Fixed Point Theory (WS 26/27)

Seminar

WS 26/27

OrganizersProf. Benjamin Kaminski, Tobias Gürtler, Lucas Kehrer, Lena Verscht, Anran Wang
Places8

Find the full list of topics that we will cover below!

Prerequisites

MandatoryProgrammierung 1
Programmierung 2
Grundzüge der Theoretischen Informatik
RecommendedSemantics
Introduction to Computational Logic
Automata, Games and Verification
IdealVerification

Reports

The report must be prepared using the ACM template acmart-pacmpl-template.tex with the following options in the preamble:

\documentclass[acmsmall,dvipsnames,x11names,svgnames,cleveref, nonacm]{acmart}
\settopmatter{printfolios=true,printccs=false,printacmref=false}

The report must not exceed 10 pages, excluding references.

Presentations

As a block seminar at the end of the semester.

More information TBA.

Timeline / Deadlines (tentative)

Kick-off meeting
October 30
Room 528,
Building E1 3
Bidding for topicsuntil November 3 – via email to Benjamin Kaminski –
Student-topic assignment announcedby November 5– on this website –
Detailed report outline +
1 page of main part due
TBD– via email to your supervisor –
Registration in LSF dueTBD– via LSF (your responsibility) –
Final report dueTBD– via email to your supervisor –
Make an appointment for mandatory practice presentation with your supervisorby
TBD
– make appointment with your supervisor –
Seminar presentationsw/c TBDlikely Room 528, Building E1 3
w/c = week commencing

Topics

Topics marked (BA) are particularly well-suited for Bachelor students.

Graphical Fixed Point Theory

Random Fixed Points

Unique Fixed Points for Probabilistic Programs

Banach Fixed Point Theorem (BA)

Reverse Directional Fixed Point Theory

Antitone Functions (BA)

Fixed Point Equations

Expressive Equivalence of Fixed Point Logics

Model-guided Synthesis

Expected Rewards as Least Fixed Points (BA)

Latticed k-Induction

Parameterized Coinduction

Modality for Recursion

⁠Matrices for Fixed Points in Probabilistic Programming (BA)

Invariant Synthesis in Probabilistic Programming

⁠Lower Bounds for Least Fixed Points (BA)