arXiv subjects

Darion Haase

Publications and source records attributed to Darion Haase.

5 recordsLinked to original sources

arXiv2026

Caesar: A Deductive Verifier for Probabilistic Programs

Caesar is a deductive verifier for probabilistic programs. At its core lies HeyVL, a quantitative intermediate verification language based on the real-valued logic HeyLo. HeyVL allows users to express a probabilistic program, its specifications, and proof rules in a programming-language style, so that new proof rules can be easily integrated into the verifier. Caesar translates HeyVL programs into verification conditions, which are then checked using the Z3 SMT solver. It also includes a backend based on probabilistic model checking for a subset of HeyVL. We report on the results of five years of development of Caesar, highlighting its main features and architecture. In particular, we describe recent improvements such as additional proof rules, a model-checking backend, and better diagnostics.

cs.PL↗

arXiv2026

Generating Functions Meet Occupation Measures: Invariant Synthesis for Probabilistic Loops (Extended Version)

A fundamental computational task in probabilistic programming is to infer a program's output (posterior) distribution from a given initial (prior) distribution. This problem is challenging, especially for expressive languages that feature loops or unbounded recursion. While most of the existing literature focuses on statistical approximation, in this paper we address the problem of mathematically exact inference. To achieve this for programs with loops, we rely on a relatively underexplored type of probabilistic loop invariant, which is linked to a loop's so-called occupation measure. The occupation measure associates program states with their expected number of visits, given the initial distribution. Based on this, we derive the notion of an occupation invariant. Such invariants are essentially dual to probabilistic martingales, the predominant technique for formal probabilistic loop analysis in the literature. A key feature of occupation invariants is that they can take the initial distribution into account and often yield a proof of positive almost sure termination as a by-product. Finally, we present an automatic, template-based invariant synthesis approach for occupation invariants by encoding them as generating functions. The approach is implemented and evaluated on a set of benchmarks.

cs.PL↗

arXiv2025

Error Localization, Certificates, and Hints for Probabilistic Program Verification via Slicing (Extended Version)

This paper focuses on effective user diagnostics generated during the deductive verification of probabilistic programs. Our key principle is based on providing slices for (1) error reporting, (2) proof simplification, and (3) preserving successful verification results. By formally defining these different notions on HeyVL, an existing quantitative intermediate verification language (IVL), our concepts (and implementation) can be used to obtain diagnostics for a range of probabilistic programming languages. Slicing for error reporting is a novel notion of error localization for quantitative assertions. We demonstrate slicing-based diagnostics on a variety of proof rules such as quantitative versions of the specification statement and invariant-based loop rules, and formally prove the correctness of specialized error messages and verification hints. We implemented our user diagnostics into the deductive verifier Caesar. Our novel implementation -- called \emph{Brutus} -- can search for slices which do or do not verify, corresponding to each of the three diagnostic notions. For error reporting (1), it exploits a binary search-based algorithm that minimizes error-witnessing slices. To solve for slices that verify (2 and 3), we empirically compare different algorithms based on unsatisfiable cores, minimal unsatisfiable subset enumeration, and a direct SMT encoding of the slicing problem. Our empirical evaluation of Brutus on existing and new benchmarks shows that we can find slices that are both small and informative.

cs.PL↗

arXiv2024

Exact Bayesian Inference for Loopy Probabilistic Programs using Generating Functions

We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded loops. Our method is built on a denotational semantics represented by probability generating functions, which resolves semantic intricacies induced by intertwining discrete probabilistic loops with conditioning (for encoding posterior observations). We implement our method in a tool called Prodigy; it augments existing computer algebra systems with the theory of generating functions for the (semi-)automatic inference and quantitative verification of conditioned probabilistic programs. Experimental results show that Prodigy can handle various infinite-state loopy programs and exhibits comparable performance to state-of-the-art exact inference tools over loop-free benchmarks.

cs.PL↗

arXiv2024

Unknown Biases and Timing Constraints in Timed Automata

Timed automata are the formal model for real-time systems. Extensions with discrete probabilistic branching have been considered in the literature and successfully applied. Probabilistic timed automata (PTA) do require all branching probabilities and clock constraints to be constants. This report investigates PTA in which this constraint is relaxed: both branching probabilities and clock constraints can be parametric. We formally define this PTA variant and define its semantics by an uncountable parametric Markov Decision Process (pMDP). We show that reachability probabilities in parametric L/U-PTA can be reduced to considering PTA with only parametric branching probabilities. This enables the usage of existing techniques from the literature. Finally, we generalize the symbolic backward and digital clock semantics of PTA to the setting with parametric probabilities and constraints.

cs.LO↗