Backwards Abstract Interpretation of Probabilistic Programs

Monniaux, David

doi:10.1007/3-540-45309-1_24

Cited by 22 publications

(24 citation statements)

References 16 publications

(21 reference statements)

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“…This matches the standard probabilistic program semantics [15,21]. We now describe the construction of the distribution D n+1 for the (n + 1) th loop iteration, given the distribution D n at the n th step.…”

Section: Operator Semanticsmentioning

confidence: 81%

“…Instead of the explicit representations of distributions found in these works, we characterize sets of distributions by means of bounds on moments of expressions. Alternatively, Monniaux presents a backward abstract interpretation scheme to compute the probability of an observable assertion at the program output, and characterize the output distribution [21]. The backwards approach treats the program as a measurable function, and the backward abstract interpretation follows the natural definition of the output distribution through the inverse mapping [5].…”

Section: Introductionmentioning

confidence: 99%

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Expectation Invariants for Probabilistic Program Loops as Fixed Points

Chakarov

Sankaranarayanan

2014

Static Analysis

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We present static analyses for probabilistic loops using expectation invariants. Probabilistic loops are imperative while-loops augmented with calls to random value generators. Whereas, traditional program analysis uses Floyd-Hoare style invariants to over-approximate the set of reachable states, our approach synthesizes invariant inequalities involving the expected values of program expressions at the loop head. We first define the notion of expectation invariants, and demonstrate their usefulness in analyzing probabilistic program loops. Next, we present the set of expectation invariants for a loop as a fixed point of the pre-expectation operator over sets of program expressions. Finally, we use existing concepts from abstract interpretation theory to present an iterative analysis that synthesizes expectation invariants for probabilistic program loops. We show how the standard polyhedral abstract domain can be used to synthesize expectation invariants for probabilistic programs, and demonstrate the usefulness of our approach on some examples of probabilistic program loops.

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Section: Operator Semanticsmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Expectation Invariants for Probabilistic Program Loops as Fixed Points

Chakarov

Sankaranarayanan

2014

Static Analysis

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“…The particular abstract domain we use for this purpose builds on Monniaux's work on probabilistic abstract interpretation [20,21]. However, sound analysis of probabilistic systems has also been explored by other researchers [1,12,18,29], and it is plausible that our smoothing technique could be combined with these other abstractions.…”

Section: Related Workmentioning

confidence: 99%

Bridging boolean and quantitative synthesis using smoothed proof search

Chaudhuri

Clochard

Solar-Lezama

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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We present a new technique for parameter synthesis under boolean and quantitative objectives. The input to the technique is a "sketch" -a program with missing numerical parameters -and a probabilistic assumption about the program's inputs. The goal is to automatically synthesize values for the parameters such that the resulting program satisfies: (1) a boolean specification, which states that the program must meet certain assertions, and (2) a quantitative specification, which assigns a real valued rating to every program and which the synthesizer is expected to optimize.Our method -called smoothed proof search -reduces this task to a sequence of unconstrained smooth optimization problems that are then solved numerically. By iteratively solving these problems, we obtain parameter values that get closer and closer to meeting the boolean specification; at the limit, we obtain values that provably meet the specification. The approximations are computed using a new notion of smoothing for program abstractions, where an abstract transformer is approximated by a function that is continuous according to a metric over abstract states.We present a prototype implementation of our synthesis procedure, and experimental results on two benchmarks from the embedded control domain. The experiments demonstrate the benefits of smoothed proof search over an approach that does not meet the boolean and quantitative synthesis goals simultaneously.

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“…The computations for f e+ will be done symbolically in an abstract domain such as the ones described in [23,24] (Fig. 5 and 6).…”

Section: General Casementioning

confidence: 99%

“…The reasons for those notations are explained in earlier works on the linear adjoint of Kozen's denotational semantics for probabilistic programs [23].…”

Section: Partitioning In Programsmentioning

confidence: 99%