Generating Functions for Probabilistic Programs

Lutz, Klinkenberg,; Batz, Kevin; Kaminski, Benjamin Lucien; Katoen, Joost-Pieter; Moerman, Joshua; Winkler, Tobias

doi:10.1007/978-3-030-68446-4_12

Cited by 7 publications

(23 citation statements)

References 25 publications

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“…Table 1). This is in contrast to the PGF semantics from [41] which operates on infinite sums in a non-constructive fashion.…”

Section: From Programs To Pgf Transformersmentioning

confidence: 86%

“…of prev. line (The rightmost four lines explain this annotation style which is due to [41].) Note that 0.5Y 2 + 0.5Y 3 is indeed the marginal of the input distribution in Y .…”

Section: From Programs To Pgf Transformersmentioning

confidence: 97%

“…Following [41], we show that Ψ ϕ,P is sufficiently well-behaved to allow reasoning about loops by fixed point induction.…”

Section: Reasoning About Loopsmentioning

confidence: 97%

“…The while-Loop. The fixed point semantics of the while loop is standard [41,43] and reflects the intuitive unrolling rule, namely that while (ϕ) {P } is equivalent to if (ϕ) {P while (ϕ) {P }} else {skip}. Indeed, the fixed point formula in Table 2 can be derived using the semantics of if discussed above.…”

Section: From Programs To Pgf Transformersmentioning

confidence: 99%

“…(C3) To decide problem (⋆) -even for a loop-free program L-one has to account for infinitely or even uncountably many inputs such that L yields the same distribution as encoded by S when being deployed in all possible contexts. We address challenge (C1) by exploiting the forward denotational semantics of probabilistic programs based on probability generating function (PGF) representations of (sub-)distributions [41], which benefits crucially from closedform (i.e., finite) PGF representations of possibly infinite-support distributions. A probabilistic program L hence acts as a transformer L (•) that transforms an input PGF g into an output PGF L (g) (as an instantiation of Kozen's transformer semantics [42]).…”

Section: Introductionmentioning

confidence: 99%

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Does a Program Yield the Right Distribution? Verifying Probabilistic Programs via Generating Functions

Chen¹,

Katoen²,

Lutz³

et al. 2022

Preprint

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We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a program generates exactly a specified distribution over its outputs (provided the program terminates almost surely). The class of distributions that can be specified in our formalism consists of standard distributions (geometric, uniform, etc.) and finite convolutions thereof. Our method relies on representing these (possibly infinite-support) distributions as probability generating functions which admit effective arithmetic operations. We have automated our techniques in a tool called Prodigy, which supports automatic invariance checking, compositional reasoning of nested loops, and efficient queries to the output distribution, as demonstrated by experiments.

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“…Table 1). This is in contrast to the PGF semantics from [41] which operates on infinite sums in a non-constructive fashion.…”

Section: From Programs To Pgf Transformersmentioning

confidence: 86%

“…of prev. line (The rightmost four lines explain this annotation style which is due to [41].) Note that 0.5Y 2 + 0.5Y 3 is indeed the marginal of the input distribution in Y .…”

Section: From Programs To Pgf Transformersmentioning

confidence: 97%

“…Following [41], we show that Ψ ϕ,P is sufficiently well-behaved to allow reasoning about loops by fixed point induction.…”

Section: Reasoning About Loopsmentioning

confidence: 97%

Section: From Programs To Pgf Transformersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Does a Program Yield the Right Distribution? Verifying Probabilistic Programs via Generating Functions

Chen¹,

Katoen²,

Lutz³

et al. 2022

Preprint

Self Cite

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Does a Program Yield the Right Distribution?

Chen

Katoen

Lutz

et al. 2022

Lecture Notes in Computer Science

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We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a program generates exactly a specified distribution over its outputs (provided the program terminates almost-surely). The class of distributions that can be specified in our formalism consists of standard distributions (geometric, uniform, etc.) and finite convolutions thereof. Our method relies on representing these (possibly infinite-support) distributions as probability generating functions which admit effective arithmetic operations. We have automated our techniques in a tool called $$\textsc {Prodigy}$$ P R O D I G Y , which supports automatic invariance checking, compositional reasoning of nested loops, and efficient queries to the output distribution, as demonstrated by experiments.

show abstract