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.
The ACL2 theorem-proving system has seen sustained industrial use since
the mid 1990s. Companies that have and are using ACL2 include AMD, ARM,
Centaur Technology, General Electric, IBM, Intel, Kestrel Institute,
Motorola/Freescale, Oracle, and Rockwell Collins. ACL2 has been
accepted for industrial application because it is an integrated
programming/proof environment supporting a subset of the ANSI standard
Common Lisp programming language. Software and hardware systems have
been modeled and analyzed with the ACL2 theorem-proving system.
The ACL2 programming language can be used to develop efficient and
robust programs. The ACL2 analysis machinery provides many features
permitting domain-specific, human-supplied guidance at various levels
of abstraction. ACL2 specifications often serve as efficient execution
engines for the modeled artifacts while permitting formal analysis and
proof of properties. ACL2 provides support for the development and
verification of other formal analysis tools. ACL2 did not find its way
into industrial use merely because of its technical features. The ACL2
user/development community has a shared vision of making formal
specification and mechanized verification routine — we have been
committed to this vision for the quarter century since the Computational
Logic, Inc., Verified Stack.
Distributed protocols such as Paxos play an important role in many computer systems.
Therefore, a bug in a distributed protocol may have tremendous effects.
Accordingly, a lot of effort has been invested in verifying such protocols.
However, due to the infinite state space (e.g., unbounded number of nodes, messages) and protocols complexity, verification is both undecidable and hard in practice.
I will describe a deductive approach for verification of distributed protocols, based on first-order logic, inductive invariants and user interaction.
The use of first-order logic and a decidable fragment of universally quantified invariants allows to completely automate some verification tasks.
Tasks that remain undecidable (e.g. finding inductive invariants) are solved with user interaction, based on graphically displayed counterexamples.
I will also describe the application of these techniques to verify safety of several variants of Paxos, and a way to extend the approach to verify liveness and temporal properties.
Oded Padon is a fourth year PhD student in Tel Aviv University, under the supervision of Prof. Mooly Sagiv.
His research focuses on verification of distributed protocols using first-order logic.
He is a recipient of the 2017 Google PhD fellowship in programming languages.