3 research outputs found
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
Grammars with Restricted Derivation Trees
V tĂ©to disertaÄŤnĂ práci jsou studovány teoretickĂ© vlastnosti gramatik s omezenĂ˝mi derivaÄŤnĂmi stromy. Po uvedenĂ souÄŤasnĂ©ho stavu poznánĂ v tĂ©to oblasti je vĂ˝zkum zaměřen na tĹ™i základnĂ typy omezenĂ derivaÄŤnĂch stromĹŻ. Nejprve je pĹ™edstaveno zcela novĂ© tĂ©ma, kterĂ© je zaloĹľeno na omezenĂ Ĺ™ezĹŻ a je zkoumána vyjadĹ™ovacĂ sĂla takto omezenĂ© gramatiky. PotĂ© je zkoumáno nÄ›kolik novĂ˝ch vlastnostĂ omezenĂ kladenĂ©ho na cestu derivaÄŤnĂch stromĹŻ. ZejmĂ©na je studován vliv vymazávacĂch pravidel na vyjadĹ™ovacĂ sĂlu gramatik s omezenou cestou a pro tyto gramatiky jsou zavedeny dvÄ› normálnĂ formy. NáslednÄ› je popsána nová souvislost mezi gramatikami s omezenou cestou a nÄ›kterĂ˝mi pseudouzly. Dále je prezentován protiargument k vyjadĹ™ovacĂ sĂle tohoto modelu, která byla dosud povaĹľována za dobĹ™e známou vlastnost. Nakonec je zavedeno zobecnÄ›nĂ modelu s omezenou cestou na ne jednu, ale nÄ›kolik cest. Tento model je následnÄ› studován zejmĂ©na z hlediska vlastnostĂ vkládánĂ, uzávÄ›rovĂ˝ch vlastnostĂ a vlastnostĂ syntaktickĂ© analĂ˝zy.This doctoral thesis studies theoretical properties of grammars with restricted derivation trees. After presenting the state of the art concerning this investigation area, the research is focused on the three main kinds of the restrictions placed upon the derivation trees. First, it introduces completely new investigation area represented by cut-based restriction and examines the generative power of the grammars restricted in this way. Second, it investigates several new properties of path-based restriction placed upon the derivation trees. Specifically, it studies the impact of erasing productions on the generative power of grammars with restricted path and introduces two corresponding normal forms. Then, it describes a new relation between grammars with restricted path and some pseudoknots. Next, it presents a counterargument to the generative power of grammars with controlled path that has been considered as well-known so far. Finally, it introduces a generalization of path-based restriction to not just one but several paths. The model generalized in this way is studied, namely its pumping, closure, and parsing properties.