Related papers: Evolving Recursive Definitions with Applications t…
D-finite functions and P-recursive sequences are defined in terms of linear differential and recurrence equations with polynomial coefficients. In this paper, we introduce a class of numbers closely related to D-finite functions and…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…
Although AI agents have demonstrated impressive capabilities in long-horizon reasoning, their reliability is severely hampered by the ``Spiral of Hallucination,'' where early epistemic errors propagate irreversibly. Existing methods face a…
We consider two approaches for assessing the reliability of the individual predictions of a classifier: Robustness Quantification (RQ) and Uncertainty Quantification (UQ). We explain the conceptual differences between the two approaches,…
Product Quantization, a dictionary based hashing method, is one of the leading unsupervised hashing techniques. While it ignores the labels, it harnesses the features to construct look up tables that can approximate the feature space. In…
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…
Probabilistic programming is considered as a framework, in which basic components of cognitive architectures can be represented in unified and elegant fashion. At the same time, necessity of adopting some component of cognitive…
We investigate the problem of finite entailment of ontology-mediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCRPQs), extending the well-known class of union of conjunctive queries,…
Encodings, that is, injective functions from words to words, have been studied extensively in several settings. In computability theory the notion of encoding is crucial for defining computability on arbitrary domains, as well as for…
Uncertainty quantification (UQ) methods for large language models are predominantly designed by hand based on domain knowledge and heuristics, limiting their scalability and generality. We apply LLM-powered evolutionary search to…
In this paper we describe a new approach to programming which generalizes object-oriented programming. It is based on using a new programming construct, called concept, which generalizes classes. Concept is defined as a pair of two classes:…
Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation, in order to open up a new line of attack. Our paper studies this…
We give a new characterization of the class of rational string functions from formal language theory using order-preserving interpretations with respect to a very weak monadic programming language. This refines the known characterization of…
Systematic compositionality is the ability to recombine meaningful units with regular and predictable outcomes, and it's seen as key to humans' capacity for generalization in language. Recent work has studied systematic compositionality in…
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
The aim of this paper is to propose an alternative behavioural definition of computation (and of a computer) based simply on whether a system is capable of reacting to the environment-the input-as reflected in a measure of programmability.…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Declarative styles such as functional programming (FP) are rapidly gaining ground on their imperative cousins, including procedural and object-oriented programming. The shift is subtle because it is happening within the context of…
The characteristic novelty of what is generally meant by a "physical unclonable function" (PUF) is precisely defined, in order to supply a firm basis for security evaluations and the proposal of new security mechanisms. A PUF is defined as…