47 research outputs found
On the Expressive Power of Datalog: Tools and a Case Study
AbstractWe study here the language Datalog(≠), which is the query language obtained from Datalog by allowing equalities and inequalities in the bodies of the rules. We view Datalog(≠) as a fragment of an infinitary logic Lω and show that Lω can be characterized in terms of certain two-person pebble games. This characterization provides us with tools for investigating the expressive power of Datalog(≠). As a case study, we classify the expressibility of fixed subgraph homeomorphism queries on directed graphs. S. Fortune, J. Hopcroft, and J. Wyllie (Theoret. Comput. Sci.10 (1980), 111-121) classified the computational complexity of these queries by establishing two dichotomies, which are proper only if P ≠ NP. Without using any complexity-theoretic assumptions, we show here that the two dichotomies are indeed proper in terms of expressibility in Datalog(≠)
Frameworks for logically classifying polynomial-time optimisation problems.
We show that a logical framework, based around a fragment of existential second-order logic formerly proposed by others so as to capture the class of polynomially-bounded P-optimisation problems, cannot hope to do so, under the assumption that P ≠ NP. We do this by exhibiting polynomially-bounded maximisation and minimisation problems that can be expressed in the framework but whose decision versions are NP-complete. We propose an alternative logical framework, based around inflationary fixed-point logic, and show that we can capture the above classes of optimisation problems. We use the inductive depth of an inflationary fixed-point as a means to describe the objective functions of the instances of our optimisation problems
On the speed of constraint propagation and the time complexity of arc consistency testing
Establishing arc consistency on two relational structures is one of the most
popular heuristics for the constraint satisfaction problem. We aim at
determining the time complexity of arc consistency testing. The input
structures and can be supposed to be connected colored graphs, as the
general problem reduces to this particular case. We first observe the upper
bound , which implies the bound in terms of
the number of edges and the bound in terms of the number of
vertices. We then show that both bounds are tight up to a constant factor as
long as an arc consistency algorithm is based on constraint propagation (like
any algorithm currently known).
Our argument for the lower bounds is based on examples of slow constraint
propagation. We measure the speed of constraint propagation observed on a pair
by the size of a proof, in a natural combinatorial proof system, that
Spoiler wins the existential 2-pebble game on . The proof size is bounded
from below by the game length , and a crucial ingredient of our
analysis is the existence of with . We find one
such example among old benchmark instances for the arc consistency problem and
also suggest a new, different construction.Comment: 19 pages, 5 figure
Deduction with XOR Constraints in Security API Modelling
We introduce XOR constraints, and show how they enable a theorem prover to reason effectively about security critical subsystems which employ bitwise XOR. Our primary case study is the API of the IBM 4758 hardware security module. We also show how our technique can be applied to standard security protocols
Dependence Logic with Generalized Quantifiers: Axiomatizations
We prove two completeness results, one for the extension of dependence logic
by a monotone generalized quantifier Q with weak interpretation, weak in the
meaning that the interpretation of Q varies with the structures. The second
result considers the extension of dependence logic where Q is interpreted as
"there exists uncountable many." Both of the axiomatizations are shown to be
sound and complete for FO(Q) consequences.Comment: 17 page
Solving order constraints in logarithmic space.
We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space
Four Lessons in Versatility or How Query Languages Adapt to the Web
Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule- and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and re-published. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logic-based) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for tree-shaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”