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Logic seminar

usually takes place each Monday at 16:00 in IM, rear building, ground floor
Chair: Pavel Pudlak, Neil Thapen, Jan Krajíček
More information on the old seminar web page. The programme is announced via the mailing list.

Quantified Boolean formulas: proof systems, circuit complexity, and solving

Olaf Beyersdorff
Friedrich Schiller University Jena
Monday, 11. January 2021 - 15:30 to 17:00
This talk will start with an overview of the relatively young field of QBF proof complexity, explaining QBF proof systems (including QBF resolution) and an assessment of which lower bound techniques are available for QBF proof systems. In the main part of the talk, I will explain hardness characterisations for QBF proof systems in terms of circuit complexity, yielding very direct connections between circuit lower bounds and QBF proof system lower bounds. The talk will also cover the relations between QBF resolution and QCDCL solving algorithms. Modelling QCDCL as proof systems we show that QCDCL and Q-Resolution are incomparable.

This talk is based on two recent papers, joint with Joshua Blinkhorn and Meena Mahajan (LICS'20) and with Benjamin Boehm (ITCS'21).

Propositional branching program proofs and logics for L and NL

Sam Buss
University of California, San Diego
Monday, 14. December 2020 - 15:30 to 17:00
We introduce systems of propositional logic for reasoning directly with decision trees, non-deterministic decision trees, branching programs and non-deterministic branching programs. These propositional systems allow reasoning about properties in non-uniform logarithmic space and non-deterministic logarithmic space. We also report on work-in-progress to use these propositional proof systems for the bounded arithmetic theories VL and VNL with proof theoretic strength corresponding to logarithmic space and non-deterministic logarithmic space. The talk will start with an overview of the propositional proof systems which are already known to have close correspondences with bounded arithmetic. The new results are joint work with Anupam Das and Alexander Knop.

Interactive theorem proving for the working logician

Jeremy Avigad
Carnegie Mellon University
Monday, 7. December 2020 - 15:30 to 17:00
Over the last few decades, computational proof assistants have made it possible to construct formal axiomatic derivations of increasing complexity. They are now used to verify that hardware and software designs meet their specifications, as well as to verify the correctness of mathematical proofs. The practice has taken root and promises to play an important role in mathematics and computer science.

In this talk, I will survey the technology, with an emphasis on formal mathematics. I will then discuss aspects of interactive theorem proving that may be of interest to the working logician, and places where a better theoretical understanding can lead to progress. Specifically, I'll discuss the need for practical foundations, search procedures, decision procedures, and proof systems.

Automating tree-like resolution in time n^o(log n/ log log n) is ETH-hard

Susanna F. de Rezende
Monday, 30. November 2020 - 15:30 to 17:00
It is known that tree-like resolution is automatable in time n^O(log n). In this talk we will show that under ETH tree-like resolution is not automatable in time n^o(log n/ log log n). We will also provide an alternative, arguably simpler proof of the result of Alekhnovich and Razborov (SIAM J. Comput. 2008) that unless the fixed parameter hierarchy collapses, tree-like resolution is not automatable in polynomial time. The proof builds on a joint work with Mika Göös, Jakob Nordström, Toni Pitassi, Robert Robere and Dmitry Sokolov (ECCC 2020), which presents a simplification of the breakthrough result of Atserias and Müller (JACM 2020).