Learning Probabilistic Termination Proofs

Abate, Alessandro; Giacobbe, Mirco; Roy, Diptarko

doi:10.1007/978-3-030-81688-9_1

Cited by 14 publications

(9 citation statements)

References 44 publications

(49 reference statements)

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“…[10] can prove bounds on expected values via symbolic reasoning and Doob's decomposition, which, however, requires user-supplied invariants and hints. [1] employs a CEGIS loop to train a neural network dedicated to learning a ranking supermartingale witnessing UPAST of (possibly continuous) probabilistic programs. They also use counterexamples provided by SMT solvers to guide the learning process.…”

Section: Related Workmentioning

confidence: 99%

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

Batz

Chen

Junges

et al. 2023

Lecture Notes in Computer Science

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Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such quantitative reachability properties by generating inductive invariants on source-code level. Our implementation shows promise: It finds invariants for (in)finite-state programs, can beat state-of-the-art probabilistic model checkers, and is competitive with modern tools dedicated to invariant synthesis and expected runtime reasoning.

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Section: Related Workmentioning

confidence: 99%

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

Batz

Chen

Junges

et al. 2023

Lecture Notes in Computer Science

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“…This is a qualitative reachability property, in contrast to the quantitative properties studied here. In particular, [3] use a CEGIS-based approach to synthesise neural RSMs.…”

Section: Martingalesmentioning

confidence: 99%

“…Widely applied in many areas of artificial intelligence, neural networks are increasingly used as representations of formal certificates for the correctness of systems. Previous work has applied machine learning to the formal verification of computer programs [3,26,40,43,45,51,61], and of dynamical and control systems [2,14,34,44,46,53].…”

Section: Introductionmentioning

confidence: 99%

Quantitative Verification With Neural Networks For Probabilistic Programs and Stochastic Systems

Abate¹,

Edwards²,

Giacobbe³

et al. 2023

Preprint

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We present a machine learning approach to quantitative verification. We investigate the quantitative reachability analysis of probabilistic programs and stochastic systems, which is the problem of computing the probability of hitting in finite time a given target set of states. This general problem subsumes a wide variety of other quantitative verification problems, from the invariant and the safety analysis of discrete-time stochastic systems to the assertion-violation and the termination analysis of single-loop probabilistic programs. We exploit the expressive power of neural networks as novel templates for indicating supermartingale functions, which provide general certificates of reachability that are both tight and sound. Our method uses machine learning to train a neural certificate that minimises an upper bound for the probability of reachability over sampled observations of the state space. Then, it uses satisfiability modulo theories to verify that the obtained neural certificate is valid over every possible state of the program and conversely, upon receiving a counterexample, it refines neural training in a counterexample-guided inductive synthesis loop, until the solver confirms the certificate. We experimentally demonstrate on a diverse set of benchmark probabilistic programs and stochastic dynamical models that neural indicating supermartingales yield smaller or comparable probability bounds than existing state-of-the-art methods in all cases, and further that the approach succeeds on models that are entirely beyond the reach of such alternative techniques.

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“…We are not aware of other data-driven methods for learning probabilistic invariants, but a recent work Abate et al [36] proves probabilistic termination by learning ranking supermartingales from trace data. Our method for learning sub-invariants (Section 6) can be seen as a natural generalization of their approach.…”

Section: Data-driven Invariant Synthesismentioning

confidence: 99%

Data-Driven Invariant Learning for Probabilistic Programs

Bao

Trivedi

Pathak³

et al. 2023

Preprint

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Morgan and McIver’s weakest pre-expectation framework is one of the most well-established methods for deductive verification of probabilistic programs. Roughly,the idea is to generalize binary state assertions to real-valued expectations, whichcan measure expected values of probabilistic program quantities. While loop-freeprograms can be analyzed by mechanically transforming expectations, verifyingloops usually requires finding an invariant expectation, a difficult task.We propose a new view of invariant expectation synthesis as a regression prob-lem: given an input state, predict the average value of the post-expectation inthe output distribution. Guided by this perspective, we develop the first data-driven invariant synthesis method for probabilistic programs. Unlike prior workon probabilistic invariant inference, our approach can learn piecewise continuousinvariants without relying on template expectations. We also develop a data-driven approach to learn sub-invariants from data, which can be used to upper-or lower-bound expected values. We implement our approaches and demonstratetheir effectiveness on a variety of benchmarks from the probabilistic programmingliterature.

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Learning Probabilistic Termination Proofs

Cited by 14 publications

References 44 publications

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

Quantitative Verification With Neural Networks For Probabilistic Programs and Stochastic Systems

Data-Driven Invariant Learning for Probabilistic Programs

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