TY - GEN
T1 - Space complexity in propositional calculus
AU - Alekhnovich, Michael
AU - Ben-Sasson, Eli
AU - Razborov, Alexander A.
AU - Wigderson, Avi
PY - 2000
Y1 - 2000
N2 - We study space complexity in the framework of propositional proofs. We consider a natural model analogous to space bounded Turing machines with a read-only input tape, and such popular propositional proof systems as Resolution, Polynomial Calculus and Frege systems. We study two different space measures. The first, introduced by [5] for Resolution and extended here to other systems, is the structured measure which counts the number of clauses/monomials kept is memory simultaneously. The other is an unstructured measure related to the number of bits describing the memory content. We develop lower bound techniques that enable proving tight linear lower bounds for the first measure, and tight quadratic lower bounds for the second, for large classes of tautologies (including familiar ones like the pigeonhole principle) in both Resolution and (extensions of) Polynomial Calculus. We also prove some structural results concerning the clause space for Resolution and Frege Systems.
AB - We study space complexity in the framework of propositional proofs. We consider a natural model analogous to space bounded Turing machines with a read-only input tape, and such popular propositional proof systems as Resolution, Polynomial Calculus and Frege systems. We study two different space measures. The first, introduced by [5] for Resolution and extended here to other systems, is the structured measure which counts the number of clauses/monomials kept is memory simultaneously. The other is an unstructured measure related to the number of bits describing the memory content. We develop lower bound techniques that enable proving tight linear lower bounds for the first measure, and tight quadratic lower bounds for the second, for large classes of tautologies (including familiar ones like the pigeonhole principle) in both Resolution and (extensions of) Polynomial Calculus. We also prove some structural results concerning the clause space for Resolution and Frege Systems.
UR - http://www.scopus.com/inward/record.url?scp=0033684394&partnerID=8YFLogxK
U2 - 10.1145/335305.335347
DO - 10.1145/335305.335347
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AN - SCOPUS:0033684394
SN - 1581131844
SN - 9781581131840
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 358
EP - 367
BT - Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000
T2 - 32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Y2 - 21 May 2000 through 23 May 2000
ER -