Related papers: Multiply-Recursive Upper Bounds with Higman's Lemm…
Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…
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…
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…
In the search for statistical dependency rules, a crucial task is to restrict the search space by estimating upper bounds for the goodness of yet undiscovered rules. In this paper, we show that all well-behaving goodness measures achieve…
This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of the result in the previous paper "Complete controllability of continuous-time recurrent neural networks" (Sontag and…
A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the…
Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
We study constructively the relations between the finite cases of Dickson's lemma. Although there are many constructive proofs of them, the novel aspect of our proofs is the extraction of a corresponding bound. We provide some new one-step…
We develop a new framework for deriving time-uniform concentration bounds for the output of stochastic sequential algorithms satisfying certain recursive inequalities akin to those defining the almost-supermartingale processes introduced by…
In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We…
In this paper, we study the optimal singular controls for stochastic recursive systems, in which the control has two components: the regular control, and the singular control. Under certain assumptions, we establish the dynamic programming…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We prove that the restriction of the vertex-reinforced jump process to a subset of the vertex set is a mixture of vertex-reinforced jump processes. A similar statement holds for the non-linear hyperbolic supersymmetric sigma model. This is…
This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost-sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is…
A step-reinforced random walk is a discrete-time non-Markovian process with long range memory. At each step, with a fixed probability p, the positively step-reinforced random walk repeats one of its preceding steps chosen uniformly at…
We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…