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09:15-10:15 Session 65A: NSV Invited Talk: Jean-Michel Muller
Location: FH, Hörsaal 2
Getting tight error bounds in floating-point arithmetic: illustration with complex functions, and the real x^n function

ABSTRACT. The specifications provided by the IEEE 754 standard for floating-point arithmetic allows one to design very simple algorithms for functions such as $x^n$, or complex multiplication and division, that are much more accurate that what one might think at first glance. We will show how tight error bounds are obtained for these algorithms, and discuss how generic exemples can be built to show the tightness of these error bounds.

10:15-10:45Coffee Break
10:45-12:45 Session 66AG: NSV Contributed Talks: Formal Methods in Numerical Programs
Location: FH, Hörsaal 2
Theorem-Proving Analysis of Digital Control Logic Interacting with Continuous Dynamics

ABSTRACT. This work outlines an equation-based formulation of a digital control program and transducer interacting with a continuous physical process, and an approach using the Coq theorem prover for verifying the performance of the combined hybrid system. Considering thermal dynamics with linear dissipation for simplicity, we focus on a generalizable, physically consistent description of the interaction of the real-valued temperature and the digital program acting as a thermostat. Of interest in this work is the discovery and formal proof of bounds on the temperature, the degree of variation, and other performance characteristics. Our approach explicitly addresses the need to mathematically represent the decision problem inherent in an analog-to-digital converter, which for rare values can take an arbitrarily long time to produce a digital answer (the so-called Buridan's Principle); this constraint ineluctably manifests itself in the verification of thermostat performance. Furthermore, the temporal causality constraints in the thermal physics must be made explicit to obtain a consistent model for analysis. We discuss the significance of these findings toward the verification of digital control for more complex physical variables and fields.

Transformation of a PID Controller for Numerical Accuracy

ABSTRACT. Numerical programs performing floating-point computations are very sensible to the way formulas are written. Several techniques have been proposed concerning the transformation of expressions in order to improve their accuracy and now we aim at going a step further by automatically transforming larger pieces of code containing several assignments and control structures. This article presents a case study in this direction. We consider a PID controller and we transform its code in order to improve its accuracy. The experimental data obtained when we compare the different versions of the code (which are mathematically equivalent) show that those transformations have a significant impact on the accuracy of the computations.

Policy iteration in finite templates domain
SPEAKER: Assale Adje

ABSTRACT. We prove in this paper that Policy Iteration can be generally defined in finite domain of templates using Lagrange duality. Such policy iteration algorithm converges to a fixed point when for very simple technique condition holds. This fixed point furnishes a safe over-approximation of the set of reachable values taken by the variables of a program. We prove also that Policy Iteration can be easily initialised for small programs when templates are correctly chosen.

13:00-14:30Lunch Break
14:30-16:00 Session 75AG: NSV Contributed Talks: Certified Numerical Computation
Location: FH, Hörsaal 2
Certifying Square Root and Division Elimination
SPEAKER: Pierre Neron

ABSTRACT. This paper presents a program transformation that removes square roots and divisions from functional programs without recursion, producing code that can be exactly computed. This transformation accepts different subsets of languages as input and it provides a certifying mechanism when the targeted language is Pvs. In this case, we provide a relation between every function definition in the output code and its corresponding one in the input code, that specifies the behavior of the produced function with respect to the input one. This transformation has been implemented in OCaml and has been tested on different algorithms from the NASA ACCoRD project.

Computational complexity of iterated maps on points and sets

ABSTRACT. The computational complexity of the certified iteration of discrete dynamical systems is considered. Relations to the Lyapunov-Exponents are shown.

SetBased Decorated Intervals

ABSTRACT. The draft  IEEE standard for interval arithmetic p1788 has recently been developed  and will be  open for public review in this summer 2014

In the talk we introduce the newly developed concepts such as set-based intervals, flavors, decorations or revers function evaluations

16:00-16:30Coffee Break
16:30-19:00 Session 79A: VSL Joint Award Ceremony 1
Location: MB, Kuppelsaal
Foundations and Technology Competitions Award Ceremony

ABSTRACT. The third round of the Kurt Gödel Research Prize Fellowships Program, under the title: Connecting Foundations and Technology, aims at supporting young scholars in early stages of their academic careers by offering highest fellowships in history of logic, kindly supported by the John Templeton Foundation. Young scholars being less or exactly 40 years old at the time of the commencement of the Vienna Summer of Logic (July 9, 2014) will be awarded one fellowship award in the amount of EUR 100,000, in each of the following categories:

  • Logical Foundations of Mathematics,
  • Logical Foundations of Computer Science, and
  • Logical Foundations of Artificial Intelligence

The following three Boards of Jurors were in charge of choosing the winners:

  • Logical Foundations of Mathematics: Jan Krajíček, Angus Macintyre, and Dana Scott (Chair).
  • Logical Foundations of Computer Science: Franz Baader, Johann Makowsky, and Wolfgang Thomas (Chair).
  • Logical Foundations of Artificial Intelligence: Luigia Carlucci Aiello, Georg Gottlob (Chair), and Bernhard Nebel.


FLoC Olympic Games Award Ceremony 1

ABSTRACT. The aim of the FLoC Olympic Games is to start a tradition in the spirit of the ancient Olympic Games, a Panhellenic sport festival held every four years in the sanctuary of Olympia in Greece, this time in the scientific community of computational logic. Every four years, as part of the Federated Logic Conference, the Games will gather together all the challenging disciplines from a variety of computational logic in the form of the solver competitions.

At the Award Ceremonies, the competition organizers will have the opportunity to present their competitions to the public and give away special prizes, the prestigious Kurt Gödel medals, to their successful competitors. This reinforces the main goal of the FLoC Olympic Games, that is, to facilitate the visibility of the competitions associated with the conferences and workshops of the Federated Logic Conference during the Vienna Summer of Logic.

This award ceremony will host the

  • 3rd Confluence Competition (CoCo 2014);
  • Configurable SAT Solver Challenge (CSSC 2014);
  • Ninth Max-SAT Evaluation (Max-SAT 2014);
  • QBF Gallery 2014; and
  • SAT Competition 2014 (SAT-COMP 2014).
FLoC Closing Week 1
SPEAKER: Helmut Veith
16:30-18:00 Session 80A: NSV Invited Talk: Sumit Kumar Jha
Location: FH, Hörsaal 2
Verifying Parameterized Software Models in Computational Data Science against Behavioral Specifications

ABSTRACT. Computational data science uses a variety of numerical software models to understand, predict and control the evolution of complex systems. For example, computational systems biology employs multi-scale mechanistic stochastic rule-based models while culturomics uses detailed agent-based models. Because of the inherent uncertainty involved in precisely measuring natural systems, software models employed in computational data science include a number of unknown or imprecisely known parameters. A fundamental problem in developing such software models is to discover the set of parameter values that enable a computational model to satisfy a given set of behavioral specifications. In this talk, we will present a new massively parallel extreme-scale parameter discovery algorithm for complex intelligent software models. We will discuss preliminary results obtained using a parallel implementation of the algorithm on a small 1,792-core CUDA cluster. The talk will also identify opportunities for future research in verifying numerical software being deployed by computational data scientists.