TY - GEN

T1 - Satisfiability certificates verifiable in subexponential time

AU - Dantsin, Evgeny

AU - Hirsch, Edward A.

PY - 2011

Y1 - 2011

N2 - It is common to classify satisfiability problems by their time complexity. We consider another complexity measure, namely the length of certificates (witnesses). Our results show that there is a similarity between these two types of complexity if we deal with certificates verifiable in subexponential time. In particular, the well-known result by Impagliazzo and Paturi [IP01] on the dependence of the time complexity of k-SAT on k has its counterpart for the certificate complexity: we show that, assuming the exponential time hypothesis (ETH), the certificate complexity of k-SAT increases infinitely often as k grows. Another example of time-complexity results that can be translated into the certificate-complexity setting is the results of [CIP06] on the relationship between the complexity of k-SAT and the complexity of SAT restricted to formulas of constant clause density. We also consider the certificate complexity of CircuitSAT and observe that if CircuitSAT has subexponential-time verifiable certificates of length cn, where c < 1 is a constant and n is the number of inputs, then an unlikely collapse happens (in particular, ETH fails).

AB - It is common to classify satisfiability problems by their time complexity. We consider another complexity measure, namely the length of certificates (witnesses). Our results show that there is a similarity between these two types of complexity if we deal with certificates verifiable in subexponential time. In particular, the well-known result by Impagliazzo and Paturi [IP01] on the dependence of the time complexity of k-SAT on k has its counterpart for the certificate complexity: we show that, assuming the exponential time hypothesis (ETH), the certificate complexity of k-SAT increases infinitely often as k grows. Another example of time-complexity results that can be translated into the certificate-complexity setting is the results of [CIP06] on the relationship between the complexity of k-SAT and the complexity of SAT restricted to formulas of constant clause density. We also consider the certificate complexity of CircuitSAT and observe that if CircuitSAT has subexponential-time verifiable certificates of length cn, where c < 1 is a constant and n is the number of inputs, then an unlikely collapse happens (in particular, ETH fails).

UR - http://www.scopus.com/inward/record.url?scp=79959488137&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-21581-0_4

DO - 10.1007/978-3-642-21581-0_4

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AN - SCOPUS:79959488137

SN - 9783642215803

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 19

EP - 32

BT - Theory and Application of Satisfiability Testing - 14th International Conference, SAT 2011, Proceedings

T2 - 14th International Conference on Theory and Applications of Satisfiability Testing, SAT 2011

Y2 - 19 June 2011 through 22 June 2011

ER -