Runtime Analysis of Probabilistic Programs with Unbounded Recursion

Brázdil, Tomǎš; Kiefer, Stefan; Kučera, Antonín; Vařeková, Ivana Hutařová

doi:10.1007/978-3-642-22012-8_25

Cited by 15 publications

(19 citation statements)

References 14 publications

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“…where "⊑" is the partial order over RtEnv 5 The formal definition of the syntactic replacement proceeds by a routine induction on the structure of D(P). 6 Strictly speaking, call D n P is a pGCL-program. We therefore prefer to write ert call D n P (t ) rather than ert call D n P, D (t ).…”

Section: Finite Approximations Of Recursive Programsmentioning

confidence: 99%

“…This knowledge is necessary upon the termination of a procedure to determine whether this termination represents the "entire" program termination or the execution is to be continued with the remainder statements of the caller. This kind of book-keeping of procedure calls is done by extending MCs to pushdown Markov chains (PMC) [22] whose verification has been studied by Brázdil, Esparza and Kucera [5,6,29]. Formally, a PMC is a tuple P = (S, Γ, γ 0 , P, s init , rew), where S is a countable, non-empty set of control states, Γ is a finite stack alphabet, γ 0 ∈ Γ is a special bottom-of-stack symbol,…”

Section: Operational Modelmentioning

confidence: 99%

“…His analysis can be used to prove the soundness of experimental statistical methods to determine the average runtime of probabilistic programs. Brázdil et al [6] study the runtime of probabilistic programs with unbounded recursion by considering probabilistic pushdown automata (pPDAs). They show (using martingale theory) that for every pPDA the probability of performing a long run decreases exponentially (polynomially) in the length of the run, iff the pPDA has a finite (infinite) expected runtime.…”

Section: Related Workmentioning

confidence: 99%

“…They show (using martingale theory) that for every pPDA the probability of performing a long run decreases exponentially (polynomially) in the length of the run, iff the pPDA has a finite (infinite) expected runtime. As opposed to our program verification technique, [6] considers reasoning at the operational level. Fioriti and Hermanns [12] proposed a typing scheme for deciding almost-sure termination.…”

Section: Related Workmentioning

confidence: 99%

See 3 more Smart Citations

Weakest Precondition Reasoning for Expected Runtimes of Randomized Algorithms

Kaminski

Katoen

Matheja

et al. 2018

J. ACM

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This paper presents a wp-style calculus for obtaining bounds on the expected runtime of randomized algorithms. Its application includes determining the (possibly infinite) expected termination time of a randomized algorithm and proving positive almost-sure termination-does a program terminate with probability one in finite expected time? We provide several proof rules for bounding the runtime of loops, and prove the soundness of the approach with respect to a simple operational model. We show that our approach is a conservative extension of Nielson's approach for reasoning about the runtime of deterministic programs. We analyze the expected runtime of some example programs including the coupon collector's problem, a one-dimensional random walk and a randomized binary search.

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Section: Finite Approximations Of Recursive Programsmentioning

confidence: 99%

Section: Operational Modelmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Weakest Precondition Reasoning for Expected Runtimes of Randomized Algorithms

Kaminski

Katoen

Matheja

et al. 2018

J. ACM

View full text Add to dashboard Cite

show abstract

“…Model-checking algorithms have been proposed for both linear and branching temporal logics [12,16,26], algorithms deciding properties of several kinds of games have been described (see e.g. [15]), and distributions and expectations of performance measures such as run-time and memory consumption have been investigated [13,5,6].…”

Section: Introductionmentioning

confidence: 99%

On Probabilistic Parallel Programs with Process Creation and Synchronisation

Kiefer

Wojtczak

2011

Tools and Algorithms for the Construction and Analysis of Systems

Self Cite

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Abstract. We initiate the study of probabilistic parallel programs with dynamic process creation and synchronisation. To this end, we introduce probabilistic split-join systems (pSJSs), a model for parallel programs, generalising both probabilistic pushdown systems (a model for sequential probabilistic procedural programs which is equivalent to recursive Markov chains) and stochastic branching processes (a classical mathematical model with applications in various areas such as biology, physics, and language processing). Our pSJS model allows for a possibly recursive spawning of parallel processes; the spawned processes can synchronise and return values. We study the basic performance measures of pSJSs, especially the distribution and expectation of space, work and time. Our results extend and improve previously known results on the subsumed models. We also show how to do performance analysis in practice, and present two case studies illustrating the modelling power of pSJSs.

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New Approaches for Almost-Sure Termination of Probabilistic Programs

Huang

Chatterjee

2018

Programming Languages and Systems

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We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover, using this approach we can obtain explicit optimal bounds on tail probabilities of non-termination within a given number of steps. Second, we present a new approach based on Central Limit Theorem for the almost-sure termination problem, and show that this approach can establish almost-sure termination of programs which none of the existing approaches can handle. Finally, we discuss algorithmic approaches for the two above methods that lead to automated analysis techniques for almost-sure termination of probabilistic programs.

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Runtime Analysis of Probabilistic Programs with Unbounded Recursion

Cited by 15 publications

References 14 publications

Weakest Precondition Reasoning for Expected Runtimes of Randomized Algorithms

Weakest Precondition Reasoning for Expected Runtimes of Randomized Algorithms

On Probabilistic Parallel Programs with Process Creation and Synchronisation

New Approaches for Almost-Sure Termination of Probabilistic Programs

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