Showing papers on "Chomsky hierarchy published in 1991"

Inductive inference of monotonic formal systems from positive data

Abstract: A formal system is a finite set of expressions, such as a grammar or a Prolog program. A semantic mapping from formal systems to concepts is said to be monotonic if it maps larger formal systems to larger concepts. A formal system Γ is said to be reduced with respect to a finite setX if the concept defined by Γ containsX but the concepts defined by any proper subset Γ′ of Γ cannot contain some part ofX. Assume a semantic mapping is monotonic and formal systems consisting of at mostn expressions that are reduced with respect toX can define only finitely many concepts for any finite setX and anyn. Then, the class of concepts defined by formal systems consisting of at mostn expressions is shown to be inferable from positive data. As corollaries, the class of languages defined by length-bounded elementary formal systems consisting of at most,n axioms, the class of languages generated by context-sensitive grammars consisting of at mostn productions, and the class of minimal models of linear Prolog programs consisting of at mostn definite clauses are all shown to be inferable from positive data.

The Art of Compiler Design: Theory and Practice

Abstract: 1. The Compiler Theory Landscape. 2. Grammars: The Chomsky Hierarchy. 3. Scanners and Regular Languages. 4. Parsers and Context-Free Languages. 5. Semantic Analysis and Attribute Grammars. 6. Syntax-Directed Code Generation. 7. Automated Bottom-Up Parser Design. 8. Transformational Attribute Grammars. 9. Code Generation. 10. Non-Procedural Languages. Appendix A: Itty Bitty Modula Syntax Diagrams. Appendix B: The TAG Compiler TAG. Appendix C: Itty Bitty Stack Machine Instruction Set. Appendix D: Code Generation Tables for Four Computers.

Formal languages and power series

Abstract: Publisher Summary This chapter discusses formal language theory and focuses on a specific tool called formal power series. Formal language theory, together with automata theory, is the oldest branch of theoretical computer science. The chapter discusses the fundamental notions about formal power series and languages. It also various normal forms for grammars. The chapter describes a class of generating devices that are somewhat different from grammars but still equivalent to grammars in the sense that the family of languages generated by the new devices equals the family of recursively enumerable languages. The new devices, called Post canonical systems or Post systems, very closely resemble formal systems in logic. The productions have the shape of inference rules. The family of languages generated by Post systems equals the family of recursively enumerable languages. The chapter discusses Markov algorithms, which resemble the intuitive notion of an algorithm. Viewed as language-defining devices, Markov algorithms are equivalent to grammars and Post systems.

On Learning Smullyan's Elementary Formal Systems: Towards an Efficient Learning Method for Context-Sensitive Languages*

Abstract: Summary In this paper, we introduce a new class of representations for formal languages that is defined by Smullyan's elementary formal systems for the problem of learning formal languages. The class of representations is a natural extension of context-free grammars, and the languages defined by these representations lie between context-free languages and context-sensitive languages and contain some important classes of formal languages such as Angluin's pattern languages, thus enabling us to take an unified view of learning formal languages. We demonstrate an efficient algorithm for learning these representations in the framework of learning by making queries to a teacher modeled on Angluin's approach to learning k -bounded context-free grammars. Our algorithm may be viewed as a natural and powerful extension of Angluin's algorithm.

Relating logical neural network to conventional models of computation

Abstract: The author compares the class of languages that can be recognized by a logical neural network (LNN) with the classes of languages in Chomsky hierarchy. The computability of LNN is studied. The computation power of LNN is identical to the computation of a probabilistic automaton, that is, it is possible to recognize more than finite state languages with such machines. This indicates what can be expected from LNN, i.e. which functions this kind of network can learn. >

Preconditions for understanding (formal specification)

Abstract: The author argues that advocates of a formal method have an obligation to explain the relationship between the role of proof in that method and the role of proof in others. Such comparisons are needed to (a) clarify the 'method' behind a specific notation, (b) dispel misconceptions invited by the use of similar vocabulary with different meanings, and (c) suggest improvements to existing methods. These points are illustrated by comparing the use of preconditions in Z with that in other formal methods. >

Formal Techniques for Parallel Object-Oriented Languages

Abstract: This paper is intended to give an overview of the formal techniques that have been developed to deal with the parallel object-oriented language POOL and several related languages. We sketch a number of semantic descriptions, using several formalism: operational semantics, denotational semantics, and a new approach to semantics, which we call layered semantics. Then we summarize the progress that has been made in formal proof systems to verify the correctness of parallel object-oriented programs. Finally we survey the techniques that we are currently developing to describe the behaviour of objects independently of their implementation, leading to linguistic support for behavioural subtyping.