Related papers: A Cancellation Law for Probabilistic Processes
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
Bivariate normal distributions are often used to describe the joint probability density of a pair of random variables. These distributions arise across many domains, from telecommunications, to meteorology, ballistics, and computational…
Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…
We make a formal analogy between random sampling and fresh name generation. We show that quasi-Borel spaces, a model for probabilistic programming, can soundly interpret Stark's $\nu$-calculus, a calculus for name generation. Moreover, 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…
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…
For any branching process, we demonstrate that the typical total number $r_{\rm mp}(\nu \tau)$ of events triggered over all generations within any sufficiently large time window $\tau$ exhibits, at criticality, a super-linear dependence…
No-Cloning and No-Deleting theorems are verified with the constraint on local state transformations via the existence of incomparable states. Assuming the existence of exact cloning or deleting operation defined on a minimum number of two…
The Symmetric Exclusion Process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of…
Arguing for the need to combine declarative and probabilistic programming, B\'ar\'any et al. (TODS 2017) recently introduced a probabilistic extension of Datalog as a "purely declarative probabilistic programming language." We revisit this…
We introduce a bisimulation learning algorithm for non-deterministic transition systems. We generalise bisimulation learning to systems with bounded branching and extend its applicability to model checking branching-time temporal logic,…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
We give an alternative proof of a result by N. Gantert, Y. Hu and Z. Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary…
Property elicitation studies which attributes of a probability distribution can be determined by minimizing a risk. We investigate a generalization of property elicitation to imprecise probabilities (IP). This investigation is motivated by…
This tutorial contrasts probabilistic modeling and robust optimization to determine decisions in humanitarian logistics, specifically supply chains subject to adversarial (natural and human) disruptions. Natural disruptions induce dispatch…
In this paper, we present a hypersequent calculus for bimodal logic GR, where the two modalities represent the arithmetic provability predicates of Goedel and Rosser, respectively. We prove the cut-elimination theorem for the calculus.
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process.…
Let $X$ be the branching particle diffusion corresponding to the operator $Lu+\beta (u^{2}-u)$ on $D\subseteq \mathbb{R}^{d}$ (where $\beta \geq 0$ and $\beta\not\equiv 0$). Let $\lambda_{c}$ denote the generalized principal eigenvalue for…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
Bayesian probabilistic programming languages (BPPLs) let users denote statistical models as code while the interpreter infers the posterior distribution. The semantics of BPPLs are usually mathematically complex and unable to reason about…