Proof Complexity (Dagstuhl Seminar 18051)

Authors Albert Atserias, Jakob Nordström, Pavel Pudlák, Rahul Santhanam and all authors of the abstracts in this report

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Albert Atserias
Jakob Nordström
Pavel Pudlák
Rahul Santhanam
and all authors of the abstracts in this report

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Albert Atserias, Jakob Nordström, Pavel Pudlák, and Rahul Santhanam. Proof Complexity (Dagstuhl Seminar 18051). In Dagstuhl Reports, Volume 8, Issue 1, pp. 124-157, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The study of proof complexity was initiated in [Cook and Reckhow 1979] as a way to attack the P vs.NP problem, and in the ensuing decades many powerful techniques have been discovered for analyzing different proof systems. Proof complexity also gives a way of studying subsystems of Peano Arithmetic where the power of mathematical reasoning is restricted, and to quantify how complex different mathematical theorems are measured in terms of the strength of the methods of reasoning required to establish their validity. Moreover, it allows to analyse the power and limitations of satisfiability algorithms (SAT solvers) used in industrial applications with formulas containing up to millions of variables. During the last 10--15 years the area of proof complexity has seen a revival with many exciting results, and new connections have also been revealed with other areas such as, e.g., cryptography, algebraic complexity theory, communication complexity, and combinatorial optimization. While many longstanding open problems from the 1980s and 1990s still remain unsolved, recent progress gives hope that the area may be ripe for decisive breakthroughs. This workshop, gathering researchers from different strands of the proof complexity community, gave opportunities to take stock of where we stand and discuss the way ahead.
  • bounded arithmetic
  • computational complexity
  • logic
  • proof complexity
  • satisfiability algorithms


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