Context-free Research Articles

The language of left brackets as a morphism of a maximum prefix code

We investigate the solvability of the equivalence problem in various subclasses of the class of context-free languages. Another fundamental problem necessary for the material in this paper is also the special binary relation for a set of finite languages. Combining these two topics, we obtain in this paper the necessary and sufficient conditions for the equality of two bracketed languages for the prefix-and-suffix case.

In-vitro reconfigurability of native chemical automata, the inclusiveness of their hierarchy and their thermodynamics

Living systems process information using chemistry. Computations can be viewed as language recognition problems where both languages and automata recognizing them form an inclusive hierarchy. Chemical realizations, without using biochemistry, of the main classes of computing automata, Finite Automata (FA), 1-stack Push Down Automata (1-PDA) and Turing Machine (TM) have recently been presented. These use chemistry for the representation of input information, its processing and output information. The Turing machine uses the Belousov-Zhabotinsky (BZ) oscillatory reaction to recognize a representative Context-Sensitive Language (CSL), the 1-PDA uses a pH network to recognize a Context Free Language (CFL) and a FA for a Regular Language (RL) uses a precipitation reaction. By chemically reconfiguring them to recognize representative languages in the lower classes of the Chomsky hierarchy we illustrate the inclusiveness of the hierarchy of native chemical automata. These examples open the door for chemical programming without biochemistry. Furthermore, the thermodynamic metric originally introduced to identify the accept/reject state of the chemical output for the CSL, can equally be used for recognizing CFL and RL by the automata. Finally, we point out how the chemical and thermodynamic duality of accept/reject criteria can be used in the optimization of the energetics and efficiency of computations.

Toward a Uniform Theory of Effectful State Machines

Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g., finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs’s notion of a T - automaton , where T is a monad. We show that the generic language semantics for T -automata correctly instantiates the usual language semantics for a number of known classes of machines/languages, including regular, context-free, recursively-enumerable, and various subclasses of context free languages (e.g., deterministic and real-time ones). Moreover, our approach provides new generic techniques for studying the expressivity power of various machine-based models.

On Szilard Languages of Labelled Insertion Grammars

In this work we initiate the study of Szilard languages of labelled insertion grammars. It is well-known that there exist context-free languages which cannot be generated by any insertion grammar. We show that there exist some regular languages which cannot be Szilard language of any labelled insertion grammar. But any regular language can be given as a homomorphic image of Szilard language obtained by a labelled insertion grammar of weight 1. Also, any context-free language can be obtained as a homomorphic image of Szilard language of a labelled insertion grammar of weight 2. We show that even though insertion grammars of weight 1 can generate only context-free languages, there exist some context-sensitive language which can be obtained as Szilard language of a labelled insertion grammar of weight 1. At the end we show that any recursively enumerable language can be characterized by the homomorphic image of Szilard language obtained by a labelled insertion grammar of weight 5.

On deterministic sensing $$5'\rightarrow 3'$$ Watson–Crick finite automata: a full hierarchy in 2detLIN

Watson–Crick (abbreviated as WK) finite automata are working on double stranded DNA molecule that is also called Watson–Crick tape. Subsequently, these automata have two reading heads, one for each strand. While in traditional WK automata both heads read the whole input in the same physical direction, in $$5'\rightarrow 3'$$ WK automata the heads start from the two extremes (say $$5'$$ end of the strands) and read the input in opposite direction. In sensing $$5'\rightarrow 3'$$ WK automata the process on the input is finished when the heads meet. Since the heads of a WK automaton may read longer strings in a transition, in previous models a so-called sensing parameter took care for the proper meeting of the heads (not allowing to read the same positions of the input in the last step). Recently a new model is investigated, which works without the sensing parameter. In this paper, the deterministic counterpart is studied and is proven to accept the language class 2detLIN defined by the deterministic variant of the earlier version. However, using some of the restricted variants, e.g, all-final automata, the classes of the accepted languages are changed showing a finer hierarchy inside the class of linear context-free languages.

Linear automata with translucent letters and linear context-free trace languages

Linear automata with translucent letters are studied. These are finite-state acceptors that have two heads that read the input from opposite sides and for which a set of translucent letters is associated with each state. Thus, head 1, which proceeds from left to right, does not necessarily read the first letter of the current tape content, but it skips a prefix that consists of translucent letters only and reads the first letter after that prefix. Analogously, head 2, which proceeds from right to left, does not necessarily read the last letter, but it skips a suffix that consists of translucent letters only and reads the last letter before that. After such a read operation, the head always returns to its corresponding end of the tape. These linear automata with translucent letters are a generalization of the finite-state acceptors with translucent letters that were studied by the authors in B. Nagy and F. Otto [Finite-state acceptors with translucent letters. In BILC 2011, Proc., edited by G. Bel-Enguix, V. Dahl, and A.O. De La Pente, SciTePress, Portugal (2011) 3-13.] It is shown that these linear automata are strictly more expressive than the model with a single head, but that they still only accept languages that have a semi-linear Parikh image. On the other hand, we obtain a characterization for the class of linear context-free trace languages in terms of a specific class of linear automata with translucent letters.

On the Prefix–Suffix Duplication Reduction

This work answers some questions proposed by Bottoni, Labella, and Mitrana (Theoretical Computer Science 682, 2017) regarding the prefix–suffix reduction on words. The operation is defined as a reduction by one half of every square that is present as either a prefix or a suffix of a word, leading thus to a finite set of words associated to the starting one. The iterated case considers consecutive applications of the operations, on all the resulting words. We show that the classes of linear and context-free language are closed under iterated bounded prefix–suffix square reduction, and that for a given word we can determine in [Formula: see text] time all of its primitive prefix–suffix square roots.

Sentinel: generating GUI tests for sensor leaks in Android and Android wear apps

Due to the widespread use of Android devices and apps, it is important to develop tools and techniques to improve app quality and performance. Our work focuses on a problem related to hardware sensors on Android devices: the failure to disable unneeded sensors, which leads to sensor leaks and thus battery drain. We propose the Sentinel testing tool to uncover such leaks. The tool performs static analysis of app code and produces a model which maps GUI events to callback methods that affect sensor behavior. Edges in the model are labeled with symbols representing the acquiring/releasing of sensors and the opening/closing of UI windows. The model is traversed to identify paths that are likely to exhibit sensor leaks during run-time execution based on two context-free languages over the symbol alphabet. The reported paths are then used to generate test cases. The execution of each test case tracks the run-time behavior of sensors and reports observed leaks. This approach has been applied to both open-sourced and closed-sourced regular Android applications as well as watch faces for Android Wear smartwatches. Our experimental results indicate that Sentinel effectively detects sensor leaks, while focusing the testing efforts on a very small subset of possible GUI event sequences.

Linear-bounded composition of tree-walking tree transducers: linear size increase and complexity

Compositions of tree-walking tree transducers form a hierarchy with respect to the number of transducers in the composition. As main technical result it is proved that any such composition can be realized as a linear-bounded composition, which means that the sizes of the intermediate results can be chosen to be at most linear in the size of the output tree. This has consequences for the expressiveness and complexity of the translations in the hierarchy. First, if the computed translation is a function of linear size increase, i.e., the size of the output tree is at most linear in the size of the input tree, then it can be realized by just one, deterministic, tree-walking tree transducer. For compositions of deterministic transducers it is decidable whether or not the translation is of linear size increase. Second, every composition of deterministic transducers can be computed in deterministic linear time on a RAM and in deterministic linear space on a Turing machine, measured in the sum of the sizes of the input and output tree. Similarly, every composition of nondeterministic transducers can be computed in simultaneous polynomial time and linear space on a nondeterministic Turing machine. Their output tree languages are deterministic context-sensitive, i.e., can be recognized in deterministic linear space on a Turing machine. The membership problem for compositions of nondeterministic translations is nondeterministic polynomial time and deterministic linear space. All the above results also hold for compositions of macro tree transducers. The membership problem for the composition of a nondeterministic and a deterministic tree-walking tree translation (for a nondeterministic IO macro tree translation) is log-space reducible to a context-free language, whereas the membership problem for the composition of a deterministic and a nondeterministic tree-walking tree translation (for a nondeterministic OI macro tree translation) is possibly NP-complete.

Definition of Natural Languages Using Context-free Grammer: In Context of Dari Language

Formal definition of a natural language lets computers understand it; the languages have challenging complexity to come under representation of any formal language. Modeling assumptions, using formal languages, we can approximate the languages; and better approximation we do, more complexities of formal languages are resolved. Objective is to study current researches and possibilities to model Dari as a context-free language. Researchers have worked for more than 6 decades on definition of syntax of natural languages using context-free grammer. It is crucial that computer scientists to be able to thoroughly understand about which category of formal languages the natural language exist in in. In overall, our skill to decide the grammar type of natural languages performs a significant role in our capability to parse it. This review article concludes that discussed issue of the context-freeness of a certain language is regularly reliant on upon the level of complexity of the language. The common of languages investigated in this regard are languages of European family and Indo-Aryan languages liker Dari, Arabic and Pashto have not been adequately fortunate to be devoted thorough researches in this regard.

On the degrees of non-regularity and non-context-freeness

We study the derivational complexity of context-free and context-sensitive grammars by counting the maximal number of non-regular and non-context-free rules used in a derivation, respectively. The degree of non-regularity/non-context-freeness of a language is the minimum degree of non-regularity/non-context-freeness of context-free/context-sensitive grammars generating it. A language has finite degree of non-regularity iff it is regular. We give a condition for deciding whether the degree of non-regularity of a given unambiguous context-free grammar is finite. The problem becomes undecidable for arbitrary linear context-free grammars. The degree of non-regularity of unambiguous context-free grammars generating non-regular languages as well as that of grammars generating deterministic context-free languages that are not regular is of order Ω(n). Context-free non-regular languages of sublinear degree of non-regularity are presented. A language has finite degree of non-context-freeness iff it is context-free. Context-sensitive grammars with a quadratic degree of non-context-freeness are more powerful than those of a linear degree.

Precision-preserving yet fast object-sensitive pointer analysis with partial context sensitivity

Object-sensitivity is widely used as a context abstraction for computing the points-to information context-sensitively for object-oriented languages like Java. Due to the combinatorial explosion of contexts in large programs, k -object-sensitive pointer analysis (under k -limiting), denoted k -obj, is scalable only for small values of k , where k ⩽2 typically. A few recent solutions attempt to improve its efficiency by instructing k -obj to analyze only some methods in the program context-sensitively, determined heuristically by a pre-analysis. While already effective, these heuristics-based pre-analyses do not provide precision guarantees, and consequently, are limited in the efficiency gains achieved. We introduce a radically different approach, Eagle, that makes k -obj run significantly faster than the prior art while maintaining its precision. The novelty of Eagle is to enable k -obj to analyze a method with partial context-sensitivity, i.e., context-sensitively for only some of its selected variables/allocation sites. Eagle makes these selections during a lightweight pre-analysis by reasoning about context-free-language (CFL) reachability at the level of variables/objects in the program, based on a new CFL-reachability formulation of k -obj. We demonstrate the advances made by Eagle by comparing it with the prior art in terms of a set of popular Java benchmarks and applications.

Derivation languages and descriptional complexity measures of restricted flat splicing systems

In this paper, we associate the idea of derivation languages with a restricted variant of flat splicing systems where at each step splicing is done with an element from the initial set of words present in the system. We call these flat splicing systems as restricted flat splicing systems. We show that the families of Szilard languages of labeled restricted flat finite splicing systems of type (m,n) and REG, CF and CS are incomparable. Also, any non-empty regular, non-empty context-free and recursively enumerable language can be obtained as homomorphic image of the Szilard language of the labeled restricted flat finite splicing systems of type (1,2),(2,2) and (5,2) respectively. We also introduce the idea of control languages for restricted labeled flat finite splicing systems and show that any non-empty regular and context-free language can be obtained as a control language of labeled restricted flat finite splicing systems of type (1,2) and (2,2) respectively. At the end, we show that any recursively enumerable language can be obtained as a control language of labeled restricted flat finite splicing systems of type (5,2) when λ-labeled rules are allowed.

Real examples to motivate automata theory

Many institutions have a course on automata theory that studies the limits of computation by examining successive computational models, including deterministic finite automata (DFAs), context-free ...

Syntactical analysis of context-free languages taking into account order of application of productions

The article sets the task of syntactical analysis of monomials of context-free languages taking into account the order of application of productions in the process of outputting monomials. An attribute model of the process, which defines the description of the process being modeled as business process models, correlates with the level of context-free languages. The business process, presented in the form of a structural model, uses the alphabet and syntax of a specific modeling language, which allows the process to be described independently of the subject area. The problem of syntactical analysis is supplemented as follows. Developing a deadlock algorithm to determine whether makes is possible to obtain a monomial from the initial symbol using the productions of a given context-free language. Determining the choice of productions and number of times was used to derive this monomial and establish the order of using these productions. The article proposes the completed method of monomial labels which allows establishing the order of application of productions. Based on this method, research technologies of programming language that are of interest to the software industry can be developed.

On families of full trios containing counter machine languages

We look at nondeterministic finite automata augmented with multiple reversal-bounded counters where, during an accepting computation, the behavior of the counters is specified by some fixed pattern. These patterns can serve as a useful “bridge” to other important automata and grammar models in the theoretical computer science literature, thereby helping in their study. Various pattern behaviors are considered, together with characterizations and comparisons. For example, one such pattern defines exactly the smallest full trio containing all the bounded semilinear languages. Another pattern defines the smallest full trio containing all the bounded context-free languages. The “bridging” to other families is then applied, e.g. to certain Turing machine restrictions, as well as other families. Certain general decidability properties are also studied using this framework.

Синтаксический анализ мономов контекстно- свободных языков с учётом порядка применения продукций

Синтаксический анализ мономов контекстно- свободных языков с учётом порядка применения продукций

State Complexity of the Quotient Operation on Input-Driven Pushdown Automata

The quotient of a formal language [Formula: see text] by another language [Formula: see text] is the set of all strings obtained by taking a string from [Formula: see text] that ends with a suffix of a string from [Formula: see text], and removing that suffix. The quotient of a regular language by any language is always regular, whereas the context-free languages and many of their subfamilies, such as the linear and the deterministic languages, are not closed under the quotient operation. This paper establishes the closure of the family of languages recognized by input-driven pushdown automata (IDPDA), also known as visibly pushdown automata, under the quotient operation. A construction of automata representing the result of the operation is given, and its state complexity with respect to nondeterministic IDPDA is shown to be exactly [Formula: see text], where [Formula: see text] and [Formula: see text] are the numbers of states in the automata recognizing [Formula: see text] and [Formula: see text], respectively.

Linear context-free tree languages and inverse homomorphisms

We prove that the class of linear context-free tree languages is not closed under inverse linear tree homomorphisms. In fact, we prove a stronger result: we encode Dyck words into a linear context-free tree language and prove that its preimage under a certain linear tree homomorphism cannot be generated by any context-free tree grammar. A positive result can still be obtained: the linear monadic context-free tree languages are closed under inverse linear tree homomorphisms.

A new foundation for finitary corecursion and iterative algebras

This paper contributes to a generic theory of behaviour of “finite-state” systems. Systems are coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category. Their behaviour gives rise to the locally finite fixpoint (LFF), a new fixpoint of the endofunctor. The LFF exists provided that the endofunctor is finitary and preserves monomorphisms, is a subcoalgebra of the final coalgebra, i.e. it is fully abstract w.r.t. behavioural equivalence, and it is characterized by two universal properties: as the final locally finitely generated coalgebra, and as the initial fg-iterative algebra. Instances of the LFF are: regular languages, rational streams, rational formal power-series, regular trees etc. Moreover, we obtain e.g. (realtime deterministic resp. non-deterministic) context-free languages, constructively S-algebraic formal power-series (in general, the behaviour of finite coalgebras under the coalgebraic language semantics arising from the generalized powerset construction by Silva, Bonchi, Bonsangue, and Rutten), and the monad of Courcelle's algebraic trees.