# Stochastic Nondeterminism and Effectivity Functions

arXiv: https://arxiv.org/abs/1405.7141 · HTML: https://mlsanity.com/paper/1405.7141/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2014.

## Built on by (most cited first, 1 of 1)

- [Mixed Nondeterministic-Probabilistic Automata: Blending graphical probabilistic models with nondeterminism](https://mlsanity.com/paper/2201.07474/) (2022)

## Abstract (arXiv)

This paper investigates stochastic nondeterminism on continuous state spaces by relating nondeterministic kernels and stochastic effectivity functions to each other. Nondeterministic kernels are functions assigning each state a set o subprobability measures, and effectivity functions assign to each state an upper-closed set of subsets of measures. Both concepts are generalizations of Markov kernels used for defining two different models: Nondeterministic labelled Markov processes and stochastic game models, respectively. We show that an effectivity function that maps into principal filters is given by an image-countable nondeterministic kernel, and that image-finite kernels give rise to effectivity functions. We define state bisimilarity for the latter, considering its connection to morphisms. We provide a logical characterization of bisimilarity in the finitary case. A generalization of congruences (event bisimulations) to effectivity functions and its relation to the categorical presentation of bisimulation are also studied.