ترغب بنشر مسار تعليمي؟ اضغط هنا

Inferring Expected Runtimes of Probabilistic Integer Programs Using Expected Sizes

62   0   0.0 ( 0 )
 نشر من قبل Marcel Hark
 تاريخ النشر 2020
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

We present a novel modular approach to infer upper bounds on the expected runtime of probabilistic integer programs automatically. To this end, it computes bounds on the runtime of program parts and on the sizes of their variables in an alternating way. To evaluate its power, we implemented our approach in a new version of our open-source tool KoAT.

قيم البحث

اقرأ أيضاً

We study weakest precondition reasoning about the (co)variance of outcomes and the variance of run-times of probabilistic programs with conditioning. For outcomes, we show that approximating (co)variances is computationally more difficult than approx imating expected values. In particular, we prove that computing both lower and upper bounds for (co)variances is $Sigma^{0}_{2}$-complete. As a consequence, neither lower nor upper bounds are computably enumerable. We therefore present invariant-based techniques that do enable enumeration of both upper and lower bounds, once appropriate invariants are found. Finally, we extend this approach to reasoning about run-time variances.
Free-Choice Workflow Petri nets, also known as Workflow Graphs, are a popular model in Business Process Modeling. In this paper we introduce Timed Probabilistic Workflow Nets (TPWNs), and give them a Markov Decision Process (MDP) semantics. Since t he time needed to execute two parallel tasks is the maximum of the times, and not their sum, the expected time cannot be directly computed using the theory of MDPs with rewards. In our first contribution, we overcome this obstacle with the help of earliest-first schedulers, and give a single exponential-time algorithm for computing the expected time. In our second contribution, we show that computing the expected time is #P-hard, and so polynomial algorithms are very unlikely to exist. Further, #P-hardness holds even for workflows with a very simple structure in which all transitions times are 1 or 0, and all probabilities are 1 or 0.5. Our third and final contribution is an experimental investigation of the runtime of our algorithm on a set of industrial benchmarks. Despite the negative theoretical results, the results are very encouraging. In particular, the expected time of every workflow in a popular benchmark suite with 642 workflow nets can be computed in milliseconds.
Building upon recent work on probabilistic programs, we formally define the notion of expected runtime for quantum programs. A representation of the expected runtimes of quantum programs is introduced with an interpretation as an observable in physic s. A method for computing the expected runtimes of quantum programs in finite-dimensional state spaces is developed. Several examples are provided as applications of this method; in particular, an open problem of computing the expected runtime of quantum random walks is solved using our method.
The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A prev ious approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gamblers Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature.
Let $K in R^d$ be a convex body, and assume that $L$ is a randomly rotated and shifted integer lattice. Let $K_L$ be the convex hull of the (random) points $K cap L$. The mean width $W(K_L)$ of $K_L$ is investigated. The asymptotic order of the mean width difference $W(l K)-W((l K)_L)$ is maximized by the order obtained by polytopes and minimized by the order for smooth convex sets as $l to infty$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا