4,113 research outputs found
Domain-Type-Guided Refinement Selection Based on Sliced Path Prefixes
Abstraction is a successful technique in software verification, and
interpolation on infeasible error paths is a successful approach to
automatically detect the right level of abstraction in counterexample-guided
abstraction refinement. Because the interpolants have a significant influence
on the quality of the abstraction, and thus, the effectiveness of the
verification, an algorithm for deriving the best possible interpolants is
desirable. We present an analysis-independent technique that makes it possible
to extract several alternative sequences of interpolants from one given
infeasible error path, if there are several reasons for infeasibility in the
error path. We take as input the given infeasible error path and apply a
slicing technique to obtain a set of error paths that are more abstract than
the original error path but still infeasible, each for a different reason. The
(more abstract) constraints of the new paths can be passed to a standard
interpolation engine, in order to obtain a set of interpolant sequences, one
for each new path. The analysis can then choose from this set of interpolant
sequences and select the most appropriate, instead of being bound to the single
interpolant sequence that the interpolation engine would normally return. For
example, we can select based on domain types of variables in the interpolants,
prefer to avoid loop counters, or compare with templates for potential loop
invariants, and thus control what kind of information occurs in the abstraction
of the program. We implemented the new algorithm in the open-source
verification framework CPAchecker and show that our proof-technique-independent
approach yields a significant improvement of the effectiveness and efficiency
of the verification process.Comment: 10 pages, 5 figures, 1 table, 4 algorithm
Stein's method for dependent random variables occurring in Statistical Mechanics
We obtain rates of convergence in limit theorems of partial sums for
certain sequences of dependent, identically distributed random variables, which
arise naturally in statistical mechanics, in particular, in the context of the
Curie-Weiss models. Under appropriate assumptions there exists a real number
, a positive real number , and a positive integer such that
converges weakly to a random variable with
density proportional to . We develop Stein's method
for exchangeable pairs for a rich class of distributional approximations
including the Gaussian distributions as well as the non-Gaussian limit
distributions with density proportional to . Our
results include the optimal Berry-Esseen rate in the Central Limit Theorem for
the total magnetization in the classical Curie-Weiss model, for high
temperatures as well as at the critical temperature , where the
Central Limit Theorem fails. Moreover, we analyze Berry-Esseen bounds as the
temperature converges to one and obtain a threshold for the speed
of this convergence. Single spin distributions satisfying the
Griffiths-Hurst-Sherman (GHS) inequality like models of liquid helium or
continuous Curie-Weiss models are considered
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