Abstract
Our main result shows that a shortest proof size of tree-like resolution for the pigeonhole principle is superpolynomially larger than that of DAG-like resolution. In the proof of a lower bound, we exploit a relationship between tree-like resolution and backtracking, which has long been recognized in this field but not been used before to give explicit results.
Supported in part by Scientific Research Grant, Ministry of Japan, 10558044, 09480055 and 10205215.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. Beame and T. Pitassi, “Simplified and improved resolution lower bounds”, Proc. FOCS’96, pp. 274–282, 1996.
M. L. Bonet, J. L. Esteban, N. Galesi and J. Johannsen, “Exponential separations between restricted resolution and cutting planes proof systems”, Proc. FOCS’98, pp. 638–647, 1998.
S. Buss, “Polynomial size proofs of the propositional pigeonhole principle”, Journal of Symbolic Logic, 52, pp. 916–927, 1987.
S. Buss and T. Pitassi, “Resolution and the weak pigeonhole principle”, Proc. CSL’97, LNCS 1414, pp.149–156, 1997.
S. A. Cook and R. A. Reckhow, “The relative efficiency of propositional proof systems”, J. Symbolic Logic, 44(1), pp. 36–50, 1979.
A. Haken, “The intractability of resolution”, Theoretical Computer Science, 39, pp. 297–308, 1985.
P. Purdom, “A survey of average time analysis of satisfiability algorithms”, Journal of Information Processing, 13(4), pp.449–455, 1990.
A. A. Razborov, A. Wigderson and A. Yao, “Read-Once Branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus”, Proc. STOC’97, pp. 739–748, 1997.
A. Urquhart, “The complexity of propositional proofs”, The Bulletin of Symbolic Logic, Vol. 1, No. 4, pp. 425–467, 1995.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Iwama, K., Miyazaki, S. (1999). Tree-Like Resolution Is Superpolynomially Slower Than DAG-Like Resolution for the Pigeonhole Principle. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_14
Download citation
DOI: https://doi.org/10.1007/3-540-46632-0_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66916-6
Online ISBN: 978-3-540-46632-1
eBook Packages: Springer Book Archive