13,753 research outputs found
Dirac--Lie systems and Schwarzian equations
A Lie system is a system of differential equations admitting a superposition
rule, i.e., a function describing its general solution in terms of any generic
set of particular solutions and some constants. Following ideas going back to
the Dirac's description of constrained systems, we introduce and analyse a
particular class of Lie systems on Dirac manifolds, called Dirac--Lie systems,
which are associated with `Dirac--Lie Hamiltonians'. Our results enable us to
investigate constants of the motion, superposition rules, and other general
properties of such systems in a more effective way. Several concepts of the
theory of Lie systems are adapted to this `Dirac setting' and new applications
of Dirac geometry in differential equations are presented. As an application,
we analyze traveling wave solutions of Schwarzian equations, but our methods
can be applied also to other classes of differential equations important for
Physics.Comment: 41 page
Fault Localization in Multi-Threaded C Programs using Bounded Model Checking (extended version)
Software debugging is a very time-consuming process, which is even worse for
multi-threaded programs, due to the non-deterministic behavior of
thread-scheduling algorithms. However, the debugging time may be greatly
reduced, if automatic methods are used for localizing faults. In this study, a
new method for fault localization, in multi-threaded C programs, is proposed.
It transforms a multi-threaded program into a corresponding sequential one and
then uses a fault-diagnosis method suitable for this type of program, in order
to localize faults. The code transformation is implemented with rules and
context switch information from counterexamples, which are typically generated
by bounded model checkers. Experimental results show that the proposed method
is effective, in such a way that sequential fault-localization methods can be
extended to multi-threaded programs.Comment: extended version of paper published at SBESC'1
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