Probabilistic programming is a fascinating new direction in programming.
FaceBook, Google and Microsoft, to mention a few, are investing lots of
research efforts in probabilistic programming. Nearly every programming
Prolog, C, Python, you name it, and — yes — even Excel has been
extended with features for randomness. These languages aim to make
probabilistic modeling and machine learning accessible to any
programmer, any user.
Probabilistic programs describe recipes on how to infer conclusions
about big data from a mixture of uncertain data and real-world
observations. Bayesian networks, a key model in decision making, are
simple instances of such programs. Probabilistic programs steer
autonomous robots and self-driving cars, are key to describe security
mechanisms, naturally encode randomised algorithms, and are rapidly
encroaching AI and machine learning.
In this talk, I will explain what probabilistic programming is, give a
historical perspective, describe its applications, and indicate what
formal methods can mean for probabilistic programs.
First-order logic with quantifiers is undecidable in general, but some expressive fragments have complete instantiation. This means, it is sufficient to instantiate the quantified formulas with a finite set of ground terms computed from the formula, and then solve the resulting quantifier-free conjunction with an SMT solver. A challenge is to select the relevant instances in order to avoid producing too many new formulas that slow down the solver.
In this talk we will present a new approach that treats quantified formulas in SMT solvers in the style of a theory solver in the DPLL(T) framework. This comprises methods to detect instances of quantified formulas that are in conflict with the current boolean assignment of the ground literals or lead to a ground propagation. In particular, we will discuss how E-matching, the most common heuristic method for quantifier instantiation in SMT solvers, can be used to find these specific instances.
The presented approach is work in progress. Future work encompasses combining the approach with model-based quantifier instantiation in order to get completeness for decidable fragments.
In traditional complexity theory, the complexity of computational problems is
measured as a function of the size of the input. Nevertheless, in many situations
of practical relevance, analyzing the complexity of a problem only taking the size
of the input into consideration may not reflect the difficulty of solving that particular
problem on practical instances. Indeed, there are plenty of examples where a problem
is NP-hard but which can be solved efficiently by standard algorithms on empirically
inspired benchmarks. In parameterized complexity theory, the complexity of a problem
is measured not only in terms of the size of the input but also in terms of additional parameters that try to capture structural properties of the problem in question. In some cases, parameterized complexity theory offers a reasonable explanation of why such problems are solvable efficiently in practice: very often on practical instances, the parameters of relevance have small magnitude.
Most work in parameterized complexity theory deals with showing that certain NP-complete problems can be solved efficiently when certain relevant parameters are fixed. Nevertheless, not much has been done in classifying the parameterized complexity of problems that extremely hard from the perspective of classical complexity. In this talk, I will discuss a framework that allows
one to bring traditional tools of parameterized complexity theory to the realm of proof theory. In particular, we will define a suitable notion of width for proofs and will show how to construct proofs of small width in polynomial time.
We present an algorithm for the automatic synthesis of polynomial invariants for probabilistic transition systems.
Our approach is based on martingale theory.
We construct invariants in the form of polynomials over program variables, which give rise to martingales.
These polynomials are program invariants in the sense that their expected value upon termination is the same as their value at the start of the computation.
By exploiting geometric persistence properties of the system,
we show that suitable polynomials can be automatically inferred using sum-of-squares optimisation techniques.
Verification of concurrent software is a notoriously difficult
subject, whose complexities stem from the inability of the
existing verification methods to modularize, and thus divide and
conquer the verification problem.
Dependent types are a formal method well-known for its ability to
modularize and scale complex mathematical proofs. But, when it
comes to programming, dependent types are considered limited to
the purely functional programming model.
In this talk I will present my recent work towards reconciling
dependent types with shared memory concurrency, with the goal of
achieving modular verification for the latter. Applying the
type-theoretic paradigm to concurrency have lead to interesting
reformulations of some classical verification ideas, and to the
discovery of novel and useful abstractions for modularizing the
In this talk, I will give a perspective on inference in Bayes’ networks
(BNs) using program verification. I will argue how weakest precondition
reasoning a la Dijkstra can be used for exact inference (and more). As
exact inference is NP-complete, inference is typically done by means of
simulation. I will show how by means of wp-reasoning exact expected
sampling times of BNs can be obtained in a fully automated fashion. An
experimental evaluation on BN benchmarks demonstrates that very large
expected sampling times (in the magnitude of millions of years) can be
inferred within less than a second. This provides a means to decide
whether sampling-based methods are appropriate for a given BN. The key
ingredients are to reason at program code in a compositional manner.
Automated invariant generation is a fundamental challenge in program analysis and verification, going back many decades, and remains a topic of active research. In this talk I’ll present a select overview and survey of work on this problem, and discuss unexpected connections to other fields including quantum computing, group theory, and algebraic geometry. (No previous knowledge of these fields will be assumed.)
The operation of traditional computer networks is known to be a difficult manual and error-prone task. Over the last years, even tech-savvy companies have reported major issues with their network, due to misconfigurations, leading to disruptive downtimes. As a response to the difficulty of maintaining policy compliance, and given the critical role that computer networks (including the Internet, datacenter networks, enterprise networks) play today, researchers have started developing more principled approaches to networking and specification. Over the last years, we have witnessed great advances in the development of mathematical foundations for computer networks and the emergence of high-level network programming languages such as NetKAT. While powerful, however, existing formal frameworks often come with potentially high (super-polynomial) running times — even without considering failure scenarios.
This talk first gives an overview of the “softwarization” trends in communicaiton networks and motivates why formal methods are currently the “hot topic” in this area. I will then present a what-if analysis framework which allows us to verify important properties such as policy compliance and reachability in communication networks in polynomial time, even in the presence of (multiple) failures. Our framework relies on an automata-theoretic approach, and applies both to the widely deployed MPLS networks as well as to the emerging Segment Routing networks. In addition to the theory underlying our approach (presented at INFOCOM 2018 together with Jiri Srba, patent pending), I will also report on our query language, the tool we develop at Aalborg University, as well as on our first evaluation results.
I would also like to use the opportunity of this talk to provide a brief overview of our other research activities, especially the ones related to network security and the design of demand-aware and self-adjusting networks. We are currently eager to establish connections and collaborations within Vienna and Austria in general, related to all the presented topics and beyond. More details about our research activities can also be found at https://net.t-labs.tu-berlin.de/~stefan/
We work on a new algorithm for parametric identification in signal temporal logic. For a real-valued signal and a parameterized temporal logic formula, we want to find the set of parameter values that makes the formula satisfied by the signal. Such a procedure has multiple uses. For example, as part of the process of deriving a model from simulation traces, it can be used to find the values of model parameters. Or it can be used to evaluate formulas containing universal and existential quantifiers. We have a working algorithm for identification of spatial parameters in piecewise-constant signals, which performs well in our experiments. Identification of time parameters is an ongoing work.
A common approach to solving problems in rigorous systems engineering is
to reduce them to constraint solving problems with a quantifier prefix
exists-forall. Here, the existential quantifier ranges over a
proof/certificate/program/controller to be found, and the universal
quantifier is used for specifying a property that the found object
Recently, there has been a lot of work on algorithms for solving such
problems by iteratively learning the object to be found from concrete
counter-examples to the property. Many of those algorithms follow a
general scheme, often called counter-example guided inductive synthesis
(CEGIS). In the talk, we will present an algorithm of this type that
synthesizes certificates for safety of ordinary differential equations,
so-called barrier certificates. We will draw general conclusions
regarding the usage of counter-example guided inductive synthesis in
continuous versus discrete structures.
Stefan Ratschan is a researcher at the Institute of Computer Science of
the Czech Academy of Sciences in Prague. He received his Ph.D. at the
Research Institute for Symbolic Computation at Johannes Kepler
University Linz, Austria, and has since then also been affiliated with
the University of Girona, Spain, and the Max-Planck-Institute for
Informatics, Saarbrücken, Germany. He currently heads the Department of
Computational Mathematics at the Institute of Computer Science of the
Czech Academy of Sciences. The main scientific interests of Stefan
Ratschan are in the areas of formal verification of cyber-physical
systems and of constraint solving.