Tensor Probabilistic Model Checking of Finite-Horizon Markov Chains (Extended Version)

2026-07-31

AI Summary

This work addresses the problem of verifying the probability that a dense Markov chain reaches a target state within a finite number of steps—a task for which existing approaches suffer from limited scalability due to the density of the transition matrix. To overcome this challenge, the paper presents the first formalization of probabilistic model checking as dense tensor operations and introduces an end-to-end compiler toolchain tailored for efficient execution on hardware accelerators. The proposed method preserves correctness while substantially improving verification performance. Experimental evaluation demonstrates that the prototype tool, Tessa, achieves significant speedups over the current state-of-the-art on standard benchmarks.

Abstract

We reexamine the problem of verifying Markov chains with respect to step-bounded reachability probabilities. Prevailing approaches rely on encoding the state-transition matrix using either explicit or symbolic representations. While these approaches are effective for sparse transition dynamics, they scale less favorably in the dense regime. Our insight is to cast probabilistic model checking of Markov chains as computations over dense tensors. This methodology enables the use of off-the-shelf compiler toolchains for optimized execution of these tensor computations on hardware accelerators. We prove the soundness of the methodology of mapping probabilistic model checking to tensor computations. We implement our approach in a tool called Tessa . Empirical evaluation shows that Tessa unlocks massive speedups over state-of-theart methods on selected benchmarks from the literature.

Problem

• Markov Chains
• Probabilistic Model Checking
• Step-bounded Reachability
• Dense Transition Matrices
• Tensor Computations

Innovation

• tensor computation
• probabilistic model checking
• Markov chains
• hardware acceleration
• dense transition matrices