Related papers: The multiplicative complexity of interval checking
We formally study iterated block ciphers that alternate between two sequences of independent and identically distributed (i.i.d.) rounds. It is demonstrated that, in some cases the effect of alternating increases security, while in other…
In this article we address the problem of automatic answer checking in interactive learning systems that support mathematical notation. This problem consists of the problem of establishing identities in formal mathematical systems and hence…
Integrity checking is a crucial issue, as databases change their instance all the time and therefore need to be checked continuously and rapidly. Decades of research have produced a plethora of methods for checking integrity constraints of…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…
It is observed that for testing between simple hypotheses where the cost of Type I and Type II errors can be quantified, it is better to let the optimization choose the test size.
We often add arithmetic to extend the expressiveness of query languages and study the complexity of problems such as testing query containment and finding certain answers in the framework of answering queries using views. When adding…
For a given level of accuracy in option prices, the paper considers the problem of deciding when exactly, as one or more of the pricing parameters change, a barrier option degenerates into a simpler type of option. This problem is…
Module checking has been introduced in late 1990s to verify open systems, i.e., systems whose behavior depends on the continuous interaction with the environment. Classically, module checking has been investigated with respect to…
We consider Lagrange interpolation on the set of finitely many intervals. This problem is closely related to the least deviating polynomial from zero on such sets. We will obtain lower and upper estimates for the corresponding Lebesgue…
The problem of handling adaptivity in data analysis, intentional or not, permeates a variety of fields, including test-set overfitting in ML challenges and the accumulation of invalid scientific discoveries. We propose a mechanism for…
Extremum seeking systems are powerful methods able to steer the input of a (dynamical) cost function towards an optimizer, without any prior knowledge of the cost function. To achieve their objective, they typically combine time-periodic…
When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-{\alpha} for all values of p, and a shorter approximate interval, which may…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
The higher criticism of a family of tests starts with the individual uncorrected p-values of each test. It then requires a procedure for deciding whether the collection of p-values indicates the presence of a real effect and if possible…
AB-testing is a very popular technique in web companies since it makes it possible to accurately predict the impact of a modification with the simplicity of a random split across users. One of the critical aspects of an AB-test is its…
We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that…