5,789 research outputs found
Temporal Data Modeling and Reasoning for Information Systems
Temporal knowledge representation and reasoning is a major research field in Artificial
Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to
model and process time and calendar data is essential for many applications like appointment
scheduling, planning, Web services, temporal and active database systems, adaptive
Web applications, and mobile computing applications. This article aims at three complementary
goals. First, to provide with a general background in temporal data modeling
and reasoning approaches. Second, to serve as an orientation guide for further specific
reading. Third, to point to new application fields and research perspectives on temporal
knowledge representation and reasoning in the Web and Semantic Web
The Parma Polyhedra Library: Toward a Complete Set of Numerical Abstractions for the Analysis and Verification of Hardware and Software Systems
Since its inception as a student project in 2001, initially just for the
handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library
has been continuously improved and extended by joining scrupulous research on
the theoretical foundations of (possibly non-convex) numerical abstractions to
a total adherence to the best available practices in software development. Even
though it is still not fully mature and functionally complete, the Parma
Polyhedra Library already offers a combination of functionality, reliability,
usability and performance that is not matched by similar, freely available
libraries. In this paper, we present the main features of the current version
of the library, emphasizing those that distinguish it from other similar
libraries and those that are important for applications in the field of
analysis and verification of hardware and software systems.Comment: 38 pages, 2 figures, 3 listings, 3 table
Constraint Satisfaction and Semilinear Expansions of Addition over the Rationals and the Reals
A semilinear relation is a finite union of finite intersections of open and
closed half-spaces over, for instance, the reals, the rationals, or the
integers. Semilinear relations have been studied in connection with algebraic
geometry, automata theory, and spatiotemporal reasoning. We consider semilinear
relations over the rationals and the reals. Under this assumption, the
computational complexity of the constraint satisfaction problem (CSP) is known
for all finite sets containing R+={(x,y,z) | x+y=z}, <=, and {1}. These
problems correspond to expansions of the linear programming feasibility
problem. We generalise this result and fully determine the complexity for all
finite sets of semilinear relations containing R+. This is accomplished in part
by introducing an algorithm, based on computing affine hulls, which solves a
new class of semilinear CSPs in polynomial time. We further analyse the
complexity of linear optimisation over the solution set and the existence of
integer solutions.Comment: 22 pages, 1 figur
An Exactly Solvable Model for Nonlinear Resonant Scattering
This work analyzes the effects of cubic nonlinearities on certain resonant
scattering anomalies associated with the dissolution of an embedded eigenvalue
of a linear scattering system. These sharp peak-dip anomalies in the frequency
domain are often called Fano resonances. We study a simple model that
incorporates the essential features of this kind of resonance. It features a
linear scatterer attached to a transmission line with a point-mass defect and
coupled to a nonlinear oscillator. We prove two power laws in the small
coupling \to 0 and small nonlinearity \to 0 regime. The asymptotic
relation ~ C^4 characterizes the emergence of a small frequency
interval of triple harmonic solutions near the resonant frequency of the
oscillator. As the nonlinearity grows or the coupling diminishes, this interval
widens and, at the relation ~ C^2, merges with another evolving
frequency interval of triple harmonic solutions that extends to infinity. Our
model allows rigorous computation of stability in the small and
limit. In the regime of triple harmonic solutions, those with largest and
smallest response of the oscillator are linearly stable and the solution with
intermediate response is unstable
On the decidability of the existence of polyhedral invariants in transition systems
Automated program verification often proceeds by exhibiting inductive
invariants entailing the desired properties.For numerical properties, a
classical class of invariants is convex polyhedra: solution sets of system of
linear (in)equalities.Forty years of research on convex polyhedral invariants
have focused, on the one hand, on identifying "easier" subclasses, on the other
hand on heuristics for finding general convex polyhedra.These heuristics are
however not guaranteed to find polyhedral inductive invariants when they
exist.To our best knowledge, the existence of polyhedral inductive invariants
has never been proved to be undecidable.In this article, we show that the
existence of convex polyhedral invariants is undecidable, even if there is only
one control state in addition to the "bad" one.The question is still open if
one is not allowed any nonlinear constraint
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