Bounded Model Checking for Probabilistic Programs

In this paper we investigate the applicability of standard model checking approaches to verifying properties in probabilistic programming. As the operational model for a standard probabilistic program is a potentially infinite parametric Markov decision process, no direct adaption of existing techniques is possible. Therefore, we propose an on-the-fly approach where the operational model is successively created and verified via a step-wise execution of the program. This approach enables to take key features of many probabilistic programs into account: nondeterminism and conditioning. We discuss the restrictions and demonstrate the scalability on several benchmarks

Understanding Probabilistic Programs

We present two views of probabilistic programs and their relationship. An operational interpretation as well as a weakest pre-condition semantics are provided for an elementary probabilistic guarded command language. Our study treats important features such as sampling, conditioning, loop divergence, and non-determinism

Finding polynomial loop invariants for probabilistic programs

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.Comment: accompanies an ATVA 2017 submissio

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

PrIC3: Property Directed Reachability for MDPs

IC3 has been a leap forward in symbolic model checking. This paper proposes PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic model checking of MDPs. Our main focus is to develop the theory underlying PrIC3. Alongside, we present a first implementation of PrIC3 including the key ingredients from IC3 such as generalization, repushing, and propagation

Maximizing the Conditional Expected Reward for Reaching the Goal

The paper addresses the problem of computing maximal conditional expected accumulated rewards until reaching a target state (briefly called maximal conditional expectations) in finite-state Markov decision processes where the condition is given as a reachability constraint. Conditional expectations of this type can, e.g., stand for the maximal expected termination time of probabilistic programs with non-determinism, under the condition that the program eventually terminates, or for the worst-case expected penalty to be paid, assuming that at least three deadlines are missed. The main results of the paper are (i) a polynomial-time algorithm to check the finiteness of maximal conditional expectations, (ii) PSPACE-completeness for the threshold problem in acyclic Markov decision processes where the task is to check whether the maximal conditional expectation exceeds a given threshold, (iii) a pseudo-polynomial-time algorithm for the threshold problem in the general (cyclic) case, and (iv) an exponential-time algorithm for computing the maximal conditional expectation and an optimal scheduler.Comment: 103 pages, extended version with appendices of a paper accepted at TACAS 201

Probabilistic abstract interpretation: From trace semantics to DTMC’s and linear regression

In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties

Chylous ascites following robotic lymph node dissection on a patient with metastatic cervical carcinoma

Chylous ascites is an uncommon postoperative complication of gynecological surgery. We report a case of chylous ascites following a robotic lymph node dissection for a cervical carcinoma. A 38-year-old woman with IB2 cervical adenocarcinoma with a palpable 3 cm left external iliac lymph node was taken to the operating room for robotic-assisted laparoscopic pelvic and para-aortic lymph node dissection. Patient was discharged on postoperative day 2 after an apparent uncomplicated procedure. The patient was readmitted the hospital on postoperative day 9 with abdominal distention and a CT-scan revealed free fluid in the abdomen and pelvis. A paracentesis demonstrated milky-fluid with an elevated concentration of triglycerides, confirming the diagnosis of chylous ascites. She recovered well with conservative measures. The risk of postoperative chylous ascites following lymph node dissection is still present despite the utilization of new technologies such as the da Vinci robot

On dynamical probabilities, or: how to learn to shoot straight

© IFIP International Federation for Information Processing 2016.In order to support, for example, a quantitative analysis of various algorithms, protocols etc. probabilistic features have been introduced into a number of programming languages and calculi. It is by now quite standard to define the formal semantics of (various) probabilistic languages, for example, in terms of Discrete Time Markov Chains (DTMCs). In most cases however the probabilities involved are represented by constants, i.e. one deals with static probabilities. In this paper we investigate a semantical framework which allows for changing, i.e. dynamic probabilities which is still based on time-homogenous DTMCs, i.e. the transition matrix representing the semantics of a program does not change over time

A customized stand-alone photometric Raman sensor applicable in explosive atmospheres: a proof-of-concept study

This paper presents an explosion-proof two-channel Raman photometer designed for chemical process monitoring in hazardous explosive atmospheres. Due to its design, alignment of components is simplified and economic in comparison to spectrometer systems. Raman spectrometers have the potential of becoming an increasingly important tool in process analysis technologies as part of molecular-specific concentration monitoring. However, in addition to the required laser power, which restricts use in potentially explosive atmospheres, the financial hurdle is also high. Within the scope of a proof of concept, it is shown that photometric measurements of Raman scattering are possible. The use of highly sensitive detectors allows the required excitation power to be reduced to levels compliant for operation in potentially explosive atmospheres. The addition of an embedded platform enables stable use as a self-sufficient sensor, since it carries out all calculations internally.Multi-pixel photon counters (MPPCs) with large detection areas of 1350&thinsp;µm2 are implemented as detectors. As a result, the sensitivity of the sensor is strongly increased. This gain in sensitivity is primarily achieved through two characteristics: first, the operating principle avalanche breakdown to detect single photons is used; second, the size of the image projected onto the MPPC is much bigger than the pixel area in competing Raman-Spectrometers resulting in higher photon flux. This combination enables reduction of the required excitation power to levels compliant for operation in potentially explosive atmospheres. All presented experiments are performed with strongly attenuated laser power of 35&thinsp;mW. These include the monitoring of the analytes ethanol and hydrogen peroxide as well as the reversible binding of CO2 to amine. Accordingly, the described embedded sensor is ideally suited as a process analytical technology (PAT) tool for applications in environments with limitations on power input.</p