10,248 research outputs found
Abstract Learning Frameworks for Synthesis
We develop abstract learning frameworks (ALFs) for synthesis that embody the
principles of CEGIS (counter-example based inductive synthesis) strategies that
have become widely applicable in recent years. Our framework defines a general
abstract framework of iterative learning, based on a hypothesis space that
captures the synthesized objects, a sample space that forms the space on which
induction is performed, and a concept space that abstractly defines the
semantics of the learning process. We show that a variety of synthesis
algorithms in current literature can be embedded in this general framework.
While studying these embeddings, we also generalize some of the synthesis
problems these instances are of, resulting in new ways of looking at synthesis
problems using learning. We also investigate convergence issues for the general
framework, and exhibit three recipes for convergence in finite time. The first
two recipes generalize current techniques for convergence used by existing
synthesis engines. The third technique is a more involved technique of which we
know of no existing instantiation, and we instantiate it to concrete synthesis
problems
Optimal Union-Find in Constraint Handling Rules
Constraint Handling Rules (CHR) is a committed-choice rule-based language
that was originally intended for writing constraint solvers. In this paper we
show that it is also possible to write the classic union-find algorithm and
variants in CHR. The programs neither compromise in declarativeness nor
efficiency. We study the time complexity of our programs: they match the
almost-linear complexity of the best known imperative implementations. This
fact is illustrated with experimental results.Comment: 12 pages, 3 figures, to appear in Theory and Practice of Logic
Programming (TPLP
Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis
The safety of infinite state systems can be checked by a backward
reachability procedure. For certain classes of systems, it is possible to prove
the termination of the procedure and hence conclude the decidability of the
safety problem. Although backward reachability is property-directed, it can
unnecessarily explore (large) portions of the state space of a system which are
not required to verify the safety property under consideration. To avoid this,
invariants can be used to dramatically prune the search space. Indeed, the
problem is to guess such appropriate invariants. In this paper, we present a
fully declarative and symbolic approach to the mechanization of backward
reachability of infinite state systems manipulating arrays by Satisfiability
Modulo Theories solving. Theories are used to specify the topology and the data
manipulated by the system. We identify sufficient conditions on the theories to
ensure the termination of backward reachability and we show the completeness of
a method for invariant synthesis (obtained as the dual of backward
reachability), again, under suitable hypotheses on the theories. We also
present a pragmatic approach to interleave invariant synthesis and backward
reachability so that a fix-point for the set of backward reachable states is
more easily obtained. Finally, we discuss heuristics that allow us to derive an
implementation of the techniques in the model checker MCMT, showing remarkable
speed-ups on a significant set of safety problems extracted from a variety of
sources.Comment: Accepted for publication in Logical Methods in Computer Scienc
Inverse modelling of image-based patient-specific blood vessels : zero-pressure geometry and in vivo stress incorporation
In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo stress field of the final, loaded structure. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations, but can be significantly accelerated by a quasi-Newton technique in which a least-squares model is used to approximate the inverse of the Jacobian. The here proposed backward displacement method allows for a straightforward implementation of the algorithm in combination with existing structural solvers, even if the structural solver is a black box, as only an update of the coordinates of the mesh needs to be performed
Well Structured Transition Systems with History
We propose a formal model of concurrent systems in which the history of a
computation is explicitly represented as a collection of events that provide a
view of a sequence of configurations. In our model events generated by
transitions become part of the system configurations leading to operational
semantics with historical data. This model allows us to formalize what is
usually done in symbolic verification algorithms. Indeed, search algorithms
often use meta-information, e.g., names of fired transitions, selected
processes, etc., to reconstruct (error) traces from symbolic state exploration.
The other interesting point of the proposed model is related to a possible new
application of the theory of well-structured transition systems (wsts). In our
setting wsts theory can be applied to formally extend the class of properties
that can be verified using coverability to take into consideration (ordered and
unordered) historical data. This can be done by using different types of
representation of collections of events and by combining them with wsts by
using closure properties of well-quasi orderings.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
Quantifier-Free Interpolation of a Theory of Arrays
The use of interpolants in model checking is becoming an enabling technology
to allow fast and robust verification of hardware and software. The application
of encodings based on the theory of arrays, however, is limited by the
impossibility of deriving quantifier- free interpolants in general. In this
paper, we show that it is possible to obtain quantifier-free interpolants for a
Skolemized version of the extensional theory of arrays. We prove this in two
ways: (1) non-constructively, by using the model theoretic notion of
amalgamation, which is known to be equivalent to admit quantifier-free
interpolation for universal theories; and (2) constructively, by designing an
interpolating procedure, based on solving equations between array updates.
(Interestingly, rewriting techniques are used in the key steps of the solver
and its proof of correctness.) To the best of our knowledge, this is the first
successful attempt of computing quantifier- free interpolants for a variant of
the theory of arrays with extensionality
CFD investigation of a complete floating offshore wind turbine
This chapter presents numerical computations for floating offshore wind turbines for a machine of 10-MW rated power. The rotors were computed using the Helicopter Multi-Block flow solver of the University of Glasgow that solves the Navier-Stokes equations in integral form using the arbitrary Lagrangian-Eulerian formulation for time-dependent domains with moving boundaries. Hydrodynamic loads on the support platform were computed using the Smoothed Particle Hydrodynamics method. This method is mesh-free, and represents the fluid by a set of discrete particles. The motion of the floating offshore wind turbine is computed using a Multi-Body Dynamic Model of rigid bodies and frictionless joints. Mooring cables are modelled as a set of springs and dampers. All solvers were validated separately before coupling, and the loosely coupled algorithm used is described in detail alongside the obtained results
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