We study the worst case complexity of computing ε-approximations of volumes of d-dimensional regions g([0, 1]d), by sampling the function g. Here, g is an s times continuously differentiable injection from [0, 1]d to Rd , where we assume that s ≥ 1. Since the problem can be solved exactly when d = 1, we concentrate our attention on the case d ≥ 2. This problem is a special case of the surface i...

We apply the cache partitioning technique on a network stack to derive the influence of caches on worst case execution times of complex applications. We demonstrate that the overhead caused by cache misses when receiving packets of typical sizes from the network is reduced from 310% to 90% compared to the best case. For the transmit direction, cache partitioning results in a reduction of the ov...

Let V be a finite set of n elements and F = {X1, X2, . . . , Xm} a family of m subsets of V. Two sets Xi and Xj of F overlap if Xi∩Xj 6= ∅, Xj \ Xi 6= ∅, and Xi \ Xj 6= ∅. Two sets X, Y ∈ F are in the same overlap class if there is a series X = X1, X2, . . . , Xk = Y of sets of F in which each XiXi+1 overlaps. In this note, we focus on efficiently identifying all overlap classes in O(n + ∑m i=1...

ion loses information – The computed WCET bound usually overestimates the exact WCET and vice versa for the BCET The WCET bound represents the worst-case guarantee the method or tool can give How much is lost depends both on the methods used for timing analysis and on overall system properties (Timing Predictability) – hardware architecture – characteristics of the software 9 Rômulo Silva de Ol...

Parametric uncertainty can represent parametric tolerance, parameter noise or parameter disturbances. The effects of these uncertainties on the time evolution of a system can be extremely significant, mostly when studying closed-loop operation of control systems. The presence of uncertainty makes the modeling process challenging, since it is impossible to express the behavior of the system with...

We consider the problem of evaluating an expression over sets. The sets are preprocessed and are therefore sorted, and the operators can be any of union, intersection, difference, complement, and symmetric difference (exclusive union). Given the expression as a formula and the sizes of the input sets, we are interested in the worst-case complexity of evaluation (in terms of the size of the sets...

The Worst-Case Execution Time of tasks with strict deadlines must be predictable: it must be possible to estimate this time both safely and tightly at an acceptable computing cost. Static WCET analysis is facilitated if parts of code can be analyzed more or less independently of one another. This is why it is desirable to prevent timing interferences between blocks. In this paper, we show how i...

We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log2(N) + 1 experiments are sufficient and in the worst case necessary to determine the causal relations among N ≥ 2 variables when no latent variables, no sample selection bias and no feedback cycles are present. For all K, 0 < K < 1 2N we provide an upper bound on the n...

This paper presents an new, proximate-optimal solution to the pathconstrained time-parameterization problem. This new algorithm has three distinguishing features: First, the run-time worst-case complexity of the proximate time-optimal algorithm is linear with respect to path-length and it is shown to be more efficient than any other truly time-optimal algorithm. Second, for a given robotic syst...

Improved cost estimates are given for the problem of computing the inverse of an n×n matrix of univariate polynomials over a field. A deterministic algorithm is demonstrated that has worst case complexity (n3s) field operations, where s ≥ 1 is an upper bound for the average column degree of the input matrix. Here, the “+o(1)” in the exponent indicates a missing factor c1(log ns)2 for positive r...