Related papers: The Probabilistic Termination Tool Amber
In this paper, we derive power guarantees of some sequential tests for bounded mean under general alternatives. We focus on testing procedures using nonnegative supermartingales which are anytime valid and consider alternatives which…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
Existing probabilistic scanners and parsers impose hard constraints on the way lexical and syntactic ambiguities can be resolved. Furthermore, traditional grammar-based parsing tools are limited in the mechanisms they allow for taking…
In this work, we study the fully automated inference of expected result values of probabilistic programs in the presence of natural programming constructs such as procedures, local variables and recursion. While crucial, capturing these…
Couplings are a powerful mathematical tool for reasoning about pairs of probabilistic processes. Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by…
Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…
We present POLAR, a polynomial arithmetic-based framework for efficient bounded-time reachability analysis of neural-network controlled systems (NNCSs). Existing approaches that leverage the standard Taylor Model (TM) arithmetic for…
We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded loops. Our method is built on a denotational semantics represented by probability generating…
The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their Mean Unsigned Error is unsatisfactory for several reasons linked to the…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and…
This paper describes a natural language parsing algorithm for unrestricted text which uses a probability-based scoring function to select the "best" parse of a sentence. The parser, Pearl, is a time-asynchronous bottom-up chart parser with…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…
Bisimulation is crucial for verifying process equivalence in probabilistic systems. This paper presents a novel logical framework for analyzing bisimulation in probabilistic parameterized systems, namely, infinite families of finite-state…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
We consider a minimal extension of the language of arithmetic, such that the bounded formulas provably total in a suitably-defined theory \`a la Buss (expressed in this new language) precisely capture polytime random functions. Then, we…
Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified implements…
We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with…