J
Jan Krajíček
Researcher at Charles University in Prague
Publications - 123
Citations - 4083
Jan Krajíček is an academic researcher from Charles University in Prague. The author has contributed to research in topics: Proof complexity & Mathematical proof. The author has an hindex of 30, co-authored 117 publications receiving 3868 citations. Previous affiliations of Jan Krajíček include University of Oxford & Isaac Newton Institute.
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Book
Bounded Arithmetic, Propositional Logic and Complexity Theory
TL;DR: This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs.
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Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic
TL;DR: A new proof of the interpolation theorem based on a communication complexity approach is given which allows a similar estimate for a larger class of proofs and several corollaries are derived.
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Propositional Proof Systems, the Consistency of First Order Theories and the Complexity of Computations
Jan Krajíček,Pavel Pudlák +1 more
TL;DR: The problem of the length of proofs of statements in finitely, axiomatized theory S is studied, in relation with problems of propositional proof systems.
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Bounded arithmetic and the polynomial hierarchy
TL;DR: The main tool is a Herbrand-type witnessing theorem for ∃∀∃Пbi-formulas provable in Ti2 where the witnessing functions are □pi+1.
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On the weak pigeonhole principle
TL;DR: It is established a connection between provability of WPHP in fragments of bounded arithmetic and cryptographic assumptions (the existence of one-way functions) and the proof complexities of the weak pigeonhole principle and the Ramsey theorem.