If we take the class of context-free phrase structure grammars (CFPSGs) and modify it so that (i) grammars are allowed to make use of finite feature systems and (ii) rules are permitted to manipulate the features in arbitrary ways, then what we end up with is equivalent to what we started out with Suppose, however, that we take the class of contextfree phrase structure grammars and modify it so that (i) grammars are allowed to employ a single designated feature that takes stacks of items drawn from some finite set as its values, and (ii) rules are permitted to push items onto, pop items from, and copy the stack What we end up with now is no longer equivalent to the CF-PSGs but is significantly more powerful, namely the indexed grammars (Aho, 1968) This class of grammars has been alluded to a number of times in the recent linguistic literature: by Klein (1981) in connection with nested comparative constructions, by Dahl (1982) in connection with topicalised pronouns, by Engdahl (1982) and Gazdar (1982) in connection with Scandinavian unbounded dependencies, by Huybregts (1984) and Pulman and Ritchie (1984) in connection with Dutch, by Marsh and Partee (1984) in connection with variable binding, and doubtless elsewhere as well

Applicability of Indexed Grammars to Natural Languages

Attribute grammars and recursive program schemes II

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.

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

A new method for testing compilers is presented. The compiler is exercized by compilable programs, automatically generated by a test generator. The generator is driven by a tabular description of the source language. This description is in a formalism which nicely extends context-free grammars in a context-dependent direction, but still retains the structure and readability of BNF. The generator produces a set of programs which cover all grammatical constructions of the source language, unless user supplied directives instruct otherwise. The programs generated can also be used to evaluate the performance of different compilers of the same source language.

An Automatic Generator for Compiler Testing

https://ris.utwente.nl/ws/files/6737374/Engelfriet86pushdown.pdf

Pushdown machines for the macro tree transducer

By specializing the semantic-rules for attributed context-free grammars introduced by Knuth (Math. Systems Theory 2, 127–145) simple-L-attributed grammars are defined. The translations determined by these grammars are languages called value-languages. In this paper the question of classifying value-languages is considered. It is shown that the value-languages of simple-L-attributed grammars are exactly the IO-macrolanguages.

IO-macrolanguages and attributed translations

A new type of acceptor is introduced for the class of indexed languages. The class of languages recognized by the deterministic version of this acceptor, called deterministic indexed languages, is closed under complemention. The class of deterministic context-free languages is properly contained in the class of deterministic indexed languages, which itself is properly contained in the class of indexed languages.

On deterministic indexed languages

In this paper we investigate Szilard languages of IO-grammars. First we show, similar to the proof in Moriya [Information and Control 22 (1973), 139–162], that these languages are context-sensitive. It is known that there are context-free languages L such that no context-free grammar for L has a context-free Szilard language. Since a context-free language L is also an IO-language the question arises if there exists an IO-grammar for L with a context-free Szilard language. To solve this problem we first provide an algorithm which transforms an IO-grammar into a simple normal form. Then it is possible to construct a context-free grammar generating the Szilard language of the normal form IO-grammar. Hence every IO-language has an IO-grammar with a context-free Szilard language.

Szilard languages of IO-grammars

A Homomorphic Characterization of Indexed Languages.

The class of deterministic indexed languages will be further investigated. A number of closure and non-closure results are presented. All this results have an analogon in the theory of deterministic context-free languages.

Johann Specht

Papers

IO-macrolanguages and attributed translations

On deterministic indexed languages

Szilard languages of IO-grammars

A Homomorphic Characterization of Indexed Languages.

Closure properties of deterministic indexed languages