Related papers: Probabilistic Recursion Theory and Implicit Comput…
We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
We develop a technique for generalising from data in which models are samplers represented as program text. We establish encouraging empirical results that suggest that Markov chain Monte Carlo probabilistic programming inference techniques…
A real number \alpha is called recursively enumerable if there exists a computable, increasing sequence of rational numbers which converges to \alpha. The randomness of a recursively enumerable real \alpha can be characterized in various…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
In this paper we present the probabilistic typed natural deduction calculus TPTND, designed to reason about and derive trustworthiness properties of probabilistic computational processes, like those underlying current AI applications.…
In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging…
In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent…
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
We define a class of functions termed "Computable in the Limit", based on the Machine Learning paradigm of "Identification in the Limit". A function is Computable in the Limit if it defines a property P_p of a recursively enumerable class A…
Standard probability theory has been extremely successful but there are some conceptually possible scenarios, such as fair infinite lotteries, that it does not model well. For this reason alternative probability theories have been…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…
An interplay between the Lambert series and Euler's Pentagonal Number Theorem gives an Euler-type recurrence relation for any given arithmetical function. As consequences of this, we present Euler-type recurrence relations for some…