Weighted programming: A programming paradigm for specifying mathematical models

We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic branching and (2) weighting execution traces. Weights can be numbers but also other objects like words from an alphabet, polynomials, formal power series, or cardinal numbers. We argue that weighted programming as a paradigm can be used to specify mathematical models beyond probability distributions (as is done in probabilistic programming). We develop weakest-precondition- and weakest-liberal-precondition-style calculi à la Dijkstra for reasoning about mathematical models specified by weighted programs. We present several case studies. For instance, we use weighted programming to model the ski rental problem - an optimization problem. We model not only the optimization problem itself, but also the best deterministic online algorithm for solving this problem as weighted programs. By means of weakest-precondition-style reasoning, we can determine the competitive ratio of the online algorithm on source code level

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

compass 3 0

COMPASS (COrrectness, Modeling and Performance of AeroSpace Systems) is an international research effort aiming to ensure system-level correctness, safety, dependability and performability of on-board computer-based aerospace systems. In this paper we present COMPASS 3.0, which brings together the results of various development projects since the original inception of COMPASS. Improvements have been made both to the frontend, supporting an updated modeling language and user interface, as well as to the backend, by adding new functionalities and improving the existing ones. New features include Timed Failure Propagation Graphs, contract-based analysis, hierarchical fault tree generation, probabilistic analysis of non-deterministic models and statistical model checking

Faster and symbolic CTMC model checking

This paper reports on the implementation and the experiments with symbolic model checking of continuous-time Markov chains using multi-terminal binary decision diagrams (MTBDDs). Properties are expressed in Continuous Stochastic Logic (CSL) [7] which includes the means to express both transient and steady-state performance measures. We show that all CSL operators can be treated using standard operations on MTBDDs, thus allowing a rather straightforward implementation of symbolic CSL model checking on existing MTBDD-based platforms such as the verifier PRISM. The main result of the paper is an improvement of O(N)]]> in the time complexity of checking time-bounded until-formulas, where N is the number of states in the CTMC under consideration. This result yields a drastic speed-up in the verification time of model checking CTMCs, both in the symbolic and non-symbolic case

Parameterisation of Three-Valued Abstractions

Three-valued abstraction is an established technique in software model checking. It proceeds by generating an abstract state space model over the values true, false and unknown, where the latter value is used to represent the loss of information due to abstraction. Temporal logic properties can then be evaluated on such three-valued models. In case of an unknown result, the abstraction is iteratively refined, until a level of abstraction is reached where the property of interest can be either proven or refuted. In this paper, we introduce parameterised three-valued model checking. In our new type of abstract models, unknown parts can be either associated with the constant value unknown or with expressions over boolean parameters. Our parameterisation is an alternative way to state that the truth value of certain predicates or transitions is actually not known and that the checked property has to yield the same result under each possible parameter instantiation. A novel feature of our approach is that it allows for establishing logical connections between parameters: While unknown parts in pure three-valued models are never related to each other, our parameterisation approach enables to represent facts like 'a certain pair of transitions has unknown but complementary truth values', or 'the value of a predicate is unknown but remains constant along all states of a certain execution path'. We demonstrate that such facts can be automatically derived from the software system to be verified and that covering these facts in an abstract model can be crucial for the success and efficiency of checking temporal logic properties. Moreover, we introduce a fully automatic software verification framework based on counterexample-guided abstraction refinement and parameterisation.The revised post-proceedings are supposed to appear later (presumably 2015) in the LNCS series published by Springer-VerlagNational Research Foundation (NRF) of South Africahttp://www.ic.ufal.br/evento/cbsoft2014/en/program-sbmf.htm