Automata Theory (Formal Languages)

Abstract. We consider the problem of finding near-optimal solutions for a variety of A/I)-hard scheduling problems for which the objective is to minimize the total weighted completion time. Recent work has led to the development of several techniques that yield constant worst-case bounds in a number of settings. We continue this line of research by providing improved performance guarantees for several of the most basic scheduling models, and by giving the first constant performance guarantee for a number of more realistically constrained scheduling problems. For example, we give an improved performance guarantee for minimizing the total weighted completion time subject to release dates on a single machine, and subject to release dates and/or precedence constraints on identical parallel machines. We also give improved bounds on the power of preemption in scheduling jobs with release dates on parallel machines. We give improved on-line algorithms for many more realistic scheduling mod...

In this paper we will attempt to classify Lindenmayer systems based on properties of sets of rules and the kind of strings those rules generate. This classification will be referred to as a ‘parametrization’ of the L-space: the L-space is the phase space in which all possible L-developments are represented.

"This paper presents a formal development of a cardiac pacing
system based on a Boston Scientific’s model, a pilot case study from the Grand Challenge in Software Verification. We present a summary of our Z model of the system, its translation into Perfect Developer, and the code generation and execution. Further practical result and analysis are also in the context of this paper.
Keywords: formal modelling, Z, refinement, Perfect Developer, pacemaker."

Abstract. Visibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it is equivalent to a visibly counter automaton, i.e. an automaton that uses its stack only as counter. In particular, this allows to decide whether a given visibly pushdown language is a regular restriction of the set of well-matched words, meaning that the language can be accepted by a finite automaton if only well-matched words are considered as input. 1

Many years ago — I don’t want to say how many, it’s depressing — I taught a course on the http://roose.in/
automata-theoretic approach to model checking at the Technical University of Munich, basing it
on lectures notes for another course on the same topic that Moshe Vardi had recently taught in
Israel. Between my lectures I extended and polished the notes, and sent them to Moshe. At that
time he and Orna Kupferman were thinking of writing a book, and the idea came up of doing it
together. We made some progress, but life and other work got in the way, and the project has been
postponed so many times that it I don’t dare to predict a completion date.

We train neural networks to optimize a Minimum Description Length score, i.e., to balance between the complexity of the network and its accuracy at a task. We show that networks optimizing this objective function master tasks involving memory challenges and go beyond context-free languages. These learners master languages such as anbn, anbncn, anb2n, anbmcn+m, and they perform addition. Moreover, they often do so with 100% accuracy. The networks are small, and their inner workings are transparent. We thus provide formal proofs that their perfect accuracy holds not only on a given test set, but for any input sequence. To our knowledge, no other connectionist model has been shown to capture the underlying grammars for these languages in full generality.

n this talk we review some foundational notions that underlie theories of natural language syntax and, more generally, structure in formal symbolic systems. We introduce and explain the main features of the models that are used to characterise structure in a linguistic signal; these models are what we call grammars: finite sets of rules that operate over pre-defined alphabets of symbols and generate sequences, or strings. All grammars used in linguistic research and computer science belong in an inclusive hierarchy known as the Chomsky Hierarchy where they are classified depending on the properties of the structures they can generate (e.g,, is there embedding? Do we need some kind of memory buffer to account for dependencies in a signal? Can we have dependencies between non-adjacent symbols?): this is the space of normal grammars and the one we are most familiar with. We also venture into what lies outside the Chomsky Hierarchy, and explore the properties of systems that does not abide to the rules of normal grammars and thus cannot be pinpointed within the Chomsky Hierarchy: these are Lindenmayer grammars (L-grammars). We define, characterise, and classify L-grammars based on properties of the sets of rules defined in these formalisms and the kind of strings those rules generate. Just as the space of normal grammars is classified into Regular, Context-Free, Context-Sensitive, and Unrestricted (with proper containment relations holding among them; see Chomsky, 1959: Theorem 1), we contend here that the space of L-grammars is a very rich landscape of grammars which cluster into kinds that are not mutually translatable: symmetric and asymmetric grammars.

Artykuł opublikowany w 13 numerze czasopisma "Problemy Studiów Nauczycielskich" przedstawia podręcznik dla studentów kształcących się w kierunku nauczania informatyki, wydany nakładem Wyższej Szkoły Pedagogicznej w Krakowie. W artykule uzasadniona jest celowość uwzględnienia teoretycznych podstaw informatyki w profilu wykształcenia przyszłych nauczycieli informatyki, a także przedstawiona jest zawartość (spis treści) wydanego podręcznika.

Use of Computational and Automata Theory is common now a day in lexical analysis in compilers and programming languages, morphological analysis, image compression, bioinformatics etc. However in computer games and computing game theory its use is not widespread. This paper summarizes the design of an arcade game using automata theory tools. Deterministic finite state automaton (DFSA) and non-deterministic finite state automaton (NDFSA) are used primarily in various levels of designing the game.

Debido a su carácter marcadamente algebraico, la materia de Teoría de Autómatas y Lenguajes Formales puede ser percibida como excesivamente teórica, con el consiguiente riesgo de rechazo por parte del alumno. Compartimos aquí nuestra experiencia dentro de esta asignatura, a la que hemos logrado dar un carácter mucho más práctico mediante una serie de ejercicios de programación empleando unas librerías de código, proporcionadas por el docente, que implementan las estructuras algebraicas básicas de la materia. Dichas prácticas y las librerías de código empleadas en su implementación, se abordan aquí.

An introductory summary of some aspects of formal language theory intended for an audience doing AGL experiments but without training on the formal side of things.
Presented at the workshop 'Formal Grammars, Informally'. Reading, December, 2017.

This work analyses the relationship between Temporal Logic and Automata Theory. Firstly, we introduce the historical background of both fields. Then we explain the core concepts, and we construct an finite automaton from a temporal logic formula. Finally, we present some considerations on regarding flow of time as a graph-like process.

Scope & Topics 9 th International Conference on Bioinformatics and Bioscience (ICBB 2022) is the application of information science and technology to the field of biology to increase the understanding of all biological process. The aim of this conference is to publish all the latest and outstanding research articles in all areas of bioinformatics and Biometrics. Researchers and scientists from the fields of biology, computer science, mathematics, statistics and physics are invited to share their developments and new techniques in the fields of Biometrics and Bioinformatics.

Proof-theoretic models of grammar are based on the view that an explicit characterization of a language comes in the form of the recursive enumeration of strings in that language. That recursive enumeration is carried out by a procedure which strongly generates a set of structural descriptions Σ and weakly generates a set of strings S; a grammar is thus a function that pairs an element of Σ with elements of S (Chomsky, 1965). Structural descriptions are obtained by means of Context-Free phrase structure rules (e.g., X-bar theory) or via recursive combinatorics (Merge) and structure is assumed to be uniform: binary branching trees all the way down. In this work we will analyse natural language constructions for which such a rigid conception of phrase structure results descriptively inadequate, and propose a solution for the problem of phrase structure grammars assigning too much or too little structure to natural language strings: we propose that the grammar can oscillate between levels of computational complexity in local domains, which correspond to elementary trees in a lexicalised Tree Adjoining Grammar.

We present a novel procedural framework for interactively modeling building façades. Common procedural approaches, such as shape grammars, assume that building façades are organized in a tree structure, while in practice this is often not the case. Consequently, the complexity of their layout description becomes unmanageable for interactive editing. In contrast, we obtain a façade by composing multiple overlapping layers, where each layer contains a single rectilinear grid of façade elements described by two simple generator patterns. This way, the design process becomes more intuitive and the editing effort for complex layouts is significantly reduced. To achieve this, we present a method for the automated merging of different layers in the form of a mixed discrete and continuous optimization problem. Finally, we provide several modeling examples and a comparison to shape grammars in order to highlight the advantages of our method when designing realistic building façades.

En este trabajo presentamos una metodología, y algoritmos para la obtención de las formas normales de las palabras de un monoide finitamente presentado. Esta metodología se apoya en algunos resultados de la teoría de los lenguajes formales, en particular, de los lenguajes regulares. La metodología puede resumirse en los siguientes pasos: 1.-Dada una presentación finita de un monoide, construir un autómata finito que acepte el lenguaje de las formas normales. 2. -A partir del autómata, construir la expresión regular que describe al lenguaje de las formas normales.

International Journal of Computational Science and Information Technology (IJCSITY) focuses on Complex systems, information and computation using mathematics and engineering techniques. This is an open access peer-reviewed journal will act as a major forum for the presentation of innovative ideas, approaches, developments, and research projects in the area of Computation theory and applications. It will also serve to facilitate the exchange of information between researchers and industry professionals to discuss the latest issues and advancement in the area of advanced Computation and its applications The topics suggested by this journal can be discussed in term of concepts, surveys, state of the art, research, standards, implementations, running experiments, applications, and industrial case studies. Authors are invited to submit complete unpublished papers, which are not under review in any other conference or journal. Topics of interest include but are not limited to, the following  Algorithms and data structures

Resumen Debido a su carácter marcadamente algebraico, la materia de Teoría de Autómatas y Lenguajes Formales puede ser percibida como excesivamente teórica, con el consiguiente riesgo de rechazo por parte del alumno. Compartimos aquí nuestra experiencia dentro de esta asignatura, a la que hemos logrado dar un carácter mucho más práctico mediante una serie de ejercicios de programación empleando unas librerías de código, proporcionadas por el docente, que implementan las estructuras algebraicas ...

For the past two decades, it has widely been assumed by linguists that there is a single computational operation, Merge, which is unique to language, distinguishing it from other cognitive domains. The intention of this paper is to progress the discussion of language evolution in two ways: (i) survey what the ethological record reveals about the uniqueness of the human computational system, and (ii) explore how syntactic theories account for what ethology may determine to be human-specific. It is shown that the operation Label, not Merge, constitutes the evolutionary novelty which distinguishes human language from non-human computational systems; a proposal lending weight to a Weak Continuity Hypothesis and leading to the formation of what is termed Computational Ethology. Some directions for future ethological research are suggested.

The machine project aims to design and implement formal models of computation such as Finite Automata and Pushdown Accepter in the development of a lexical and syntax analyzer for an eXtensible Markup Language or XML. The XML Parser was developed using C#.NET Programming Language. It accepts the contents of an XML and stores in a string data type. Each token on the string is extracted using Regular Expressions and the syntax was analyzed to be balanced using a series of if and else conditions based on the format of an XML document. The XML Parser outputs a YES when the input string is in a valid XML Format; otherwise, the output is NO. The system was tested using three main parameters, correctness, efficiency and code elegance. It registered a 100% correctness using the test cases at hackerank, O(n2) time and space complexity and a rating of average for code elegance measured using Visual Studio Code Metrics Calculator.

Aloe barbadensis (aloe-vera) also famous as a first aid plant is a valuable natural medicine. Its leaves have parallel venation that contains a soothing thick gel inside it and is useful for treatment and curing of wounds and diseases. In this paper, investigations were carried out to study the effect of dc and ac resistances of the aloe barbadensis leaves. The resistance of the leaf measured shows a proportional change with the change in the length of the leaf. The resistance of the leaf tissue increases with the increased distance between the electrodes due to circumvent current path. Both, fresh and the dry leaf of a aloe barbadensis plant was taken for the investigations. For fresh leaf, the dc resistance increases steeply along the length of a leaf while ac resistance comparatively shows a very slow increase in resistance, where as the results verified some fascinating changes in resistance as the leaf dried up.

Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. The transcendence degree (trdeg) of a set \(\{f_1, \dotsc, f_m\} \subset \mathbb{F}[x_1, \dotsc, x_n]\) of polynomials is the maximal size r of an algebraically independent subset. In this paper we design blackbox and efficient linear maps ϕ that reduce the number of variables from n to r but maintain trdeg{ϕ(f i )} i  = r, assuming f i ’s sparse and small r. We apply these fundamental maps to solve several cases of blackbox identity testing: Given a circuit C and sparse subcircuits f 1,…,f m of trdeg r such that D: = C(f 1,…,f m ) has polynomial degree, we can test blackbox D for zeroness in poly(size(D)) r time. Define a ΣΠΣΠ δ (k,s,n) circuit C to be of the form ∑  i = 1 k  ∏  j = 1 s f i,j , where f i,j are sparse n-variate polynomials of degree at most δ. For k = 2, we give a \(poly(\delta sn)^{\delta^2}\) time blackbox identity test. For a general depth-4 circuit we define a notion of rank. Assuming there is a rank bound R for minimal simple ΣΠΣΠ δ (k,s,n) identities, we give a \(poly(\delta snR)^{Rk\delta^2}\) time blackbox identity test for ΣΠΣΠ δ (k,s,n) circuits. This partially generalizes the state of the art of depth-3 to depth-4 circuits. The notion of trdeg works best with large or zero characteristic, but we also give versions of our results for arbitrary fields.

I would like to thank people who contributed to this thesis and to my personality during the time I was writing it. First of all, I would like to thank my advisor Hasan Ibne Akram for his constant encouragement, guidance and feedback. Secondly, I would like to thank Heiko and Manuel for improving my programming skills. I am also very grateful to my close friend Denis and to my family for inspirational conversations.

International Journal of Information Science & techniques (IJIST) focuses on system modeling and information techniques in real engineering and scientific problems This journal provides a forum that impacts the development of scientific computing, complex systems, control theory, signal and image processing, scheduling, data mining, discrete systems. It also acts as a path to exchange novel ideas about new modeling techniques.

Original version of my PhD dissertation (University of Reading), a much shorter version of which (~ 60% shorter) was defended on 1/2018.

This work is a study of the nature of cognitive computation, with a focus on the relation between computation, linguistic theory, and grammar. We review traditional notions of computation and analyse their applicability to natural language, distinguishing the latter from formal languages as these are usually studied in computer science.
The main theoretical result of the thesis is that imposing a single computational template for the assignment of structural descriptions to natural language sentences, while long accepted, is both empirically inadequate and theoretically more costly than a strongly cyclic approach in which computational dependencies vary, oscillating up and down the Chomsky Hierarchy of formal grammars. Specifically, we defend the idea that such a system delivers the simplest possible structural description that captures semantic dependencies between syntactic objects in local substrings. This hypothesis will be referred to as the theory of mixed computation. The analysis of theories of computation starting with the seminal work of Alan Turing (1936) will reveal that the theory of computable functions must not be identified with the theory of effective computation; this then permits us to argue for the necessity of introducing aspects of interaction in the study of physically realized computational procedures which configure dynamical systems. We show that mixed computation lends itself naturally to modelling dynamical systems.
Empirically, we present evidence for mixed computation derived from an analysis of strong locality conditions in natural language syntax, that is, locality constraints whose violation cannot be repaired or ameliorated. Specifically, we set our focus on the Coordinate Structure Constraint (Ross, 1967), which pertains to the extraction of terms from coordinated structures and how it can be shown to arise from a mixed-computation analysis. Data from English, Spanish, and Latin support the identification of two kinds of coordinated structures: one is finite state in nature, and cannot be probed into. The other is phrase structural (context-free), and its internal complexity is visible to further syntactic operations, including extraction. We argue that data from locality conditions as well as cyclicity in natural-language syntax are accounted for naturally under a dynamical model of mixed computation.

We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or ǫ-transitions. Our approach employs monads with a parametrized fixpoint operator † to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen as the unit of a free monoid. More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions. This allows to consider a wide range of other examples, including Mazurkiewicz traces for concurrent systems.

We present a Generalized LR parsing algorithm for unrestricted context-free grammars working in complexity O(n 3 ). It differs from previous approaches in the use of dynamic programming techniques to cope with the non determinism, instead of a graph-structured stack. The steps for deriving our algorithm from classical Earley's parsing algorithm are shown.

This work describes dafsa, a Python library for computing graphs from lists of strings for identifying, visualizing, and inspecting patterns of substrings. The library is designed for usage by linguists in studies on morphology and formal grammars, and is intended for faster, easier, and simpler generation of visualizations. It collects frequency weights by default, it can condense structures, and it provides several export options. Figure 1 depicts a basic DAFSA, based upon five English words and generated with default settings.

ABSTRACT This article presents a software tool for the synthesis of supervisory control based on untimed finite state automata. The tool has a friendly graphical interface for the creation of models and, among other features, allows: automata simulation; analysis of problems related to the implementation of the control logic; and code generation for multiple devices. The code generation is based on a template system that allows the easy inclusion of support for new devices. Currently the tool is able to generate code for some microcontrollers and programmable logic controllers. Another feature of the tool is the capability of being easily extended with new algorithms and modules.

The objective of this project is to provide a brief explanation of the concept of a cellular automaton and its elements, highlighting the behavior of three cellular automata.
Resumen

El objetivo de este proyecto es entregar una breve explicación del concepto de un autómata celular y sus elementos destacando el comportamiento tres autómatas celulares.

La teoría de autómatas, también llamada teoría algebraica de máquinas, permite estudiar de un modo sistemático las máquinas, más o menos complicadas, que realizan un procesamiento de la información y que actúan de manera discreta; es decir, la información se supone codificada a partir de un conjunto finito de símbolos que el autómata trata secuencialmente, uno detrás de otro. La teoría de autómatas proporciona métodos para el análisis y la síntesis de tales máquinas. Los trabajos sobre lenguajes y gramáticas formales han evolucionado en una dirección que les ha conducido a encontrarse con la teoría de autómatas como herramienta matemática de gran utilidad. Este artículo pretende ser una introducción básica a dicha teoría de autómatas.

Until now, the results about "contextual automata" is reduced to a single example that characterise a more specific class of contextual language. The definition of new types of automata which characterise the other contextual languages is considered an "open problem". In this article we present the state of the art in the field of contextual automata.

We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K 1,4 as an induced subgraph. Our results provide a dichotomy for Dominating Set in K 1, -free graphs and show that the problem is fixed-parameter tractable if and only if ≤ 3. Finally, we show that our algorithmization can also be used to show that the related Connected Dominating Set problem is fixed-parameter tractable on claw-free graphs. *

Fuzzy co-clustering can be improved if we handle two main problem first is outlier and second curse of dimensionality .outlier problem can be reduce by implementing page replacement algorithm like FIFO, LRU or priority algorithm in a set of frame of web pages efficiently through a search engine. The web page which has zero priority (outlier) can be represented in separate slot of frame. Whereas curse of dimensionality problem can be improved by implementing FCC_STF algorithm for web pages obtain by search engine that reduce the outlier problem first. The algorithm FCCM and FUZZY CO-DOK are compared with FCC_STF algorithm with merit and demerits on the bases of different fuzzifier used. FCC_STF algorithm in which fuzzifier fused into one entity who have shown high performance by experiment result of values (A1,B1,Vcj,A2,B2) seem to less sensitive to local maxima and obtain optimization search space in 2-D for web pages by plotting graph between J(fcc_stf ) and Vcj.

We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal µ-calculus where the application of the least fixpoint operator µp.ϕ is restricted to formulas ϕ that are continuous in p. Our proof is automata-theoretic in nature; in particular, we introduce a class of automata characterizing the expressive power of WMSO over tree models of arbitrary branching degree. The transition map of these automata is defined in terms of a logic FOE ∞ 1 that is the extension of firstorder logic with a generalized quantifier ∃ ∞ , where ∃ ∞ x.ϕ means that there are infinitely many objects satisfying ϕ. An important part of our work consists of a model-theoretic analysis of FOE ∞ 1 .

Debido a su carácter marcadamente algebraico, la materia de Teoría de Autómatas y Lenguajes Formales puede ser percibida como excesivamente teórica, con el consiguiente riesgo de rechazo por parte del alumno. Compartimos aquí nuestra experiencia dentro de esta asignatura, a la que hemos logrado dar un carácter mucho más práctico mediante una serie de ejercicios de programación empleando unas librerías de código, proporcionadas por el docente, que implementan las estructuras algebraicas básicas de la materia. Dichas prácticas y las librerías de código empleadas en su implementación, se abordan aquí.

We extend the Expressionist project, and thereby the re-emerging area of grammar-based text generation, by applying a technique from software verification to a critical search problem related to content generation from grammars. In Expressionist, authors attach tags (corresponding to pertinent meanings) to nonterminal symbols in a context-free grammar , which enables the targeted generation of content that expresses requested meanings (i.e., has the requested tags). While previous work has demonstrated methods for requesting content with a single required tag, requests for multiple tags yields a search task over domains that may realistically span quintillions or more elements. In this paper, we reduce Expressionist grammars to symbolic visibly pushdown automata, which allows us to locate in massive search spaces generable outputs that satisfy moderately complex criteria related to tags. While the satisficing of more complex tag criteria is still not feasible using this technique, we forecast a number of opportunities for future directions.