-pedagogical conditions. Results . The international system PISA was chosen as a diagnostic tool for tracking the development of the ability to work with a text. It is adapted for use by students of non-linguistic universities studying a foreign language, and has been successfully used in pedagogical practice to assess the initial level of development of skills to work with a text, the final level, as well as intermediate results. Conclusion: this work will be used as the basis for substantiating and modeling the didactic system of teaching students of non-linguistic universities to work with a professionally-oriented foreign language text.

Generalizations of Code Languages with Marginal Errors

The [Formula: see text]-prefix-free, [Formula: see text]-suffix-free and [Formula: see text]-infix-free languages generalize the prefix-free, suffix-free and infix-free languages by allowing marginal errors. For example, a string [Formula: see text] in a [Formula: see text]-prefix-free language [Formula: see text] can be a prefix of up to [Formula: see text] different strings in [Formula: see text]. We also define finitely prefix-free languages in which a string [Formula: see text] can be a prefix of finitely many strings. We present efficient algorithms that determine whether or not a given regular language is [Formula: see text]-prefix-free, [Formula: see text]-suffix-free or [Formula: see text]-infix-free, and analyze the time complexity of the algorithms. We establish undecidability results for deciding these properties for (linear) context-free languages.

Transverse properties of parabolic subgroups of Garside groups

Let G be a Garside group endowed with the generating set $${\cal S}$$ of non-trivial simple elements, and let H be a parabolic subgroup of G. We determine a transversal T of H in G such that each θ ∈ T is of minimal length in its right-coset, Hθ, for the word length with respect to $${\cal S}$$ . We show that there exists a regular language L on $${\cal S} \cup {{\cal S}^{- 1}}$$ and a bijection ev: L → T satisfying $$\lg \left(U \right) = {\lg _{\cal S}}\left({ev\left(U \right)} \right)$$ for all U ∈ L. From this we deduce that the coset growth series of H in G is rational. Finally, we show that G has fellow projections on H but does not have bounded projections on H.

Geometrically closed positive varieties of languages

A recently introduced operation of geometrical closure on formal languages is investigated from the viewpoint of algebraic language theory. Positive varieties V containing exclusively languages with regular geometrical closure are fully characterised by inclusion of V in W, a known positive variety arising in the study of the commutative closure. It is proved that the geometrical closure of a language from the intersection of W with the variety of all star-free languages SF always falls into RLT, which is introduced as a subvariety of R, the variety of languages recognised by R-trivial monoids. All classes between RLT and W∩SF are thus geometrically closed: for instance, the level 3/2 of the Straubing-Thérien hierarchy, the DA-recognisable languages, or the variety R. It is also shown that W∩SF is the largest geometrically closed positive variety of star-free languages, while there is no largest geometrically closed positive variety of regular languages.

Power, positive closure, and quotients on convex languages

We study the state complexity and nondeterministic state complexity of the k-th power, positive closure, right quotient, and left quotient on the classes of prefix-, suffix-, factor-, and subword-free, -closed, and -convex regular languages, and on the classes of right, left, two-sided, and all-sided ideal languages. We show that the nondeterministic state complexity of the k-th power is kn for closed and convex languages, and k(n−1)+1 in the remaining classes, while its state complexity is n+(k−1)2n−2 for right ideals, k(n−1)+1 for other ideals and factor- and subword-closed languages, and k(n−2)+2 for prefix-, factor-, and subword-free languages. We next prove that the nondeterministic state complexity of positive closure is 1 for factor- and subword-closed languages and n for all other classes, while its state complexity is 2 for factor- and subword-closed languages, 2n−2+1 for prefix-closed and suffix-free languages, and n for all other considered classes. We also study left and right quotients by a language from the considered class or by a regular language, and get tight upper bounds in all cases except for state complexity of left quotient of all-sided ideals and subword-closed languages by a regular language, and nondeterministic state complexity of left quotient on subword-convex languages. Assuming that both dividend K and divisor L belong to a given class, the upper bound m on the complexity of the right quotient is tight for free, closed, convex, and right ideal languages, while the complexity of the right quotient of two left ideals is one. The nondeterministic state complexity of the left quotient is m+1 for left ideal, prefix-free, prefix-closed, and factor convex languages, it is m for suffix-free and suffix-closed languages and it is one for right ideals. If the divisor is an arbitrary regular language, then the upper bound m on the complexity of right quotient is always tight, and the upper bound m+1 on the complexity of left quotient is tight unless the dividend is an all-sided ideal, suffix-free, or subword-closed language. In these cases, the complexity of the left quotient is at most m. In four cases, our witnesses are defined over a growing alphabet. All the remaining witnesses are described over a small fixed alphabet, and whenever the binary alphabet is used, it is optimal.

Structure-Constrained Process Graphs for the Process Semantics of Regular Expressions

Milner (1984) introduced a process semantics for regular expressions as process graphs. Unlike for the language semantics, where every regular (that is, DFA-accepted) language is the interpretation of some regular expression, there are finite process graphs that are not bisimilar to the process interpretation of any regular expression. For reasoning about graphs that are expressible by regular expressions modulo bisimilarity it is desirable to have structural representations of process graphs in the image of the interpretation. For '1-free' regular expressions, their process interpretations satisfy the structural property LEE (loop existence and elimination). But this is not in general the case for all regular expressions, as we show by examples. Yet as a remedy, we describe the possibility to recover the property LEE for a close variant of the process interpretation. For this purpose we refine the process semantics of regular expressions to yield process graphs with 1-transitions, similar to silent moves for finite-state automata.

Further Remarks on the Operational Nonterminal Complexity

For a regular language [Formula: see text], let [Formula: see text] be the minimal number of nonterminals necessary to generate [Formula: see text] by right linear grammars. Moreover, for natural numbers [Formula: see text] and an [Formula: see text]-ary regularity preserving operation [Formula: see text], let the range [Formula: see text] be the set of all numbers [Formula: see text] such that there are regular languages [Formula: see text] with [Formula: see text] for [Formula: see text] and [Formula: see text]. We show that, for the circular shift operation [Formula: see text], [Formula: see text] is infinite for all [Formula: see text], and we completely determine the set [Formula: see text]. Moreover, we give a precise range for the left right quotient and a partial result for the left quotient. Furthermore, we add some values to the range for the operation intersection which improves the result of [ 2 ].

Parallel Algorithms for Minimal Nondeterministic Finite Automata Inference

The goal of this paper is to develop the parallel algorithms that, on input of a learning sample, identify a regular language by means of a nondeterministic finite automaton (NFA). A sample is a pair of finite sets containing positive and negative examples. Given a sample, a minimal NFA that represents the target regular language is sought. We define the task of finding an NFA, which accepts all positive examples and rejects all negative ones, as a constraint satisfaction problem, and then propose the parallel algorithms to solve the problem. The results of comprehensive computational experiments on the variety of inference tasks are reported. The question of minimizing an NFA consistent with a learning sample is computationally hard.

On the Commutative Equivalence of Algebraic Formal Series and Languages

The problem of the commutative equivalence of context-free and regular languages is studied. Conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated.

State complexity of GF(2)-operations on unary languages

The paper investigates the state complexity of two operations on regular languages, known as GF(2)-concatenation and GF(2)-inverse (Bakinova et al., “Formal languages over GF(2)”, LATA 2018), in the case of a one-symbol alphabet. The GF(2)-concatenation is a variant of the classical concatenation obtained by replacing Boolean logic in its definition with the GF(2) field; it is proved that GF(2)-concatenation of two unary languages recognized by an m-state and an n-state DFA is recognized by a DFA with 2mn states, and this number of states is necessary in the worst case, as long as m and n are relatively prime. This operation is known to have an inverse, and the state complexity of the GF(2)-inverse operation over a unary alphabet is proved to be exactly 2n−1+1, with the proof based on primitive polynomials over GF(2). For a generalization of the GF(2)-inverse, called the GF(2)-star, the state complexity in the unary case is exactly 2n.

Operational union-complexity

Union-free languages are described by regular expressions using only concatenation and Kleene-star. Every regular language can be given as a union of finitely many union-free languages. By the minimal number of union-free languages needed in such union-free decompositions of a regular language, its union-complexity is defined. In this paper, the union-complexity of the languages obtained by various operations is studied, e.g., having two languages with union-complexities n and m, respectively, what could be the union-complexity of their union/concatenation/shuffle. Particularly, it is shown that the Kleene-star of any regular language has union-complexity 1. In some cases, e.g., at union and concatenation, the resulting language has a bounded union-complexity. In some other cases, e.g., at complement, the resulted language can have arbitrarily large union-complexity. At (k-th) power of a language, the case of the unary alphabet and the general case (alphabet with at least two symbols) have different upper bounds. While, in case of shuffle, there is an unbounded growth in the general case, while for languages over the unary alphabet the growth is bounded. Tight upper bounds are shown for all of the above mentioned cases (whenever the growth is bounded). At intersection we also show an unbounded growth in the general case, especially, over a binary alphabet.

Descriptional complexity of iterated uniform finite-state transducers

We introduce the deterministic computational model of an iterated uniform finite-state transducer (iufst). An iufst performs the same length-preserving transduction on several left-to-right sweeps. The first sweep acts on the input string, any other sweep processes the output of the previous one. The iufst accepts by halting in an accepting state at the end of a sweep.First, we study constant sweep boundediufsts. We prove their computational power coincides with the class of regular languages. We show their descriptional power vs. deterministic finite automata, and the state cost of implementing language operations. We prove the NL-completeness of typical decision problems.Next, we analyze non-constant sweep boundediufsts. We show they can accept non-regular languages provided an at least logarithmic amount of sweeps is allowed. We exhibit a proper non-regular language hierarchy depending on sweep complexity. The non-semidecidability of typical decision problems is also addressed.

Subpath Queries on Compressed Graphs: A Survey

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 in time proportional to the query’s length. The earliest optimal-time solution to the problem, the suffix tree, dates back to 1973 and requires up to two orders of magnitude more space than the plain text just to be stored. In the year 2000, two breakthrough works showed that efficient queries can be achieved without this space overhead: a fast index be stored in a space proportional to the text’s entropy. These contributions had an enormous impact in bioinformatics: today, virtually any DNA aligner employs compressed indexes. Recent trends considered more powerful compression schemes (dictionary compressors) and generalizations of the problem to labeled graphs: after all, texts can be viewed as labeled directed paths. In turn, since finite state automata can be considered as a particular case of labeled graphs, these findings created a bridge between the fields of compressed indexing and regular language theory, ultimately allowing to index regular languages and promising to shed new light on problems, such as regular expression matching. This survey is a gentle introduction to the main landmarks of the fascinating journey that took us from suffix trees to today’s compressed indexes for labeled graphs and regular languages.

Foreign Language Usage and National and European Identification in the Netherlands

Multilingualism is considered a pathway to European identification but might also undermine national identification. We examine regular foreign language usage and two psychological constructs that can explain the relationship between multilingualism and European and national identification in the Netherlands: greater mental openness and a deprovincialized worldview. Using structural equation modeling, the results of two studies conducted with national Dutch samples show that foreign language usage predicted greater mental openness (cultural in Study 1, and cognitive in Study 2), which then predicted greater European identification. Foreign language usage also predicted greater deprovincialization which, in turn, predicted lower national identification.

On restarting automata with auxiliary symbols and small window size

Here we show that for monotone RWW- (and RRWW-) automata, window size two is sufficient, both in the nondeterministic as well as in the deterministic case. For the former case, this is done by proving that each context-free language is already accepted by a monotone RWW-automaton of window size two. In the deterministic case, we first prove that each deterministic pushdown automaton can be simulated by a deterministic monotone RWW-automaton of window size three, and then we present a construction that transforms a deterministic monotone RWW-automaton of window size three into an equivalent automaton of the same type that has window size two. Furthermore, we study the expressive power of shrinking RWW- and RRWW-automata the window size of which is just one or two. We show that for shrinking RRWW-automata that are nondeterministic, window size one suffices, while for nondeterministic shrinking RWW-automata, we already need window size two to accept all growing context-sensitive languages. In the deterministic case, shrinking RWW- and RRWW-automata of window size one accept only regular languages, while those of window size two characterize the Church-Rosser languages.

Parallelisable Regular Languages

In this paper, we have defined Parallelisable strings and languages in order to reduce the recognition time of strings. Parallelisable languages have been introduced and their recognition has been studied through parallelisable finite automaton. We have restricted our study to languages that comprise of words that contain a common subword. By introducing parallelism on the subword we have been able to reduce the recognition time. Also, we have studied the properties of parallel regular languages.

Developing Aural and Oral Skills of Beginner Learners of English as a Foreign Language Through Explicit Metacognitive Strategies Training

Learners of foreign languages from different levels of education need to be active agents of their learning process. They need to develop strategic competence to become proficient learners and users of the foreign language. One way to foster this active and strategic role is to instruct learners in the use of Metacognitive Strategies. This work of research studied the effect of Metacognitive Strategies training on students’ aural and oral skills. Forty-two seventh graders from a public institution participated in a six-workshop training cycle on strategies for planning, monitoring and evaluating learning tasks, following the model of the Cognitive Academic Language Learning Approach- CALLA (preparation, presentation, practice, evaluation and expansion). The findings showed that Metacognitive Strategies positively impacted students’ aural and oral skills, favored their vocabulary repertoire, produced a favorable change in their attitudes towards listening and speaking, and raised their feeling of success and self-efficacy. This implies that Metacognitive Strategies should be incorporated into the regular language class to help students become more self-regulated learners.

Evaluation of Schema Languages: RNG and WXS on Interface Complexity Metric

A complex interface can disorient the user in a mild situation while designing web-based application. Thus, measure should be taken to reduce the complexity and provide reasonable qualities (simplicity, generality and usability) to the user. This paper evaluates Interface Complexity Metric (ICM) between two xml schema languages: World Wide Web Consortium XML Schema (WXS) and Regular Language for Next Generation (RNG) to weigh human insight on the factors affecting effort for comprehending schema documents; taking into account elements and attributes of xml documents; acquired from Web Services Description Language (WSDL). It is probable to lure decisions about the professed qualities; that out of one hundred and twenty (120) schema documents implemented in rng and wxs; rng has the lowest complexity values for almost all the schema documents when compared with wxs because rng exhibits better presentation with high degree of simplicity, generality and usability qualities than wxs. Therefore, this is benefited to developers in assisting them in writing less lengthy code and simplifying software modularization.