285 research outputs found
Structure Theorem and Strict Alternation Hierarchy for FO^2 on Words
It is well-known that every first-order property on words is expressible
using at most three variables. The subclass of properties expressible with only
two variables is also quite interesting and well-studied. We prove precise
structure theorems that characterize the exact expressive power of first-order
logic with two variables on words. Our results apply to both the case with and
without a successor relation. For both languages, our structure theorems show
exactly what is expressible using a given quantifier depth, n, and using m
blocks of alternating quantifiers, for any m \leq n. Using these
characterizations, we prove, among other results, that there is a strict
hierarchy of alternating quantifiers for both languages. The question whether
there was such a hierarchy had been completely open. As another consequence of
our structural results, we show that satisfiability for first-order logic with
two variables without successor, which is NEXP-complete in general, becomes
NP-complete once we only consider alphabets of a bounded size
Distribution Constraints: The Chase for Distributed Data
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating dependencies (tgds and egds) extended with node variables ranging over computing nodes. In particular, they can express co-partitioning constraints and constraints about range-based data distributions by using comparison atoms. The main technical contribution is the study of the implication problem of distribution constraints. While implication is undecidable in general, relevant fragments of so-called data-full constraints are exhibited for which the corresponding implication problems are complete for EXPTIME, PSPACE and NP. These results yield bounds on deciding parallel-correctness for conjunctive queries in the presence of distribution constraints
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
Two-Variable Logic with Two Order Relations
It is shown that the finite satisfiability problem for two-variable logic
over structures with one total preorder relation, its induced successor
relation, one linear order relation and some further unary relations is
EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures
that do not include the induced successor relation. As a special case, the
EXPSPACE upper bound applies to two-variable logic over structures with two
linear orders. A further consequence is that satisfiability of two-variable
logic over data words with a linear order on positions and a linear order and
successor relation on the data is decidable in EXPSPACE. As a complementing
result, it is shown that over structures with two total preorder relations as
well as over structures with one total preorder and two linear order relations,
the finite satisfiability problem for two-variable logic is undecidable
History-Register Automata
Programs with dynamic allocation are able to create and use an unbounded
number of fresh resources, such as references, objects, files, etc. We propose
History-Register Automata (HRA), a new automata-theoretic formalism for
modelling such programs. HRAs extend the expressiveness of previous approaches
and bring us to the limits of decidability for reachability checks. The
distinctive feature of our machines is their use of unbounded memory sets
(histories) where input symbols can be selectively stored and compared with
symbols to follow. In addition, stored symbols can be consumed or deleted by
reset. We show that the combination of consumption and reset capabilities
renders the automata powerful enough to imitate counter machines, and yields
closure under all regular operations apart from complementation. We moreover
examine weaker notions of HRAs which strike different balances between
expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS
Parallel-Correctness and Containment for Conjunctive Queries with Union and Negation
Single-round multiway join algorithms first reshuffle data over many servers
and then evaluate the query at hand in a parallel and communication-free way. A
key question is whether a given distribution policy for the reshuffle is
adequate for computing a given query, also referred to as parallel-correctness.
This paper extends the study of the complexity of parallel-correctness and its
constituents, parallel-soundness and parallel-completeness, to unions of
conjunctive queries with and without negation. As a by-product it is shown that
the containment problem for conjunctive queries with negation is
coNEXPTIME-complete
- …