Related papers: Tighter Loop Bound Analysis (Technical report)
This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs.…
Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…
There exist several results on deciding termination and computing runtime bounds for triangular weakly non-linear loops (twn-loops). We show how to use results on such subclasses of programs where complexity bounds are computable within…
We present a novel modular approach to infer upper bounds on the expected runtime of probabilistic integer programs automatically. To this end, it computes bounds on the runtime of program parts and on the sizes of their variables in an…
Efficient computation of trajectories of switched affine systems becomes possible, if for any such hybrid system, we can manage to efficiently compute the sequence of switching times. Once the switching times have been computed, we can…
We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of…
We present the new version of the Loop Acceleration Tool (LoAT), a powerful tool for proving non-termination and worst-case lower bounds for programs operating on integers. It is based on a novel calculus for loop acceleration, i.e.,…
We present algorithms for efficiently learning regularizers that improve generalization. Our approach is based on the insight that regularizers can be viewed as upper bounds on the generalization gap, and that reducing the slack in the…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
High utility pattern mining is an interesting yet challenging problem. The intrinsic computational cost of the problem will impose further challenges if efficiency in addition to the efficacy of a solution is sought. Recently, this problem…
In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…
We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…
We develop a new analysis for the length of controlled bad sequences in well-quasi-orderings based on Higman's Lemma. This leads to tight multiply-recursive upper bounds that readily apply to several verification algorithms for…
We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…
There exist several results on deciding termination and computing runtime bounds for triangular weakly non-linear loops (twn-loops). We show how to use results on such subclasses of programs where complexity bounds are computable within…