20,090 research outputs found
Constraint-based reachability
Iterative imperative programs can be considered as infinite-state systems
computing over possibly unbounded domains. Studying reachability in these
systems is challenging as it requires to deal with an infinite number of states
with standard backward or forward exploration strategies. An approach that we
call Constraint-based reachability, is proposed to address reachability
problems by exploring program states using a constraint model of the whole
program. The keypoint of the approach is to interpret imperative constructions
such as conditionals, loops, array and memory manipulations with the
fundamental notion of constraint over a computational domain. By combining
constraint filtering and abstraction techniques, Constraint-based reachability
is able to solve reachability problems which are usually outside the scope of
backward or forward exploration strategies. This paper proposes an
interpretation of classical filtering consistencies used in Constraint
Programming as abstract domain computations, and shows how this approach can be
used to produce a constraint solver that efficiently generates solutions for
reachability problems that are unsolvable by other approaches.Comment: In Proceedings Infinity 2012, arXiv:1302.310
Degenerations of toric varieties over valuation rings
We develop a theory of multi-stage degenerations of toric varieties over
finite rank valuation rings, extending the Mumford--Gubler theory in rank one.
Such degenerations are constructed from fan-like structures over totally
ordered abelian groups of finite rank. Our main theorem describes the geometry
of successive special fibers in the degeneration in terms of the polyhedral
geometry of a system of recession complexes associated to the fan.Comment: 13 pages. v3: Added Example 4.1.8 and new references. To appear in
Bulletin of the London Mathematical Societ
Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity
In the modeling of dislocations one is lead naturally to energies
concentrated on lines, where the integrand depends on the orientation and on
the Burgers vector of the dislocation, which belongs to a discrete lattice. The
dislocations may be identified with divergence-free matrix-valued measures
supported on curves or with 1-currents with multiplicity in a lattice. In this
paper we develop the theory of relaxation for these energies and provide one
physically motivated example in which the relaxation for some Burgers vectors
is nontrivial and can be determined explicitly. From a technical viewpoint the
key ingredients are an approximation and a structure theorem for 1-currents
with multiplicity in a lattice
- âŠ