Related papers: Confluence and Convergence in Probabilistically Te…
This paper presents a novel technique for state space reduction of probabilistic specifications, based on a newly developed notion of confluence for probabilistic automata. We prove that this reduction preserves branching probabilistic…
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…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
Let $(X,\mathcal{B},m,\tau)$ be a dynamical system with $\ds (X,\mathcal{B},m)$ a probability space and $\ds \tau$ an invertible, measure preserving transformation. The present paper deals with the almost everywhere convergence in…
We study the almost sure convergence of randomly truncated stochastic algorithms. We present a new convergence theorem which extends the already known results by making vanish the classical condition on the noise terms. The aim of this work…
An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so; it…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Confluence is a critical property of computational systems which is related with determinism and non ambiguity and thus with other relevant computational attributes of functional specifications and rewriting system as termination and…
Absolutely representing system (ARS) in a Banach space $X$ is a set $D \subset X$ such that every vector $x$ in $X$ admits a representation by an absolutely convergent series $x = \sum_i a_i x_i$ with $(a_i)$ reals and $(x_i) \subset D$. We…
We present a constructive formalization of Abstract Rewriting Systems (ARS) in the Agda proof assistant, focusing on standard results in term rewriting. We define a taxonomy of concepts related to termination and confluence and investigate…
We present novel semiring semantics for abstract reduction systems (ARSs). More precisely, we provide a weighted version of ARSs, where the reduction steps induce weights from a semiring. Inspired by provenance analysis in database theory…
This paper presents new variants of the averaged alternating modified reflections (AAMR) method for the best approximation problem. Under a mild constraint qualification, we first show its weak convergence and then establish a convergence…
A very simple but useful almost sure convergence theorem of probability is given.
In this paper we consider the problem of proving properties of infinite behaviour of formalisms suitable to describe (infinite state) systems with recursion and parallelism. As a formal setting, we consider the framework of Process…
In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
We study confluence in the setting of higher-order infinitary rewriting, in particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that fully-extended, orthogonal iCRSs are confluent modulo identification of…
We consider the non-overlapping irreversible random sequential adsorption (RSA) process on one-dimensional finite line, which is known also as the car parking process. The probability of each coverage in saturating states is analytically…
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…