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Samuel R. (Sam) Buss (born August 6, 1957) is an American computer scientist and mathematician who has made major contributions to the fields of mathematical logic, complexity theory and proof complexity. He is currently a professor at the University of California, San Diego, Department of Computer Science and Department of Mathematics.
Download as PDF; Printable version; In other projects ... Proof theory is a major branch [1] ... S. Buss, ed. (1998) Handbook of Proof Theory. Elsevier. G. Gentzen ...
Download as PDF; Printable version; ... A proof of the non-trivial direction of the theorem can be constructed according to the following steps: ... Buss, Samuel R ...
Download as PDF; Printable version; ... Now, the hybrid theory {, ... In Buss, Samuel R. (ed.). Handbook of Proof Theory. Studies in Logic and the Foundations of ...
A propositional proof system is given as a proof-verification algorithm P(A,x) with two inputs.If P accepts the pair (A,x) we say that x is a P-proof of A.P is required to run in polynomial time, and moreover, it must hold that A has a P-proof if and only if A is a tautology.
Gaisi Takeuti (竹内 外史, Takeuchi, Gaishi, January 25, 1926 – May 10, 2017 [1]) was a Japanese mathematician, known for his work in proof theory. [2] After graduating from Tokyo University, he went to Princeton to study under Kurt Gödel. He later became a professor at the University of Illinois at Urbana–Champaign.
Propositional proof system can be compared using the notion of p-simulation. A propositional proof system P p-simulates Q (written as P ≤ p Q) when there is a polynomial-time function F such that P(F(x)) = Q(x) for every x. [1] That is, given a Q-proof x, we can find in polynomial time a P-proof of the same tautology.
In mathematical logic, realizability is a collection of methods in proof theory used to study constructive proofs and extract additional information from them. [1] Formulas from a formal theory are "realized" by objects, known as "realizers", in a way that knowledge of the realizer gives knowledge about the truth of the formula.