Natural languages contain regular, context-free, and contextsensitive syntactic constructions, yet none of these classes of formal languages can be identified in the limit from positive examples. Mildly context-sensitive languages are able to represent some context-sensitive constructions, those most common in natural languages, such as multiple agreement, crossed agreement, and duplication. Th...

Grammarware engineering, and grammar-dependent software development has received considerable attention in recent years. Despite of this fact, grammar refactoring as a significant cornerstone of grammarware engineering is still weakly understood and little practiced. In this paper, we address this issue by proposing universal algorithm for automated refactoring of context-free grammars called m...

Residuated lattices form one of the theoretical backbones of the Lambek Calculus as the standard free models. They also appear in grammatical inference as the syntactic concept lattice, an algebraic structure canonically defined for every language L based on the lattice of all distributionally definable subsets of strings. Recent results show that it is possible to build representations, such a...

Higher-order grammars are an extension of regular and context-free grammars, where nonterminals may take parameters. They have been extensively studied in 1980’s, and restudied recently in the context of model checking and program verification. We show that the class of unsafe order-(n+1) word languages coincides with the class of frontier languages of unsafe order-n tree languages. We use inte...

Context-free languages (CFLs) are highly important in computer language processing technology as well as in formal language theory. The Pumping Lemma is a property that is valid for all context-free languages, and is used to show the existence of non context-free languages. This paper presents a formalization, using the Coq proof assistant, of the Pumping Lemma for context-free languages.

We show the interconvertibility of context-free-language reachability problems and a class of set-constraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a context-free-language reachability problem whose answer gi...

A fuzzy language is defined to be a fuzzy subset of the set of strings over a finite alphabet. The notions of union, intersection, concatenation, Kleene closure, and grammar for such languages are defined as extensions of the corresponding notions in the theory of formal languages. An explicit expression for the membership function of the language Z,(G) generated by a fuzzy grammar G is given, ...

We present grammatical (or equational) descriptions of the set of normal inhabitants fM j ` M : A; M in -normal form g of a given type A under a given basis , both for the standard simple type system (in partial discharge convention) and for the system in total discharge convention (or Prawitz-style natural deduction system). It is shown that in the latter system we can describe the set by a ( ...

For many decades, the search for language classes that extend the context-free laguages enough to include various languages that arise in practice, while still keeping as many of the useful properties that context-free grammars have – most notably cubic parsing time – has been one of the major areas of research in formal language theory. In this thesis we add a new family of classes to this fie...

The change within the linguistic framework of transformational grammar from GB–theory to minimalism brought up a particular type of formal grammar, as well. We show that this type of a minimalist grammar (MG) constitutes a subclass of mildly context–sensitive grammars in the sense that for each MG there is a weakly equivalent linear context–free rewriting system (LCFRS). Moreover, an infinite h...