相关论文: A new function algebra of EXPTIME functions by saf…
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…
A recurrence scheme is defined for the numerical determination of high degree polynomial approximations to functions as, for instance, inverse powers near zero. As an example, polynomials needed in the two-step multi-boson (TSMB) algorithm…
We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an…
The main goal in this manuscript is to present a class of functions satisfying a certain orthogonality property for which there also exists a three term recurrence formula. This class of functions, which can be considered as an extension to…
In this article, we illustrate the asymptotic behaviour of exponential functions of nabla fractional calculus. For this purpose, we propose a novel matrix technique to compute these functions numerically.
Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…
In this work, we take a fresh look at some old and new algorithms for off-policy, return-based reinforcement learning. Expressing these in a common form, we derive a novel algorithm, Retrace($\lambda$), with three desired properties: (1) it…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We introduce a variation of coded computation that ensures data security and master's privacy against workers, which is referred to as private secure coded computation. In private secure coded computation, the master needs to compute a…
We give some connections between various functions defined on finitely presented groups (isoperimetric, isodiametric, Todd-Coxeter radius, filling length functions, etc.), and we study the relation between those functions and the…
We introduce a variant of linear logic with second order quantifiers and type fixpoints, both restricted to purely linear formulas. The Church encodings of binary words are typed by a standard non-linear type `Church,' while the Scott…
Bayesian nonparametric mixture models provide a flexible framework for data analysis but are often hindered by the computational expense of traditional inference methods like MCMC. A fast, recursive algorithm proposed by Newton (2002)…
We study generating functions in the context of Rota-Baxter algebras. We show that exponential generating functions can be naturally viewed in a very special case of complete free commutative Rota-Baxter algebras. This allows us to use free…
We introduce a new bounded theory RS^1_2 and show that the functions which are Sigma^b_1-representable in it are precisely random functions which can be computed in polynomial time. Concretely, we pass through a class of oracle functions…
Barrier functions (BFs) characterize safe sets of dynamical systems, where hard constraints are never violated as the system evolves over time. Computing a valid safe set and BF for a nonlinear (and potentially unmodeled), non-autonomous…
We examine exponential sums of the form $\sum_{n \le X} w(n) e^{2\pi i\alpha n^k}$, for $k=1,2$, where $\alpha$ satisfies a generalized Diophantine approximation and where $w$ are different arithmetic functions that might be multiplicative,…
An approach is suggested defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed.…
In recent work, Zeilberger and the author used a functional equations approach for enumerating permutations with r occurrences of the pattern 12...k. In particular, the approach yielded a polynomial-time enumeration algorithm for any fixed…