We investigate the complexity of a variety of normal-form transformations for extended context-free grammars, where by extended we mean that the set of right-hand sides for each nonterminal in such a grammar is a regular set. The study is motivated by the implementation project GraMa which will provide a C++ toolkit for the symbolic manipulation of context-free objects just as Grail does for regular objects. Our results generalize known complexity bounds for context-free grammars but do so in nontrivial ways. Specifically, we introduce a new representation scheme for extended context-free grammars (the symbol-threaded expression forest), a new normal form for these grammars (dot normal form) and new regular expression algorithms. 1 Introduction In the 1960's, extended context-free grammars were introduced, based on Backus--Naur form, as a useful abbreviatory notation that made context-free grammars easier to write. More recently, the Standardized General Markup Language (SGML...

Subset construction is the method of converting a nondeterministic finite-state machine into a deterministic one. The process of determinization is an important one in any implementation of finite-state machines since nondeterministic machines are often easier to describe than their deterministic equivalents and the conversion of regular expressions to finite-state machines usually produces nondeterministic machines. We discuss one aspect of subset construction; namely, the computation of the instructions of the equivalent deterministic machine. Although the discussion is to some extent independent of any specific assumptions, we draw some conclusions within the context of INR and Grail, both packages for the manipulation of finite-state machines. The aim of the discussion is to present the problem and suggest some possible solutions; we do not intend to and cannot be definitive since much remains unknown. z This research was supported by grants from the Natural Sciences and Engineeri...

We investigate the complexity of a variety of normal-form transformations for extended context-free grammars, where by extended we mean that the set of right-hand sides for each nonterminal in such a grammar is a regular set. The study is motivated by the implementation project GraMa which will provide a C++ toolkit for the symbolic manipulation of context-free objects just as Grail does for regular objects. Our results generalize known bounds for context-free grammars but do so in nontrivial ways. Specifically, we introduce a new representation scheme for extended contextfree grammars (the symbol-threaded expression forest), a new normal form for these grammars (dot normal form) and new regular expression algorithms. 1 Introduction in the 1960's, extended context-free grammars were introduced, using Backus--Naur form, as a useful abbreviatory notation that made context-free grammars easier to write. More recently, the Standardized General Markup Language (SGML) [13] used a similar ab...

We investigate the complexity of a variety of normal-form transformations for transition diagram systems, which are a parsing view of extended context-free grammars. A transition diagram system is a finite collection of finite-state machines each of which is labeled with a unique nonterminal symbol. The study is motivated by the implementation project GraMa which will provide a C++ toolkit for the symbolic manipulation of context-free objects just as Grail does for regular objects. 1 Introduction In the 1960's, extended context-free grammars (as Backus--Naur form) were introduced as a useful abbreviatory notation that made context-free grammars easier to write. More recently, the Standardized General Markup Language (SGML) [17] used a similar abbreviatory notation to define extended context-free grammars for documents. Currently, XML [4], which is a simplified version of SGML, is being promoted as the markup language for the web, instead of HTML (a specific grammar or DTD specified us...