Ranking and Repulsing Supermartingales for Approximating Reachability

05/28/2018
by   Toru Takisaka, et al.
0

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating reachability probabilities. Based on the existing works that stretch across different communities (formal verification, control theory, etc.), we offer a unifying account. In particular, we emphasize the role of order-theoretic fixed points---a classic topic in computer science---in the analysis of probabilistic programs. This leads us to two new martingale-based techniques, too. We give rigorous proofs for their soundness and completeness. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/28/2018

Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs

Computing reachability probabilities is a fundamental problem in the ana...
research
03/16/2022

On Higher-Order Reachability Games vs May Reachability

We consider the reachability problem for higher-order functional program...
research
07/28/2020

Inductive Reachability Witnesses

In this work, we consider the fundamental problem of reachability analys...
research
08/25/2022

Backwards Reachability for Probabilistic Timed Automata: A Replication Report

Backwards reachability is an efficient zone-based approach for model che...
research
01/15/2023

Quantitative Verification With Neural Networks For Probabilistic Programs and Stochastic Systems

We present a machine learning approach to quantitative verification. We ...
research
03/27/2022

The Lattice-Theoretic Essence of Property Directed Reachability Analysis

We present LT-PDR, a lattice-theoretic generalization of Bradley's prope...
research
08/11/2020

Upper approximating probabilities of convergence in probabilistic coherence spaces

We develop a theory of probabilistic coherence spaces equipped with an a...

Please sign up or login with your details

Forgot password? Click here to reset