11 research outputs found
Dynamic Complexity of Formal Languages
The paper investigates the power of the dynamic complexity classes DynFO,
DynQF and DynPROP over string languages. The latter two classes contain
problems that can be maintained using quantifier-free first-order updates, with
and without auxiliary functions, respectively. It is shown that the languages
maintainable in DynPROP exactly are the regular languages, even when allowing
arbitrary precomputation. This enables lower bounds for DynPROP and separates
DynPROP from DynQF and DynFO. Further, it is shown that any context-free
language can be maintained in DynFO and a number of specific context-free
languages, for example all Dyck-languages, are maintainable in DynQF.
Furthermore, the dynamic complexity of regular tree languages is investigated
and some results concerning arbitrary structures are obtained: there exist
first-order definable properties which are not maintainable in DynPROP. On the
other hand any existential first-order property can be maintained in DynQF when
allowing precomputation.Comment: Contains the material presenten at STACS 2009, extendes with proofs
and examples which were omitted due lack of spac
A Strategy for Dynamic Programs: Start over and Muddle through
In the setting of DynFO, dynamic programs update the stored result of a query
whenever the underlying data changes. This update is expressed in terms of
first-order logic. We introduce a strategy for constructing dynamic programs
that utilises periodic computation of auxiliary data from scratch and the
ability to maintain a query for a limited number of change steps. We show that
if some program can maintain a query for log n change steps after an
AC-computable initialisation, it can be maintained by a first-order dynamic
program as well, i.e., in DynFO. As an application, it is shown that decision
and optimisation problems defined by monadic second-order (MSO) formulas are in
DynFO, if only change sequences that produce graphs of bounded treewidth are
allowed. To establish this result, a Feferman-Vaught-type composition theorem
for MSO is established that might be useful in its own right
Dynamic Graph Queries
Graph databases in many applications - semantic web, transport or biological networks among others - are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries often combine first-order and navigational features.
Motivated by recent results on maintaining dynamic reachability, we study the dynamic evaluation of traditional query languages for graphs in the descriptive complexity framework. Our focus is on maintaining regular path queries, and extensions thereof, by first-order formulas. In particular we are interested in path queries defined by non-regular languages and in extended conjunctive regular path queries (which allow to compare labels of paths based on word relations). Further we study the closely related problems of maintaining distances in graphs and reachability in product graphs.
In this preliminary study we obtain upper bounds for those problems in restricted settings, such as undirected and acyclic graphs, or under insertions only, and negative results regarding quantifier-free update formulas. In addition we point out interesting directions for further research
Conjunctive Queries for Logic-Based Information Extraction
This thesis offers two logic-based approaches to conjunctive queries in the
context of information extraction. The first and main approach is the
introduction of conjunctive query fragments of the logics FC and FC[REG],
denoted as FC-CQ and FC[REG]-CQ respectively. FC is a first-order logic based
on word equations, where the semantics are defined by limiting the universe to
the factors of some finite input word. FC[REG] is FC extended with regular
constraints. The second approach is to consider the dynamic complexity of FC.Comment: Based on the author's PhD thesis and contains work from two
conference publications (arXiv:2104.04758, arXiv:1909.10869) which are joint
work with Dominik D. Freydenberge
Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)
The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..