Controlled grammar

Abstract: A Petri net controlled grammar is a context-free grammar with a control by a Petri net whose transitions are labeled with rules of the grammar or the empty string and the associated language consists of all terminal strings which can be derived in the grammar and the sequence of rules in a derivation is in the image of a successful occurrence of transitions of the net. We present some results on the generative capacities of such grammars that Petri nets are restricted to some known structural subclasses of Petri nets.

Abstract: Guidelines and consistency rules of UML are used to control the degrees of freedom provided by the language to prevent faults. Guidelines are used in specific domains (e.g., avionics) to recommend the proper use of technologies. Consistency rules are used to deal with inconsistencies in models. However, guidelines and consistency rules use informal restrictions on the uses of languages, which makes checking difficult. In this paper, we consider these problems from a language-theoretic view. We propose the formalism of C-Systems, short for "formal language control systems". A C-System consists of a controlled grammar and a controlling grammar. Guidelines and consistency rules are formalized as controlling grammars that control the uses of UML, i.e. the derivations using the grammar of UML. This approach can be implemented as a parser, which can automatically verify the rules on a UML user model in XMI format. A comparison to related work shows our contribution: a generic top-down and syntax-based approach that checks language level constraints at compile-time.

Abstract: A tree controlled grammar is specified as a pair (G,G^') where G is a context-free grammar and G^' is a regular grammar. Its language consists of all terminal words with a derivation in G such that all levels of the corresponding derivation tree-except the last level-belong to L(G^'). We define the nonterminal complexity V ar(H) of H=(G,G^') as the sum of the numbers of nonterminals of G and G^'. In Turaev et al. (2011) [23] it is shown that tree controlled grammars H with V ar(H)@?9 are sufficient to generate all recursively enumerable languages. In this paper, we improve the bound to seven. Moreover, we show that all linear and regular simple matrix languages can be generated by tree controlled grammars with a nonterminal complexity bounded by three, and we prove that this bound is optimal for the mentioned language families. Furthermore, we show that any context-free language can be generated by a tree controlled grammar (G,G^') where the number of nonterminals of G and G^' is at most four.