12 research outputs found
The synchronized graphs trace the context-sensitive languages
International audienceMorvan and Stirling have proved that the context-sensitive languages are exactly the traces of graphs de ned by transducers with labelled nal states. We prove that this result is still true if we restrict to the traces of graphs de ned by synchronized transducers with labelled nal states. From their construction, we deduce that the context-sensitive languages are the languages of path labels leading from and to rational vertex sets of letter-to-letter rational graphs
Families of automata characterizing context-sensitive languages
International audienceIn the hierarchy of infinite graph families, rational graphs are defined by rational transducers with labelled final states. This paper proves that their traces are precisely context-sensitive languages and that this result remains true for synchronized rational graphs
Symbol–Relation Grammars: A Formalism for Graphical Languages
AbstractA common approach to the formal description of pictorial and visual languages makes use of formal grammars and rewriting mechanisms. The present paper is concerned with the formalism of Symbol–Relation Grammars (SR grammars, for short). Each sentence in an SR language is composed of a set of symbol occurrences representing visual elementary objects, which are related through a set of binary relational items. The main feature of SR grammars is the uniform way they use context-free productions to rewrite symbol occurrences as well as relation items. The clearness and uniformity of the derivation process for SR grammars allow the extension of well-established techniques of syntactic and semantic analysis to the case of SR grammars. The paper provides an accurate analysis of the derivation mechanism and the expressive power of the SR formalism. This is necessary to fully exploit the capabilities of the model. The most meaningful features of SR grammars as well as their generative power are compared with those of well-known graph grammar families. In spite of their structural simplicity, variations of SR grammars have a generative power comparable with that of expressive classes of graph grammars, such as the edNCE and the N-edNCE classes
Accepting grammars and systems
We investigate several kinds of regulated rewriting (programmed,
matrix, with regular control, ordered, and variants thereof) and
of parallel rewriting mechanisms (Lindenmayer systems, uniformly
limited Lindenmayer systems, limited Lindenmayer systems and
scattered context grammars) as accepting devices, in contrast
with the usual generating mode.
In some cases, accepting mode turns out to be just as powerful as
generating mode, e.g. within the grammars of the Chomsky
hierarchy, within random context, regular control, L systems,
uniformly limited L systems, scattered context. Most of these
equivalences can be proved using a metatheorem on so-called
context condition grammars. In case of matrix grammars and
programmed grammars without appearance checking, a straightforward
construction leads to the desired equivalence result.
Interestingly, accepting devices are (strictly) more powerful than
their generating counterparts in case of ordered grammars,
programmed and matrix grammars with appearance checking (even
programmed grammarsm with unconditional transfer), and 1lET0L
systems. More precisely, if we admit erasing productions, we
arrive at new characterizations of the recursivley enumerable
languages, and if we do not admit them, we get new
characterizations of the context-sensitive languages.
Moreover, we supplement the published literature showing:
- The emptiness and membership problems are recursivley solvable
for generating ordered grammars, even if we admit erasing
productions.
- Uniformly limited propagating systems can be simulated by
programmed grammars without erasing and without appearance
checking, hence the emptiness and membership problems are
recursively solvable for such systems.
- We briefly discuss the degree of nondeterminism and the
degree of synchronization for devices with limited parallelism
Regulated Formal Models and Their Reduction
Department of Theoretical Computer Science and Mathematical LogicKatedra teoretické informatiky a matematické logikyFaculty of Mathematics and PhysicsMatematicko-fyzikálnà fakult