Showing papers on "Formal language published in 1980"

Formal Principles of Language Acquisition

Abstract: The question of language learnability is central to modern linguistics. Yet, despite its importance, research into the problems of language learnability has rarely gone beyond the informal, commonsense intuitions that currently prevail among linguists and psychologists.By focusing their inquiry on formal language learnability theory--the interface of formal mathematical linguistics, linguistic theory and cognitive psychology--the authors of this book have developed a rigorous and unified theory that opens the study of language learnability to discoveries about the mechanisms of language acquisition in human beings. Their research has important implications for linguistic theory, child language research, and the philosophy of language."Formal Principles of Language Acquisition" develops rigorous mathematical methods for demonstrating the learnability of classes of grammars. It adapts the well-developed theories of transformational grammar to establish psychological motivation for a set of formal constraints on grammars sufficient for learnability. In addition, the research deals with such matters as the complex interaction between the mechanism of language learning and the learning environment, the empirical adequacy of the learnability constraints, feasibility and attainability of classes of grammars, the role of semantics in language learnability, and the adequacy of transformational grammars as models of human linguistic competence.This first serious and extended development of a formal and precise theory of language learnability will interest researchers in psychology and linguistics, and is recommended for use in graduate courses in language acquisition, linguistic theory, psycholinguistics, and mathematical linguistics, as well as interdisciplinary courses that deal with language learning, use, and philosophy.Contents: Methodological Considerations; Foundations of a Theory of Learnability; A Learnability Result for Transformational Grammar; Degree-2 Learnability; Linguistic Evidence for the Learnability Constraints; Function, Performance and Explanations; Further Issues: Linguistic Interaction, Invariance Principle, Open Problems; Notes, Bibliography, Index.

Inductive inference of formal languages from positive data

Abstract: We consider inductive inference of formal languages, as defined by Gold (1967) , in the case of positive data, i.e., when the examples of a given formal language are successive elements of some arbitrary enumeration of the elements of the language. We prove a theorem characterizing when an indexed family of nonempty recursive formal languages is inferrable from positive data. From this theorem we obtain other useful conditions for inference from positive data, and give several examples of their application. We give counterexamples to two variants of the characterizing condition, and investigate conditions for inference from positive data that avoids “overgeneralization.”

Some open questions and recent results on tree transducers and tree languages

Abstract: Publisher Summary The theory of tree automata and tree grammars investigates computation on structured objects and the structure of computation. In both cases, the structure is represented by a tree. The tree language theory uses the methods and results of formal language theory, which is supported by algebraic methods. Since the beginning of tree language theory in 1965, the theory has grown and proved its usefulness in areas such as program scheme theory, theory of syntax-directed translation, and formal language theory itself. This chapter discusses open questions and recent results on tree transducers and tree languages and discusses possible directions of research. It describes the position of tree language theory with respect to theoretical computer science and formal language theory. An important task of theoretical computer science is to formalize and investigate the control structures and data structures used by the programmers to describe their algorithms. Insight into the formal power of such programming constructs and their trade-offs may lead to a better understanding of the nature of computation.

Open problems about regular languages

Abstract: Publisher Summary The theory of regular languages and finite automata was developed in the early 1950s and is one of the oldest branches of theoretical computer science. Regular languages constitute the best known family of formal languages, and finite automata constitute the best known family of abstract machine models. The concepts of regular languages and finite automata appear frequently in theoretical computer science and have several important applications. There is a vast literature on these subjects. Despite the fact that many researchers have worked in this field, there remain several difficult open problems. The chapter discusses six of these problems. These problems are of fundamental importance and considerable difficulty. Most of them are intimately involved with the fundamental property of finite automata, namely finiteness. In a monograph published in 1971, McNaughton and Papert included a collection of open problems concerning regular languages. Their list is headed by the star height problem and until now, no progress has been made on such an intriguing question. The bounds on star height apply only to languages whose syntactic monoids are groups. In that case, the corresponding semiautomata are permutation semiautomata.

Dialogue design implications of task allocation between man and computer

Abstract: It is argued that the form of dialogue required in man-computer interaction is dependent upon the nature of the task and the allocation for task functions between man and computer. The paper examines the design implications of two task variables; task openness and task frequency. It concludes that one of man's essential roles in the operation of man-computer systems is to cope adaptively with the openness in the system and that one of the problems of current systems is that they infer a closed model of the task that may inhibit the user in his efforts to provide an adaptive contribution. The paper considers the kinds of constrained languages appropriate for closed tasks and the command languages necessary to make flexible and powerful use of computer facilities when the task is open. It raises the dilemma of the infrequent user with open-ended tasks who needs a complex formal language but is unwilling or unable to master it. A number of solutions are offered to this dilemma. Finally, a plea is made for th...

Morphisms on free monoids and language theory

Abstract: Publisher Summary Mathematically, the simplest and most natural operation considered in language theory is a morphism between two free monoids. Many of the problems concerning such morphisms are difficult and challenging. This chapter discusses the problems concerning morphism between two free monoids in formal language theory. The active areas of research, that is, equality sets and grammar forms, fit well into the framework of studies dealing with morphisms. A daily oral language (DOL) system constitutes a very simple finitary device for language definition. Languages defined by a DOL system are referred to as DOL languages. The DOL systems constitute a convenient framework for certain properties of ω -words. The chapter discusses two problems: the construction of a strongly cube-free ω-word over an alphabet with cardinality two, that is, strong cube-freeness problem and the construction of a square-free ω-word over an alphabet with cardinality three, that is, square-freeness problem.

On the Any-Thesis and the Methodology of Linguistics

Abstract: In earlier publications, I have outlined a largely novel approach2 to the semantics of certain formal languages and the semantics of certain fragments of natural languages.3 In this approach, the truth of a sentence S is defined as the existence of a winning strategy for one of the two players, called Myself, in a certain two-person game G(S) associated with S.4 Intuitively, G(S) may be thought of as an attempt on the part of Myself to verify S against the schemes of an actively resistant opponent who is called Nature. On the basis of this idea, most of the game rules can be anticipated. For instance, I win if the game ends with a true primitive sentence, and Nature wins if it ends with a false one. For quantifier phrases like “any Y who Z” and “every Y who Z”, the game rules can also be anticipated. As special cases we have the following rules:

Formal languages and their relation to automata: what hopcroft & ullman didn't tell us

Abstract: Publisher Summary This chapter discusses the relationship between formal languages and automata. The relationship is a weak one and proceeds in only one direction. Automata are used as acceptors to define languages; therefore, the languages can be considered the external behavior of their acceptors and that end the relationship. There is no application of results from language theory to the study of automata. The chapter explains that there are deficiencies in the theory of automata and the deficiencies are reparable. The automata may be more intuitive than that of grammars; however, automata are so much more complicated that they would be used in formal proofs only with great awkwardness and when a proof by means of grammars is for some reason not feasible. A finite-state automaton is not always the best way to describe a regular set. There is no single method of representing regular sets that is always the most convenient to use.

Succinct representation random strings, and complexity classes

Abstract: A general paradigm for relating measures of succinctness of representation and complexity theory is presented. The measures are based on the new Private and Blindfold Alternation machines. These measures are used to indicate the inherent information (or "randomness") of a string, but with respect to time and space complexity classes. These measures are then used to show that the existence of strings which are random with respect to one measure but not to another can show the relationship between the corresponding complexity classes. The basic hierarchy theorems given allow different and possibly more powerful approaches to these problems.

A survey of results and open problems in the mathematical theory of l systems

Abstract: Publisher Summary L systems were originated by Aristid Lindenmayer in connection with biological considerations in 1968. The theory of L systems has a great impact on formal language theory. Two main features of the theory of L systems are parallelism in the rewriting process and the notion of a grammar conceived as a description of a dynamic process, rather than of a static one. L systems have enriched the theory of formal languages and also been able to put the theory in a totally new perspective. This chapter discusses the mathematical theory of L systems. One of the outstanding features of the theory of L systems is that its core fits into a systematic and basic mathematical framework formed by single or several iterated homomorphisms or finite substitutions on a free monoid. The chapter discusses this systematic framework. The basic construct of L systems theory is the daily oral language (DOL) system. A DOL system represents a basic mathematical structure—the iteration of a single homomorphism on a free monoid. Although mathematically most simple, DOL systems give a clear insight into the essential ideas and techniques behind L systems and parallel rewriting in general.

The Generative Power of Rule Orderings in Formal Grammars

Abstract: One way of 'restricting linguistic theory' is the L-view: place sufficient restrictions on the allowable rules of grammars so as to reduce their generative power. Another way is the G-view: disallow certain grammars, regardless of whether this results in a reduction of generative capacity. The present paper adopts the L-view and, consequently, investigates the generative power of various theories. One area in linguistics where restrictions on linguistic theory have been advocated is in the ordering (within the cycle) of the application of the rules which generate the language. We consider eight proposals: Total Ordering; Partial Ordering (= Total Ordering plus iterative application); Semi Ordering ( = Anderson's 'local ordering' without iterative application); Semi Partial Ordering ( = Semi Ordering plus iterative application); Unorder ings ( = Ringen 'Condition VI, unmodified'); Quasi Orderings ( = Ringen 'Condition VI, modified'); Random Orderings; and Simultaneous Application. If, for any grammar obeying rule ordering conditions A there is a grammar obeying rule ordering conditions B which contains exactly the same class of derivations, then rule ordering theory B is at least as powerful in strong generative capacity as rule ordering theory A. Similar considerations are used to define the notions of equivalent, more powerful, and noncomparable in strong generative capacity. A series of theorems are proved showing the relative strength of the eight rule ordering theories. Some linguists who advocate 'random ordering' actually have in mind random ordering plus some 'universal principles'. We investigate the effect of four of these principles from the standpoint of the L-view, showing that two of them are strongly equivalent to total orderings and that two of them are intermediate between total and partial orderings. We close with an indication of what the role of mathematical linguistics should be for the ordinary working linguist. Linguistics 18 (1980), 017-072. 0024-3949/80/0018-0017 $2.00 © Mouton Publishers, The Hague Brought to you by | University of Alberta Library

Interval Logics with Applications to Study of Tense and Aspect in English

Abstract: Chapter 1: Philosophical Motivation 417 §11: Introduction 417 §12: Temporal Dualism 418 Chapter 2: The Prepositional Logic I 420 §21: Formal Language LI 420 §22: Semantics for I 421 §23: Dl-sequence 423 §24: Formal System I 425 §25: The Soundness and Completeness of I 427 Chapter 3: The Prepositional Logic IM 435 §31: Formal Language LIM 435 §32: Semantics for IM 436 §33: DMI-sequence and DIM-sequence 441 §34: Formal System IM 445 §35: The Soundness and Completeness of IM 450 Chapter 4: Some Applications 450 § 41: Some Interesting Tense Operators Definable within IM 450 §42: Tense and Aspect within IM 455

Methods for specifying families of formal languages — past-present-future

Abstract: Publisher Summary This chapter discusses the formal language theory. The methods for specifying the families of formal languages relate a number of diverse activities. The chapter discusses the different ways to describe the families of languages that are of interest to computer scientists. The formal languages arose from the study of natural languages. However, it was the work of the linguist Noam Chomsky in 1956 that is regarded as the starting point. In the paper, Chomsky presented the concept of a general phrase structure grammar. Therefore, one way to define a family of languages is by generative mechanisms, that is, by grammar. A family of languages that is not closed under intersection with regular sets should not be studied for its own right but only for other purposes. Thus, the Intersection theorem is an indication towards determining appropriate families of languages to study. Instead of concern to a scattering of linguists, logicians, and mathematicians, formal languages has become an object of study to the large group of individuals interested in the rapidly developing field of computers.

On the expressive power of attribute grammars

Abstract: We examine the possibility of translating an attribute system into a recursive program scheme taking derivation trees as arguments This is possible if and only if the attribute system is strongly non-circular The strong non circularity is decidable in polynomial time Our recursive program schemes allow us to attack the equivalence problem for attribute systems and solve it in a special case properly including the case of purely synthesized systems

Grammar characterization of flowgraphs

Abstract: An extension of the scheme grammar concept given by Urschler is formalized. It is also shown that, in the usual hierarchy of the theory of formal languages, the language generated by the scheme grummar is regular (type 3). The last section gives the description of a system for the automatic structuring of programs, which applies these concepts to the Mills algorithm with some modifications.

Formal expressions of infinite graphs and their families

Abstract: We discuss some methods for rigorous expressions of infinite labeled directed graphs. In these methods, every node of a graph is identified by a string of symbols from a finite alphabet, and edges are expressed as binary relations or functions among strings. We characterize these relations with some concepts in the theory of formal languages and automata, and from this characterization, we obtain various classes of graphs. Then inclusion relationships among these classes are discussed. Although our methods originate in a very naive idea, they appear to be suitable for both theoretical treatments and computer processings, so we ourselves regard this paper as a preliminary for various discussions that our formalization enables.

On the recognition of the tautological nature of propositional formulas

Abstract: A formal language whose propositions express (in some sense) the properties of propositional formulas is described in the paper. For a certain subset of propositions of this language it is proved that each of them defines a class of propositional formulas, on which it is possible to recognize the tautological nature in a time polynomially dependent on the formula's length.

Automata, languages and programming : sixth colloquium, Graz, Austria, July 16-20, 1979

Abstract: Sharing in nondeterminism.- Sur les mots sans carre definis par un morphisme.- A characterization of abstract data as model-theoretic invariants.- Inherent ambiguities in families of grammars extended abstract.- Representing complexity classes by equality sets.- Supercounter machines.- Existential quantifiers in abstract data types.- A generalization of Ginsburg and Rose's characterization of G-S-M mappings.- Strict deterministic languages and controlled rewriting systems.- A string matching algorithm fast on the average.- Functional characterization of some semantic equalities inside ?-calculus.- Arbitration and queueing under limited shared storage requirements.- On the homomorphic characterizations of families of languages.- Two level grammars: CF-grammars with equation schemes.- Proving termination with multiset orderings.- One abstract accepting algorithm for all kinds of parsers.- Studies in abstract/concrete mappings in proving algorithm correctness.- A characterization of a dot-depth two analogue of generalized definite languages.- Partitioned LL(k) grammars.- Recursion schemes and generalized interpretations.- A rational theory of AFLs.- On the succinctness of different representations of languages.- A fixed-point theorem for recursive-enumerable languages and some considerations about fixed-point semantics of monadic programs.- Hierarchic index sequential search with optimal variable block size and its minimal expected number of comparisons.- A unique termination theorem for a theory with generalised commutative axioms.- Dags and Chomsky hierarchy.- Recent advances in the probabilistic analysis of graph-theoretic algorithms.- On the average stack size of regularly distributed binary trees.- On reductions of parallel programs.- On the height of derivation trees.- The modal logic of programs.- A comparison between two variations of a pebble game on graphs.- LL(k) parsing for attributed grammars.- On eliminating nondeterminism from Turing machines which use less than logarithm worktape space.- Structure preserving transformations on non-left-recursive grammars.- The complexity of restricted minimum spanning tree problems.- A systematic approach to formal language theory through parallel rewriting.- Extending the notion of finite index.- On the complexity of general context-free language parsing and recognition.- Space-time tradeoffs for oblivious integer multiplication.- Investigating programs in terms of partial graphs.- On the power of random access machines.- An axiomatic treatment of ALGOL 68 routines.- P-selective sets, tally languages, and the behavior of polynomial time reducibilities on NP.- Constructing call-by-value continuation semantics.- A formal semantics for concurrent systems.- On constructing LL(k) parsers.- More on advice on structuring compilers and proving them correct.- Languages of nilpotent and solvable groups (extended abstract).- Unique fixed points vs. least fixed points.- A modification of the LR(k) method for constructing compact bottom-up parsers.- Optimal decomposition of linear automata.- Bracketed two-level grammars - A decidable and practical approach to language definitions.

Models for Verifiers

Abstract: We discuss three classes of models which interpret a natural proof system for Propositional Dynamic Logic. We compare their usefulness as models for verification and show that each of the three classes satisfy the same set of formulae. One of these classes can be used to give a simple proof of completeness of a natural proof system for propositional Dynamic Logic. By the equivalence of their theodes, this implies the completeness of each of the three classes of models. Introduction Propositional Dynamic Logic (PDL) is a formal language for reasoning about programs. As with flowchart schemes, programming constructs such as assignment are suppressed and programs in POL are represented in a streamlined fo["m as regular expressions with tests. Hence the language provides a description of the flow of control of a program. PDL also acts as an assertion language in which we can represent termination, partial correctness, failure conditions and loop invariance. In this paper, we begin by describing the syntax and a proof system ID for POL. This proof system is natural in the sense that it characterizes the program operators u, ;, * and ? as representations of the program operations (nondeterministic) branching, sequential execution, iteration

A descriptive method for child language disability: the formal semantics, logic, and syntax of small languages

Abstract: A Descriptive Method for Child Language Disability: The Formal Semantics , Logic , and Syntax of Small Languages