# Inductive Synthesis for Probabilistic Programs Reaches New Horizons

arXiv: https://arxiv.org/abs/2101.12683 · HTML: https://mlsanity.com/paper/2101.12683/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 41 references that are in the map.
- First posted on arXiv 29 Jan 2021.

## Builds on (most cited first, 9 of 9)

- [A storm is Coming: A Modern Probabilistic Model Checker](https://mlsanity.com/paper/1702.04311/) (2017)
- [Bayesian Synthesis of Probabilistic Programs for Automatic Data Modeling](https://mlsanity.com/paper/1907.06249/) (2019)
- [Parameter Synthesis for Markov Models: Faster Than Ever](https://mlsanity.com/paper/1602.05113/) (2016)
- [Parametric Markov Chains: PCTL Complexity and Fraction-free Gaussian Elimination](https://mlsanity.com/paper/1709.02093/) (2017)
- [Reachability in Augmented Interval Markov Chains](https://mlsanity.com/paper/1701.02996/) (2017)
- [Shepherding Hordes of Markov Chains](https://mlsanity.com/paper/1902.05727/) (2019)
- [Counterexample-Driven Synthesis for Probabilistic Program Sketches](https://mlsanity.com/paper/1904.12371/) (2019)
- [Farkas certificates and minimal witnesses for probabilistic reachability constraints](https://mlsanity.com/paper/1910.10636/) (2019)
- [High-level Counterexamples for Probabilistic Automata](https://mlsanity.com/paper/1305.5055/) (2013)

## Built on by (most cited first, 2 of 2)

- [Abstraction-Refinement for Hierarchical Probabilistic Models](https://mlsanity.com/paper/2206.02653/) (2022)
- [Deductive Controller Synthesis for Probabilistic Hyperproperties](https://mlsanity.com/paper/2307.04503/) (2023)

## Abstract (arXiv)

This paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a PCTL specification. The method builds on a novel inductive oracle that greedily generates counter-examples (CEs) for violating programs and uses them to prune the family. These CEs leverage the semantics of the family in the form of bounds on its best- and worst-case behaviour provided by a deductive oracle using an MDP abstraction. The method further monitors the performance of the synthesis and adaptively switches between the inductive and deductive reasoning. Our experiments demonstrate that the novel CE construction provides a significantly faster and more effective pruning strategy leading to acceleration of the synthesis process on a wide range of benchmarks. For challenging problems, such as the synthesis of decentralized partially-observable controllers, we reduce the run-time from a day to minutes.