Related papers: Analyzing Expected Outcomes and Almost-Sure Termin…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for…
Suppose we are given a computably enumerable object arise from algorithmic randomness or computable analysis. We are interested in the strength of oracles which can compute an object that approximates this c.e. object. It turns out that,…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…
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 study the problem of sequentially predicting properties of a probabilistic model and its next outcome over an infinite horizon, with the goal of ensuring that the predictions incur only finitely many errors with probability 1. We…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
Given a hierarchical plan (or schedule) with uncertain task times, we propose a deterministic polynomial (time and memory) algorithm for estimating the probability that its meets a deadline, or, alternately, that its {\em makespan} is less…
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…
An index $e$ in a numbering of partial-recursive functions is called minimal if every lesser index computes a different function from $e$. Since the 1960's it has been known that, in any reasonable programming language, no effective…
Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…
We consider the problem of refuting equivalence of probabilistic programs, i.e., the problem of proving that two probabilistic programs induce different output distributions. We study this problem in the context of programs with…
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…
We define Almost Sure Productivity (ASP), a probabilistic generalization of the productivity condition for coinductively defined structures. Intuitively, a probabilistic coinductive stream or tree is ASP if it produces infinitely many…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…