63,687 research outputs found
Canonized Rewriting and Ground AC Completion Modulo Shostak Theories : Design and Implementation
AC-completion efficiently handles equality modulo associative and commutative
function symbols. When the input is ground, the procedure terminates and
provides a decision algorithm for the word problem. In this paper, we present a
modular extension of ground AC-completion for deciding formulas in the
combination of the theory of equality with user-defined AC symbols,
uninterpreted symbols and an arbitrary signature disjoint Shostak theory X. Our
algorithm, called AC(X), is obtained by augmenting in a modular way ground
AC-completion with the canonizer and solver present for the theory X. This
integration rests on canonized rewriting, a new relation reminiscent to
normalized rewriting, which integrates canonizers in rewriting steps. AC(X) is
proved sound, complete and terminating, and is implemented to extend the core
of the Alt-Ergo theorem prover.Comment: 30 pages, full version of the paper TACAS'11 paper "Canonized
Rewriting and Ground AC-Completion Modulo Shostak Theories" accepted for
publication by LMCS (Logical Methods in Computer Science
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
A Parallel Mesh-Adaptive Framework for Hyperbolic Conservation Laws
We report on the development of a computational framework for the parallel,
mesh-adaptive solution of systems of hyperbolic conservation laws like the
time-dependent Euler equations in compressible gas dynamics or
Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh
refinement is realized by the recursive bisection of grid blocks along each
spatial dimension, implemented numerical schemes include standard
finite-differences as well as shock-capturing central schemes, both in
connection with Runge-Kutta type integrators. Parallel execution is achieved
through a configurable hybrid of POSIX-multi-threading and MPI-distribution
with dynamic load balancing. One- two- and three-dimensional test computations
for the Euler equations have been carried out and show good parallel scaling
behavior. The Racoon framework is currently used to study the formation of
singularities in plasmas and fluids.Comment: late submissio
Fast generation of stability charts for time-delay systems using continuation of characteristic roots
Many dynamic processes involve time delays, thus their dynamics are governed
by delay differential equations (DDEs). Studying the stability of dynamic
systems is critical, but analyzing the stability of time-delay systems is
challenging because DDEs are infinite-dimensional. We propose a new approach to
quickly generate stability charts for DDEs using continuation of characteristic
roots (CCR). In our CCR method, the roots of the characteristic equation of a
DDE are written as implicit functions of the parameters of interest, and the
continuation equations are derived in the form of ordinary differential
equations (ODEs). Numerical continuation is then employed to determine the
characteristic roots at all points in a parametric space; the stability of the
original DDE can then be easily determined. A key advantage of the proposed
method is that a system of linearly independent ODEs is solved rather than the
typical strategy of solving a large eigenvalue problem at each grid point in
the domain. Thus, the CCR method significantly reduces the computational effort
required to determine the stability of DDEs. As we demonstrate with several
examples, the CCR method generates highly accurate stability charts, and does
so up to 10 times faster than the Galerkin approximation method.Comment: 12 pages, 6 figure
A Multi-objective Perspective for Operator Scheduling using Fine-grained DVS Architecture
The stringent power budget of fine grained power managed digital integrated
circuits have driven chip designers to optimize power at the cost of area and
delay, which were the traditional cost criteria for circuit optimization. The
emerging scenario motivates us to revisit the classical operator scheduling
problem under the availability of DVFS enabled functional units that can
trade-off cycles with power. We study the design space defined due to this
trade-off and present a branch-and-bound(B/B) algorithm to explore this state
space and report the pareto-optimal front with respect to area and power. The
scheduling also aims at maximum resource sharing and is able to attain
sufficient area and power gains for complex benchmarks when timing constraints
are relaxed by sufficient amount. Experimental results show that the algorithm
that operates without any user constraint(area/power) is able to solve the
problem for most available benchmarks, and the use of power budget or area
budget constraints leads to significant performance gain.Comment: 18 pages, 6 figures, International journal of VLSI design &
Communication Systems (VLSICS
Creation of the selection list for the Experiment Scheduling Program (ESP)
The efforts to develop a procedure to construct selection groups to augment the Experiment Scheduling Program (ESP) are summarized. Included is a User's Guide and a sample scenario to guide in the use of the software system that implements the developed procedures
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