Abstract
We introduce Mora, an automated tool for generating invariants of probabilistic programs. Inputs to Mora are so-called Prob-solvable loops, that is probabilistic programs with polynomial assignments over random variables and parametrized distributions. Combining methods from symbolic computation and statistics, Mora computes invariant properties over higher-order moments of loop variables, expressing, for example, statistical properties, such as expected values and variances, over the value distribution of loop variables.
Footnotes
This research was supported by the ERC Starting Grant 2014 SYMCAR 639270, the Wallenberg Academy Fellowship 2014 TheProSE, and the Austrian FWF project W1255-N23.
Contributor Information
Armin Biere, Email: biere@jku.at.
David Parker, Email: d.a.parker@cs.bham.ac.uk.
Miroslav Stankovič, Email: miroslav.ms.stankovic@gmail.com.
References
- 1.Barthe, G., Espitau, T., Fioriti, L.M.F., Hsu, J.: Synthesizing Probabilistic Invariants via Doob’s Decomposition. In: CAV. LNCS, vol. 9779, pp. 43–61. Springer (2016)
- 2.Bartocci, E., Kovács, L., Stankovic, M.: Automatic generation of moment-based invariants for prob-solvable loops. In: Proc. of ATVA 2019: the 17th International Symposium on Automated Technology for Verification and Analysis. LNCS, vol. 11781, pp. 255–276 (2019)
- 3.Chakarov, A., Sankaranarayanan, S.: Expectation Invariants for Probabilistic Program Loops as Fixed Points. In: SAS. LNCS, vol. 8723, pp. 85–100 (2014)
- 4.Gehr, T., Misailovic, S., Vechev, M.T.: PSI: Exact Symbolic Inference for Probabilistic Programs. In: CAV. LNCS, vol. 9779, pp. 62–83 (2016)
- 5.Ghahramani, Z.: Probabilistic Machine Learning and Artificial Intelligence. Nature 521(7553), 452–459 (2015) [DOI] [PubMed]
- 6.Humenberger, A., Jaroschek, M., Kovács, L.: Aligator.jl - A Julia Package for Loop Invariant Generation. In: CICM. LNCS, vol. 11006, pp. 111–117 (2018)
- 7.Katoen, J.P., McIver, A.K., Meinicke, L.A., Morgan, C.C.: Linear-Invariant Generation for Probabilistic Programs: Automated Support for Proof-Based Methods. In: SAS. LNCS, vol. 6337, pp. 390–406 (2010)
- 8.Kauers, M., Paule, P.: The Concrete Tetrahedron - Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates. Texts & Monographs in Symbolic Computation, Springer (2011)
- 9.Kura, S., Urabe, N., Hasuo, I.: Tail Probabilities for Randomized Program Runtimes via Martingales for Higher Moments. In: TACAS. LNCS, vol. 11428, pp. 135–153 (2019)
- 10.McIver, A., Morgan, C.: Abstraction, Refinement and Proof for Probabilistic Systems. Monographs in Computer Science, Springer (2005)