163 research outputs found
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
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 rewriting in formal language theory
Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2008.Context-free grammars are well-studied and well-behaved in terms of decidability, but many
real-world problems cannot be described with context-free grammars. Grammars with regulated
rewriting are grammars with mechanisms to regulate the applications of rules, so that
certain derivations are avoided. Thus, with context-free rules and regulated rewriting mechanisms,
one can often generate languages that are not context-free.
In this thesis we study grammars with regulated rewriting mechanisms. We consider problems
in which context-free grammars are insufficient and in which more descriptive grammars
are required. We compare bag context grammars with other well-known classes of grammars
with regulated rewriting mechanisms. We also discuss the relation between bag context grammars
and recognizing devices such as counter automata and Petri net automata. We show
that regular bag context grammars can generate any recursively enumerable language. We
reformulate the pumping lemma for random permitting context languages with context-free
rules, as introduced by Ewert and Van der Walt, by using the concept of a string homomorphism.
We conclude the thesis with decidability and complexity properties of grammars with
regulated rewriting
An Algebraic Characterization of Total Input Strictly Local Functions
This paper provides an algebraic characteriza- tion of the total input strictly local functions. Simultaneous, noniterative rules of the form A→B/C D, common in phonology, are defin- able as functions in this class whenever CAD represents a finite set of strings. The algebraic characterization highlights a fundamental con- nection between input strictly local functions and the simple class of definite string languages, as well as connections to string functions stud- ied in the computer science literature, the def- inite functions and local functions. No effec- tive decision procedure for the input strictly local maps was previously available, but one arises directly from this characterization. This work also shows that, unlike the full class, a restricted subclass is closed under composition. Additionally, some products are defined which may yield new factorization methods
- …