25 research outputs found
A parametric analysis of the state-explosion problem in model checking
AbstractIn model checking, the state-explosion problem occurs when one checks a nonflat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of model-checking problems for nonflat systems under the light of parameterized complexity, taking the number of synchronized components as a parameter. We provide precise complexity measures (in the parameterized sense) for most of the problems we investigate, and evidence that the results are robust
Foundations of Rule-Based Query Answering
This survey article introduces into the essential concepts and methods underlying rule-based query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evaluation.
The treatment of these areas is foundation-oriented, the foundations having resulted from over four decades of research in the logic programming and database communities on combinations of query languages and rules. These results have later formed the basis for conceiving, improving, and implementing several Web and Semantic Web technologies, in particular query languages such as XQuery or SPARQL for querying relational, XML, and RDF data, and rule languages like the âRule Interchange Framework (RIF)â currently being developed in a working group of the W3C.
Coverage of the article is deliberately limited to declarative languages in a classical setting: issues such as query answering in F-Logic or in description logics, or the relationship of query answering to reactive rules and events, are not addressed
On the Complexity of Inverse Mixed Integer Linear Optimization
Inverse optimization is the problem of determining the values of missing
input parameters for an associated forward problem that are closest to given
estimates and that will make a given target vector optimal. This study is
concerned with the relationship of a particular inverse mixed integer linear
optimization problem (MILP) to both the forward problem and the separation
problem associated with its feasible region. We show that a decision version of
the inverse MILP in which a primal bound is verified is coNP-complete, whereas
primal bound verification for the associated forward problem is NP-complete,
and that the optimal value verification problems for both the inverse problem
and the associated forward problem are complete for the complexity class D^P.
We also describe a cutting-plane algorithm for solving inverse MILPs that
illustrates the close relationship between the separation problem for the
convex hull of solutions to a given MILP and the associated inverse problem.
The inverse problem is shown to be equivalent to the separation problem for the
radial cone defined by all inequalities that are both valid for the convex hull
of solutions to the forward problem and binding at the target vector. Thus, the
inverse, forward, and separation problems can be said to be equivalent
Computation using s-programs
The concepts of S and Sn programs are given by Davis,
Weyuker, 1983. Several parts of the complexity theory are
carried out directly for S and Sn programs. The concepts of
non-deterministic and deterministic computation from
S-programs are defined, and deterministic simulation of
non-deterministic computation is proved. A universal
5-program for general (non-deterministic) computation is
shown to require only one duplicate line label. Complexity
results are given for these and other simulations, e.g.
Turing Machine by 5-programs and the reverse. Cook's Theorem
for Sn programs is proved in full