Inferring Expected Runtimes of Probabilistic Integer Programs Using Expected Sizes

Meyer, Fabian; Hark, Marcel; Giesl, Jürgen

doi:10.1007/978-3-030-72016-2_14

Cited by 20 publications

(17 citation statements)

References 54 publications

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“…Our second set of benchmarks, shown in Table 3, confirms the correctness of (1-inductive) bounds on the expected runtime of pGCL programs synthesized by the runtime analyzers Absynth [56] and (later) KoAT [52]; this gives a baseline for evaluating the performance of our implementation. Moreover, it demonstrates the flexibility of our approach as we effortlessly apply the expected runtime calculus [40] instead of the weakest preexpectation calculus for verification.…”

Section: Methodssupporting

confidence: 63%

Latticed k-Induction with an Application to Probabilistic Programs

Batz

Chen

Kaminski

et al. 2021

Computer Aided Verification

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We revisit two well-established verification techniques, k-induction and bounded model checking (BMC), in the more general setting of fixed point theory over complete lattices. Our main theoretical contribution is latticed k-induction, which (i) generalizes classical k-induction for verifying transition systems, (ii) generalizes Park induction for bounding fixed points of monotonic maps on complete lattices, and (iii) extends from naturals k to transfinite ordinals $$\kappa $$ κ , thus yielding $$\kappa $$ κ -induction.The lattice-theoretic understanding of k-induction and BMC enables us to apply both techniques to the fully automatic verification of infinite-state probabilistic programs. Our prototypical implementation manages to automatically verify non-trivial specifications for probabilistic programs taken from the literature that—using existing techniques—cannot be verified without synthesizing a stronger inductive invariant first.

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Section: Methodssupporting

confidence: 63%

Latticed k-Induction with an Application to Probabilistic Programs

Batz

Chen

Kaminski

et al. 2021

Computer Aided Verification

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“…These methods have lent themselves to various generalisations, including polynomial programs, programs with non-determinism, lexicographic and modular termination arguments, and persistence properties [2,[14][15][16]20,25]. Recently, for special classes of probabilistic programs or term rewriting systems, novel automated proof techniques that leverage computer algebra systems and satisfiability modulo theories (SMT) have been introduced [5,6,38,39,41]. All the above methods are sound and, under specific assumptions, complete; they represent the state of the art for the class of programs they have been designed for.…”

Section: Introductionmentioning

confidence: 99%

Learning Probabilistic Termination Proofs

Abate

Giacobbe

Roy

2021

Computer Aided Verification

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We present the first machine learning approach to the termination analysis of probabilistic programs. Ranking supermartingales (RSMs) prove that probabilistic programs halt, in expectation, within a finite number of steps. While previously RSMs were directly synthesised from source code, our method learns them from sampled execution traces. We introduce the neural ranking supermartingale: we let a neural network fit an RSM over execution traces and then we verify it over the source code using satisfiability modulo theories (SMT); if the latter step produces a counterexample, we generate from it new sample traces and repeat learning in a counterexample-guided inductive synthesis loop, until the SMT solver confirms the validity of the RSM. The result is thus a sound witness of probabilistic termination. Our learning strategy is agnostic to the source code and its verification counterpart supports the widest range of probabilistic single-loop programs that any existing tool can handle to date. We demonstrate the efficacy of our method over a range of benchmarks that include linear and polynomial programs with discrete, continuous, state-dependent, multi-variate, hierarchical distributions, and distributions with undefined moments.

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“…As such, we conduct experiments using a total of 50 challenging benchmarks, involving polynomial arithmetic, probability distributions and symbolic constants. Further, we compare Amber not only against Absynth and MGen (as in [19]), but also evaluate Amber in comparison to the recent tools LexRSM [1], KoAT2 [18] and ecoimp [2]. Note that MGen can only certify PAST and LexRSM only AST.…”

Section: Discussionmentioning

confidence: 99%

“…Amber successfully certifies 23 out of the 27 PAST benchmarks (Table 1). Although Absynth, KoAT2 and ecosimp can find expected cost upper bounds for large programs [20,18,2], they struggle on small programs whose termination is not known a priori. For instance, they struggle when a benchmark probabilistically "chooses'' between two polynomials working against each other (one moving the program state away from a termination criterion and one towards it).…”

Section: Discussionmentioning

confidence: 99%

“…The tools MGen [6] and LexRSM [1] use linear programming techniques to certify PAST and AST, respectively. The recent tools Absynth [20], KoAT2 [18] and ecoimp [2] can establish upper bounds on expected costs, therefore also on expected runtimes, and thus certify PAST. While powerful on respective AST/PAST domains, we note that none of the aforementioned tools support both proving and disproving (P)AST.…”

Section: Introductionmentioning

confidence: 99%

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The Probabilistic Termination Tool Amber

Marcel¹,

Bartocci²,

Katoen³

et al. 2021

Preprint

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We describe the Amber tool for proving and refuting the termination of a class of probabilistic while-programs with polynomial arithmetic, in a fully automated manner. Amber combines martingale theory with properties of asymptotic bounding functions and implements relaxed versions of existing probabilistic termination proof rules to prove/disprove (positive) almost sure termination of probabilistic loops. Amber supports programs parameterized by symbolic constants and drawing from common probability distributions. Our experimental comparisons give practical evidence of Amber outperforming existing state-of-the-art tools.

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Inferring Expected Runtimes of Probabilistic Integer Programs Using Expected Sizes

Cited by 20 publications

References 54 publications

Latticed k-Induction with an Application to Probabilistic Programs

Latticed k-Induction with an Application to Probabilistic Programs

Learning Probabilistic Termination Proofs

The Probabilistic Termination Tool Amber

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