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"Formal languages."
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One model for the learning of language
A major goal of linguistics and cognitive science is to understand what class of learning systems can acquire natural language. Until recently, the computational requirements of language have been used to argue that learning is impossible without a highly constrained hypothesis space. Here, we describe a learning system that is maximally unconstrained, operating over the space of all computations, and is able to acquire many of the key structures present in natural language from positive evidence alone. We demonstrate this by providing the same learning model with data from 74 distinct formal languages which have been argued to capture key features of language, have been studied in experimental work, or come from an interesting complexity class. The model is able to successfully induce the latent system generating the observed strings from small amounts of evidence in almost all cases, including for regular (e.g., aⁿ, (ab)ⁿ, and {a, b}⁺), context-free (e.g., aⁿbⁿ, aⁿbn+m
, and xxR
), and context-sensitive (e.g., aⁿbⁿcⁿ, aⁿbmcⁿdm
, and xx) languages, as well as for many languages studied in learning experiments. These results show that relatively small amounts of positive evidence can support learning of rich classes of generative computations over structures. The model provides an idealized learning setup upon which additional cognitive constraints and biases can be formalized.
Journal Article
One-on-one language teaching and learning : theory and practice
\"From the perspective of the tutor, teaching a language one-to-one is not just one more way of doing what classroom teachers do. With only one learner, it is possible to give serious attention to principles of second language acquisition such as motivation, error treatment, and learner autonomy, which are more difficult to address in classroom learning. One-on-One Language Teaching and Learning brings together a strong theoretical framework with practical suggestions and actual experiences of language learners and tutors from around the world. It applies research in the field of language acquisition and teaching to issues like building a strong tutor-student relationship, working with multilingual learners, and learning various skills and strategies. The book will be valuable for tutors of many languages, not only English, as well as learners who wants to take a more active role in one-on-one learning\"-- Provided by publisher.
Book
HOπ in Coq
We present a formalization of HOπ in Coq, a process calculus where messages carry processes. Such a higher-order calculus features two very different kinds of binder: process input, similar to λ-abstraction, and name restriction, whose scope can be expanded by communication. For the latter, we compare four approaches to represent binders: locally nameless, de Bruijn indices, nominal, and Higher-Order Abstract Syntax. In each case, we formalize strong context bisimilarity and prove it is compatible, i.e., closed under every context, using Howe’s method, based on several proof schemes we developed in a previous paper.
Journal Article
Language and the rise of the algorithm
\"A wide-ranging history of the intellectual developments that produced the modern idea of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians long before the computer age. How do you draw the line between computational rules and the complexities of making systems comprehensible to people? Here Jeffrey M. Binder offers a compelling tour of four visions of universal computation that addressed this issue in very different ways: G. W. Leibniz's calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole's nineteenth-century logic system; and the early programming language ALGOL, whose name is short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. To what extent can meaning be controlled by individuals, like the values of a and b in algebra, and to what extent is meaning inevitably social? By attending to this long-neglected question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Machine learning, in its increasing dependence on words, now places this boundary in jeopardy, making its stakes all the more urgent to understand. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction. \"-- Provided by publisher.
BOOK
UML 2 Semantics and Applications
A coherent and integrated account of the leading UML 2 semantics work and the practical applications of UML semantics development With contributions from leading experts in the field, the book begins with an introduction to UML and goes on to offer in-depth and up-to-date coverage of: The role of semantics Considerations and rationale for a UML system model Definition of the UML system model UML descriptive semantics Axiomatic semantics of UML class diagrams The object constraint language Axiomatic semantics of state machines A coalgebraic semantic framework for reasoning about interaction designs Semantics of activity diagrams Verification of UML models State invariants Model transformation specification and verification Additionally, readers are provided with expert guidance on how to resolve semantic problems and a section on applications of UML semantics with model analysis. UML 2 Semantics and Applications is an ideal resource for researchers and tool-builders working in UML, among others. It is also an excellent textbook for postgraduate teaching and research.
eBook
Linear and Branching System Metrics
We extend the classical system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as elements of arbitrary metric spaces. Trace inclusion and equivalence give rise to asymmetrical and symmetrical linear distances, while simulation and bisimulation give rise to asymmetrical and symmetrical branching distances. We study the relationships among these distances and we provide a full logical characterization of the distances in terms of quantitative versions of LTL and mu-calculus. We show that, while trace inclusion (respectively, equivalence) coincides with simulation (respectively, bisimulation) for deterministic boolean transition systems, linear and branching distances do not coincide for deterministic metric transition systems. Finally, we provide algorithms for computing the distances over finite systems, together with a matching lower complexity bound.
Journal Article
A Characterization for Decidable Separability by Piecewise Testable Languages
The separability problem for word languages of a class$\\mathcal{C}$by languages of a class$\\mathcal{S}$asks, for two given languages$I$and$E$from$\\mathcal{C}$ , whether there exists a language$S$from$\\mathcal{S}$that includes$I$and excludes$E$ , that is,$I \\subseteq S$and$S\\cap E = \\emptyset$ . In this work, we assume some mild closure properties for$\\mathcal{C}$and study for which such classes separability by a piecewise testable language (PTL) is decidable. We characterize these classes in terms of decidability of (two variants of) an unboundedness problem. From this, we deduce that separability by PTL is decidable for a number of language classes, such as the context-free languages and languages of labeled vector addition systems. Furthermore, it follows that separability by PTL is decidable if and only if one can compute for any language of the class its downward closure wrt. the scattered substring ordering (i.e., if the set of scattered substrings of any language of the class is effectively regular). The obtained decidability results contrast some undecidability results. In fact, for all (non-regular) language classes that we present as examples with decidable separability, it is undecidable whether a given language is a PTL itself. Our characterization involves a result of independent interest, which states that for any kind of languages$I$and$E$ , non-separability by PTL is equivalent to the existence of common patterns in$I$and$E$ .
Journal Article
Regular Language Representations in the Constructive Type Theory of Coq
We explore the theory of regular language representations in the constructive type theory of Coq. We cover various forms of automata (deterministic, nondeterministic, one-way, two-way), regular expressions, and the logic WS1S. We give translations between all representations, show decidability results, and provide operations for various closure properties. Our results include a constructive decidability proof for the logic WS1S, a constructive refinement of the Myhill-Nerode characterization of regularity, and translations from two-way automata to one-way automata with verified upper bounds for the increase in size. All results are verified with an accompanying Coq development of about 3000 lines.
Journal Article