Automata Theory (Formal Languages)

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.

In this work we will analyze some recent proposals about how the result of the application of a generative algorithm is recognized as a unit for the purposes of further computations, and how each correlates, either explicitly or implicitly, with a model of the mind. We will propose, in line with previous works, that a mixed approach to mental computations (including both Markovian and non-linear dependencies) can prove useful at both theoretical and empirical levels when stated explicitly. We will argue that phrase markers include both kinds of dependencies between terminals and non-terminals: labeling requirements in a theory (which, in turn, interact with other conditions on phrase structure, binarity being the most notable) give away the conception a certain theory has about the (uniform or not) functioning of the mind.

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.

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.

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.

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.

At least since Aristotle (Poetics, XX), and as emphasized by Saussure (1916), the dual character of linguistic terms –comprising both sound and meaning- has been recognized as central to natural language. Generative Linguistics has traditionally separated sound and meaning systems, and their respective representations (Chomsky, 1965, et seq.), so that only syntax derives structure, whereas the sound and meaning components are purely interpretive: a departure from European structuralism, according to which sound and meaning are intimately related and in tension (Tesniere, 1959), and also aspects of Glossematics (Hjelmslev, 1961), in which two continua, expression and content, are partitioned in what is called the form of expression and the form of content.
In this talk we depart from the Generative model, and explore the consequences of adopting a ‘syntax-as-partitioning’ approach where sound and meaning are in tension, configuring a dynamical frustration (Binder, 2008; Saddy, 2016). We propose that we are dealing with ultrametric high-dimensional fields which configure vector spaces. Given a perturbation to this system, these are parametrized and operated on syntactically. Following Saddy and expanding on Krivochen (2016), we consider the consequences of adopting a field-theoretic approach whereby syntax is a set of topological operations which, by changing the landscape of the off-phase sound (‘phonotactic’) and meaning (‘conceptual’) fields, creates structured manifolds. When syntactic operations change the topological properties of the fields from ultrametric to metric, those manifolds get closer and intersect, triggering the fading of a dimensional attractor and squeezing the core properties of the manifolds into a lower-dimensional, metrized, normal space by means of the center manifold theorem (CMT, Carr, 2006). This approach follows Tesnière and Hjelmslev insofar as (a) the computational operations available in both high-dimensional and low-dimensional spaces are defined by the sound/meaning antinomie; and (b) syntax is not a set of functions operating over discrete symbols but a fundamentally topological mechanism operating over continuous spaces, partitioning them and providing them with a metric, creating manifolds, and getting those closer together until they intersect. A derivation, we claim, oscillates between high- and low- dimensional spaces cyclically, atomizing structure via the CMT.
This approach leads to a straightforward definition of derivational cycles in syntactic computations over manifolds, and separates hard conditions from soft conditions in language as a dynamical system. We expand on the idea that a dependency can be established only if the relevant elements belong to the same workspace when the dependency is established. A cycle is thus defined by the dynamics of the metric-ultrametric interface via the CMT. They are both maximal and minimal units: they are minimally interpretable because nothing smaller can be assigned a semantic interpretation. They are maximally generable, because once a critical value for the manifold being generated is reached, a dimensional attractor fades, and no further structure can be built up in that derivational current.

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 ...

There exists a widespread myth among those who discuss these topics that mirror-image constructions are inherently "easier" than reduplications, whereas this is an artefact of the way Chomsky and others defined some of the early classes of automata and formal grammars.  This was our little attempt to explain this elementary bit of mathematics, though it seems we failed.  Nevertheless, while there is a sense in which f.ex. recursively enumerably languages require more power than recursive than context-sensitive, there is no comparable sense in which languages with reduplications require more power than those with mirror-images.

NB. If someone could tell me how to open this up for comments, I would.

This almost completed article was one of the many attempts to clarify the way in which the mathematics of formal language (and automata) theory (like various things) had been and just then was being misused and abused as a hatchet for various groups trying to either "prove" that someone else's model of human language was "inadequate" or that theirs was the cat's pajamas, relying on the relative impressionability of an audience that understood very little mathematics but believed it understood a great deal of it.  Among other things we show here (as perhaps nowhere else) the profound ambiguities in the term "strong generative capacity", the fact that the Chomsky Hierarchy (which has some limited sense for "measuring" weak generative capacity) is entirely irrelevant to "strong"--so that arguments that say that X kind of grammar may be weakly adequate for a given human language but at least we can be sure it is not strongly adequate are fundamentally confused.  There is also some discussion of how the meaning of sentences both in fact is and should be taken into account in discussing the question of what sort of grammars are "adequate" for human language--with a very very simple example.

According to the author, Hjelmslev’s Glossematics is not adequate to base Greimas’s narrative structures for several reasons. First, Glossematics could be effectively encoded as a Turing Machine. Unfotunately, it would be generative only in a weak sense: it could generate every sort of narrative structure, not their structural description. A comparison with Propp’s model underlines another lack of Glossematics: it is not recursive. For these reasons, it cannot generate the infinite hierarchical self-embedded structures which represent the relation between base-narrative programs and use-narrative programs. The author shows a sketch of a formal grammar generating all, and only the narrative structures represented through Greimas’s metalanguage. Finally, after a critical balance on this generative model, its goals and its lacks, the author expresses his sympathy for a morphodynamic framework

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.

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.

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.

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.

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.

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.

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.

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 space is infinite, because there is no halting algorithm for L-grammars; but it is also subjected to hard conditions, because there are grammars and developments which are not possible states of an L-system: a very well-known example is the space of normal grammars. Just as the space of normal grammars is parametrized 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 L-space is a very rich landscape of grammars which cluster into kinds that are not mutually translatable.

We are presenting an innovative, deterministic approach to constructing highly compressed automata commonly used in malware signature scanning. Our implementation allows building a very efficient (storage-wise) approach for automata, with particular focus on the Aho-Corasick and Commentz-Walter algorithms, using a heterogeneous architecture that not only performs faster, but also supports much larger automata. Experimental results have shown that the memory required for the construction process of our approach is two times lower than in the classic CPU-only approach, while the overall construction time for the automata is improved by at least 50% on average in our experiments.

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.

Several attempts proposed epistemic logic to specify and reason about the knowledge of agents with a discrete model of time. Many extensions of this logic have been seen in the literature to specify and reason about agents' knowledge in the real time. On the other hand, hybrid automata have been proposed as a formal model of hybrid systems. They have also been approached to model group of agents situated in continuous dynamic environment. To specify and reason about the requirements of this model, we defined a logic called RCTL in a previous work. However, a group of agents have to communicate and share their Knowledge not only in timed systems but also in continuous dynamical systems. Thus, a new logic is needed to specify the qualitative and quantitative knowledge of agents. This paper proposes a novel Logic called ERCTL that extends the logic RCTL to specify the epistemic knowledge of agents as evolution of continuous actions over time.

In this paper, we propose new models and algorithms to perform practical computations on W3C XML Schemas, which are schema minimization, schema equivalence testing, subschema testing and subschema extraction. We have conducted experiments on an e-commerce standard XSD called xCBL to demonstrate the e?ectiveness of our algorithms. One experiment has refuted the claim that the xCBL 3.5 XSD is compatible with the xCBL 3.0 XSD. Another experiment has shown that the xCBL XSDs can be effectively trimmed into small subschemas for specific applications, which has significantly reduced schema processing time.

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.

Compositional coordination models and languages play an important role in cyber-physical systems (CPSs). In this paper, we introduce a formal model for describing hybrid behaviors of connectors in CPSs. We extend the constraint automata model, which is used as the semantic model for the exogenous channelbased coordination language Reo, to capture the dynamic behavior of connectors in CPSs where the discrete and continuous dynamics co-exist and interact with each other. In addition to the formalism, we also provide a theoretical compositional approach for constructing the product automata for a Reo circuit, which is typically obtained by composing several primitive connectors in Reo.

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 .

Existing risk analysis techniques are often hard to handle in real world contexts without the use of appropriate software because of their computational complexity. This makes managers and security analysts use simplified methods to evaluate security investments. However, these methods have been shown to be inefficient in most cases. Therefore, an automated tool for risk management would be of great interest, provided that it allows reasoning on attacks and helps building security decisions. This paper provides an algebraic specification of network security risk management activities. It constitutes a helpful mean to reason about automating the risk assessment process without taking into consideration implementations issues.

http://dl.acm.org/citation.cfm?id=1035435

In this paper, we study the data interoperability problem of web services in terms of XML schema compatibility. When Web Service A sends XML messages to Web Service B, A is interoperable with B if B can accept all messages from A. That is, the XML schema R for B to receive XML instances must be compatible with the XML schema S for A to send XML instances, i.e., A is a subschema of B. We propose a formal model called Schema Automaton (SA) to model W3C XML Schema (XSD) and develop several algorithms to perform different XML schema computations. The computations include schema minimization, schema equivalence testing, subschema testing, and subschema extraction. We have conducted experiments on an e-commerce standard XSD called xCBL to demonstrate the practicality of our algorithms. One experiment has refuted the claim that the xCBL 3.5 XSD is backward compatible with the xCBL 3.0 XSD. Another experiment has shown that the xCBL XSDs can be effectively trimmed into small subschemas for specific applications, which has significantly reduced the schema processing time.

We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it selects to run its job to the server among its permissible servers having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness. We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy and price of stability of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions.

""The paper defines a specialized language ("the Notation") for a formalised description (by formulae) of the soil mapping units of the Legend of the Soil Map of Romania at the scale 1:200,000 (SMR-200). The Notation is elaborated to be used for precise (unambiguous) definition of the SMR-200 Legend, in order to facilitate its interpretation by computer programs or by different users.
The Notation comprises rules and terms unambiguously defined, which may be used to establish the formulae of soil typological units (STU) and of soil mapping units (SMU). The terms used in the STU formulae are: soil type or WRB Reference Soil Group, soil subtypes or WRB qualifiers, low taxonomic level characteristics/qualifiers of soil/land, underlying rock, soil/land use, STU location in the landform/microrelief, STU weighting in SMU area, STU frequency in SMU "areals" (delineations) and explanatory note concerning the STU. Lists of possible values (mnemonic codes in the classification systems SRCS and WRB /extended-WRB) of these terms are defined – except the explanatory notes, which are free texts. The SMUs may be described as a STU or as an association of STUs, according to the case. The formulae of STU associations are formed by combining the formulae of the component STUs using "association-operators" ("associated-with", "including") and/or "alternative-operators" ("exclusive-or", "inclusive-or"). In order to simplify the formulae of STU associations, the association’s STUs may be grouped, according to needs, by using "grouping-operators" ("[", "]"). In that way the terms common to a group/subgroup of STUs may be specified, too.""

This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing iterated epistemic states on the model of fixed points in the modal $\mu$-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- a hyperintensional epistemic $\mu$-automaton permits fixed points to entrain a principled means by which to iterate epistemic states and account thereby for necessary conditions on self-knowledge. The hyperintensional epistemic $\mu$-calculus is applied to the iteration of the epistemic states of a single agent instead of the common knowledge of a group of agents, and is thus a novel contribution to the literature.

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.

Runtime monitoring is a widely used approach to ensure code safety. Several
implementations of formal monitors have been proposed in the literature, and these differ
with respect to the set of security policies that they are capable of enforcing. In this survey,
we examine the evolution of knowledge regarding the issue of precisely which security
policies monitors are capable of enforcing.We identify three stages in this evolution. In the
first stage, we discuss initial limits on the set of enforceable properties and various ways in
which this set can be extended. The second stage presents studies that identify constraints
to the enforcement power of monitors. In the third stage, we present a final series of studies
that suggest various alternative definitions of enforcement, which specify both the set of
properties the monitors can enforce as well as the manner by which this enforcement is
provided.

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.