56,415 research outputs found
Graph-Controlled Insertion-Deletion Systems
In this article, we consider the operations of insertion and deletion working
in a graph-controlled manner. We show that like in the case of context-free
productions, the computational power is strictly increased when using a control
graph: computational completeness can be obtained by systems with insertion or
deletion rules involving at most two symbols in a contextual or in a
context-free manner and with the control graph having only four nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127
P Systems with Minimal Insertion and Deletion
In this paper we consider insertion-deletion P systems with priority of deletion over the insertion.We show that such systems with one symbol context-free insertion
and deletion rules are able to generate PsRE. If one-symbol one-sided context is added
to insertion or deletion rules but no priority is considered, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is
permitted. We also show that the priority relation is very important and in its absence
the corresponding class of P systems is strictly included in MAT
Representations and characterizations of languages in Chomsky hierarchy by means of insertion-deletion systems
Insertion-deletion operations are much investigated in linguistics
and in DNA computing and several characterizations of Turing
computability were obtained in this framework.
In this note we contribute to this research direction with a new
characterization of this type, as well as with representations of regular
and context-free languages, mainly starting from context-free insertion
systems of as small as possible complexity. For instance, each recursively
enumerable language L can be represented in a way similar to the
celebrated Chomsky-Schützenberger representation of context-free languages,
i.e., in the form L = h(L(
) ∩D), where
is an insertion system
of weight (3, 0) (at most three symbols are inserted in a context of length
zero), h is a projection, and D is a Dyck language. A similar representation
can be obtained for regular languages, involving insertion systems
of weight (2,0) and star languages, as well as for context-free languages
– this time using insertion systems of weight (3, 0) and star languages.Ministerio de Educación y Ciencia TIN2006-1342
Combining Insertion and Deletion in RNA-editing Preserves Regularity
Inspired by RNA-editing as occurs in transcriptional processes in the living
cell, we introduce an abstract notion of string adjustment, called guided
rewriting. This formalism allows simultaneously inserting and deleting
elements. We prove that guided rewriting preserves regularity: for every
regular language its closure under guided rewriting is regular too. This
contrasts an earlier abstraction of RNA-editing separating insertion and
deletion for which it was proved that regularity is not preserved. The
particular automaton construction here relies on an auxiliary notion of slice
sequence which enables to sweep from left to right through a completed rewrite
sequence.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347
Input-Driven Tissue P Automata
We introduce several variants of input-driven tissue P automata where the
rules to be applied only depend on the input symbol. Both strings and multisets are
considered as input objects; the strings are either read from an input tape or defined
by the sequence of symbols taken in, and the multisets are given in an input cell at the
beginning of a computation, enclosed in a vesicle. Additional symbols generated during a
computation are stored in this vesicle, too. An input is accepted when the vesicle reaches a
final cell and it is empty. The computational power of some variants of input-driven tissue
P automata is illustrated by examples and compared with the power of the input-driven
variants of other automata as register machines and counter automata
On insertion-deletion systems over relational words
We introduce a new notion of a relational word as a finite totally ordered
set of positions endowed with three binary relations that describe which
positions are labeled by equal data, by unequal data and those having an
undefined relation between their labels. We define the operations of insertion
and deletion on relational words generalizing corresponding operations on
strings. We prove that the transitive and reflexive closure of these operations
has a decidable membership problem for the case of short insertion-deletion
rules (of size two/three and three/two). At the same time, we show that in the
general case such systems can produce a coding of any recursively enumerable
language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure
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