Related papers: Not All Multi-Valued Partial CFL Functions Are Ref…

Let E_n={x_i=1, x_i+x_j=x_k, x_i*x_j=x_k: i,j,k \in {1,...,n}}. We prove: (1) there is an algorithm that for every computable function f:N-->N returns a positive integer m(f), for which a second algorithm accepts on the input f and any…

With the increasing power of computers and the rapid development of self-learning methodologies such as machine learning and artificial intelligence, the problem of constructing an automatic Financial Trading Systems (FTFs) becomes an…

A computable real function F on [0,1] is constructed such that there exists an exponential time algorithm for the evaluation of the function on [0,1] on Turing machine but there does not exist any polynomial time algorithm for the…

Control barrier functions (CBFs) have been widely used for synthesizing controllers in safety-critical applications. When used as a safety filter, it provides a simple and computationally efficient way to obtain safe controls from a…

Reinforcement Learning (RL) has played a central role in the recent surge of LLMs' math abilities by enabling self-improvement through binary verifier signals. In contrast, Supervised Learning (SL) is rarely considered for such…

In a functional language, the dominant control-flow mechanism is function call and return. Most higher-order flow analyses, including k-CFA, do not handle call and return well: they remember only a bounded number of pending calls because…

Compilers use control flow graph (CFG) representations of low-level programs because they are suited to program analysis and optimizations. However, formalizing the behavior and metatheory of CFG programs is non-trivial: CFG programs don't…

Creating functions is at the center of writing computer programs. But there has been little empirical research on how this is done and what are the considerations that developers use. We design an experiment in which we can compare the…

Programs that transform other programs often require access to the internal structure of the program to be transformed. This is at odds with the usual extensional view of functional programming, as embodied by the lambda calculus and SK…

Predictable Feature Analysis (PFA) (Richthofer, Wiskott, ICMLA 2015) is an algorithm that performs dimensionality reduction on high dimensional input signal. It extracts those subsignals that are most predictable according to a certain…

We know that tilesets that can tile the plane always admit a quasi-periodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity function is one way to measure the regularity of a quasi-periodic…

We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between…

Single-task RL agents are typically trained under a fixed reward function, which limits their robustness to reward misspecification and their ability to adapt to changing preferences. We introduce Reward-Conditioned Reinforcement Learning…

Recent work demonstrated the existence of Boolean functions for which Shapley values provide misleading information about the relative importance of features in rule-based explanations. Such misleading information was broadly categorized…

We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions $\{0,1\}^k\to\mathbb{R}_{\geq 0}$) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice…

Let $\mathcal{P}$ be a property of function $\mathbb{F}_p^n \to \{0,1\}$ for a fixed prime $p$. An algorithm is called a tester for $\mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$…

Safety is a fundamental requirement for autonomous systems operating in critical domains. Control barrier functions (CBFs) have been used to design safety filters that minimally alter nominal controls for such systems to maintain their…

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…

A parking function is a function $\pi:[n]\to [n]$ whose $i$th-smallest output is at most $i,$ corresponding to a parking procedure for $n$ cars on a one-way street. We refine this concept by introducing preference-restricted parking…

Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for $\sigma-$-net might be very small. Keeping the original discretization (square or triangulation), can we…