fixed point theory

A Unified Framework for Quantitative Analysis of Probabilistic Programs
Verifying probabilistic programs requires reasoning about various probabilistic behaviors, e.g., random sampling, nondeterminism, and …
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A Unified Framework for Quantitative Analysis of Probabilistic Programs
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 …
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Exact Bayesian Inference for Loopy Probabilistic Programs using Generating Functions
Latticed Craig Interpolation with an Application to Probabilistic Verification

In this work, we are primarily concerned with the question: Is Craig interpolation applicable to the automatic, quantitative …
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Latticed Craig Interpolation with an Application to Probabilistic Verification
Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants
Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite …
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Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants
Lower Bounds for Possibly Divergent Probabilistic Programs
We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to …
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Lower Bounds for Possibly Divergent Probabilistic Programs
Latticed $k$-Induction with an Application to Probabilistic Programs
We revisit two well-established verification techniques, $k$-induction and bounded model checking (BMC), in the more general setting of …
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Latticed $k$-Induction with an Application to Probabilistic Programs