6 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
Strong inapproximability of the shortest reset word
The \v{C}ern\'y conjecture states that every -state synchronizing
automaton has a reset word of length at most . We study the hardness
of finding short reset words. It is known that the exact version of the
problem, i.e., finding the shortest reset word, is NP-hard and coNP-hard, and
complete for the DP class, and that approximating the length of the shortest
reset word within a factor of is NP-hard [Gerbush and Heeringa,
CIAA'10], even for the binary alphabet [Berlinkov, DLT'13]. We significantly
improve on these results by showing that, for every , it is NP-hard
to approximate the length of the shortest reset word within a factor of
. This is essentially tight since a simple -approximation
algorithm exists.Comment: extended abstract to appear in MFCS 201
Synchronizing Data Words for Register Automata
Register automata (RAs) are finite automata extended with a finite set of
registers to store and compare data from an infinite domain. We study the
concept of synchronizing data words in RAs: does there exist a data word that
sends all states of the RA to a single state?
For deterministic RAs with k registers (k-DRAs), we prove that inputting data
words with 2k+1 distinct data from the infinite data domain is sufficient to
synchronize. We show that the synchronization problem for DRAs is in general
PSPACE-complete, and it is NLOGSPACE-complete for 1-DRAs. For nondeterministic
RAs (NRAs), we show that Ackermann(n) distinct data (where n is the size of the
RA) might be necessary to synchronize. The synchronization problem for NRAs is
in general undecidable, however, we establish Ackermann-completeness of the
problem for 1-NRAs.
Another main result is the NEXPTIME-completeness of the length-bounded
synchronization problem for NRAs, where a bound on the length of the
synchronizing data word, written in binary, is given. A variant of this last
construction allows to prove that the length-bounded universality problem for
NRAs is co-NEXPTIME-complete
On prefixal one-rule string rewrite systems
International audiencePrefixal one-rule string rewrite systems are one-rule string rewrite systems for which the left-hand side of the rule is a prefix of the right-hand side of the rule. String rewrite systems induce a transformation over languages: from a starting word, one can associate all its descendants. We prove, in this work, that the transformation induced by a prefixal one-rule rewrite system always transforms a finite language into a context-free language, a property that is surprisingly not satisfied by arbitrary one-rule rewrite systems. We also give here a decidable characterization of the prefixal one-rule rewrite systems whose induced transformation is a rational transduction
Synchronizing automata over nested words
We extend the concept of a synchronizing word from deterministic finite-state automata (DFA) to nested word automata (NWA): A well-matched nested word is called synchronizing if it resets the control state of any configuration, i. e., takes the NWA from all control states to a single control state.
We show that although the shortest synchronizing word for an NWA, if it exists, can be (at most) exponential in the size of the NWA, the existence of such a word can still be decided in polynomial time. As our main contribution, we show that deciding the existence of a short synchronizing word (of at most given length) becomes PSPACE-complete (as opposed to NP-complete for DFA). The upper bound
makes a connection to pebble games and Strahler numbers, and the lower bound goes via small-cost synchronizing words for DFA, an intermediate problem that we also show PSPACE-complete. We also characterize the complexity of a number of related problems, using the observation that the intersection nonemptiness problem for NWA
is EXP-complete
Complexity and modeling power of insertion-deletion systems
SISTEMAS DE INSERCIÓN Y BORRADO: COMPLEJIDAD Y
CAPACIDAD DE MODELADO
El objetivo central de la tesis es el estudio de los sistemas de inserción y borrado y su
capacidad computacional. Más concretamente, estudiamos algunos modelos de
generación de lenguaje que usan operaciones de reescritura de dos cadenas. También
consideramos una variante distribuida de los sistemas de inserción y borrado en el
sentido de que las reglas se separan entre un número finito de nodos de un grafo.
Estos sistemas se denominan sistemas controlados mediante grafo, y aparecen en
muchas áreas de la Informática, jugando un papel muy importante en los lenguajes
formales, la lingüística y la bio-informática. Estudiamos la decidibilidad/
universalidad de nuestros modelos mediante la variación de los parámetros de tamaño
del vector. Concretamente, damos respuesta a la cuestión más importante
concerniente a la expresividad de la capacidad computacional: si nuestro modelo es
equivalente a una máquina de Turing o no. Abordamos sistemáticamente las
cuestiones sobre los tamaños mínimos de los sistemas con y sin control de grafo.COMPLEXITY AND MODELING POWER OF
INSERTION-DELETION SYSTEMS
The central object of the thesis are insertion-deletion systems and their computational
power. More specifically, we study language generating models that use two string
rewriting operations: contextual insertion and contextual deletion, and their
extensions. We also consider a distributed variant of insertion-deletion systems in the
sense that rules are separated among a finite number of nodes of a graph. Such
systems are refereed as graph-controlled systems. These systems appear in many
areas of Computer Science and they play an important role in formal languages,
linguistics, and bio-informatics. We vary the parameters of the vector of size of
insertion-deletion systems and we study decidability/universality of obtained models.
More precisely, we answer the most important questions regarding the expressiveness
of the computational model: whether our model is Turing equivalent or not. We
systematically approach the questions about the minimal sizes of the insertiondeletion
systems with and without the graph-control