3 research outputs found
Decidable Classes of Tree Automata Mixing Local and Global Constraints Modulo Flat Theories
We define a class of ranked tree automata TABG generalizing both the tree
automata with local tests between brothers of Bogaert and Tison (1992) and with
global equality and disequality constraints (TAGED) of Filiot et al. (2007).
TABG can test for equality and disequality modulo a given flat equational
theory between brother subterms and between subterms whose positions are
defined by the states reached during a computation. In particular, TABG can
check that all the subterms reaching a given state are distinct. This
constraint is related to monadic key constraints for XML documents, meaning
that every two distinct positions of a given type have different values. We
prove decidability of the emptiness problem for TABG. This solves, in
particular, the open question of the decidability of emptiness for TAGED. We
further extend our result by allowing global arithmetic constraints for
counting the number of occurrences of some state or the number of different
equivalence classes of subterms (modulo a given flat equational theory)
reaching some state during a computation. We also adapt the model to unranked
ordered terms. As a consequence of our results for TABG, we prove the
decidability of a fragment of the monadic second order logic on trees extended
with predicates for equality and disequality between subtrees, and cardinality.Comment: 39 pages, to appear in LMCS journa
ParallelGDB: A Parallel Graph Database Based on Cache Specialization
International audienceThe need for managing massive attributed graphs is becoming common in many areas such as recommendation systems, proteomics analysis, social network analysis or bibliographic analysis. This is making it necessary to move towards parallel systems that allow managing graph databases containing millions of vertices and edges. Previous work on distributed graph databases has focused on finding ways to partition the graph to reduce network traffic and improve execution time. However, partitioning a graph and keeping the information regarding the location of vertices might be unrealistic for massive graphs. In this paper, we propose Parallel-GDB, a new system based on specializing the local caches of any node in this system, providing a better cache hit ratio. ParallelGDB uses a random graph partitioning, avoiding complex partition methods based on the graph topology, that usually require managing extra data structures. This proposed system provides an efficient environment for distributed graph databases
The emptiness problem for tree automata with global constraints
Abstract—We define tree automata with global constraints (TAGC), generalizing the class of tree automata with global equality and disequality constraints [1] (TAGED). TAGC can test for equality and disequality between subterms whose positions are defined by the states reached during a computation. In particular, TAGC can check that all the subterms reaching a given state are distinct. This constraint is related to monadic key constraints for XML documents, meaning that every two distinct positions of a given type have different values. We prove decidability of the emptiness problem for TAGC. This solves, in particular, the open question of decidability of emptiness for TAGED. We further extend our result by allowing global arithmetic constraints for counting the number of occurrences of some state or the number of different subterms reaching some state during a computation. We also allow local equality and disequality tests between sibling positions and the extension to unranked ordered trees. As a consequence of our results for TAGC, we prove the decidability of a fragment of the monadic second order logic on trees extended with predicates for equality and disequality between subtrees, and cardinality. I