Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops
Paper i proceeding, 2019

One of the main challenges in the analysis of probabilistic programs is to compute invariant properties that summarise loop behaviours. Automation of invariant generation is still at its infancy and most of the times targets only expected values of the program variables, which is insufficient to recover the full probabilistic program behaviour. We present a method to automatically generate moment-based invariants of a subclass of probabilistic programs, called Prob-solvable loops, with polynomial assignments over random variables and parametrised distributions. We combine methods from symbolic summation and statistics to derive invariants as valid properties over higher-order moments, such as expected values or variances, of program variables. We successfully evaluated our work on several examples where full automation for computing higher-order moments and invariants over program variables was not yet possible.


Ezio Bartocci

Technische Universität Wien

Laura Kovacs

Chalmers, Data- och informationsteknik, Formella metoder

Technische Universität Wien

Miroslav Stankovič

Technische Universität Wien

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 11781 LNCS 255-276

17th International Symposium on Automated Technology for Verification and Analysis, ATVA 2019
Taipei, Taiwan,


Sannolikhetsteori och statistik


Matematisk analys



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