A simplified way of proving trade-off results for resolution

We present a greatly simplified proof of the length-space trade-off result for resolution in [P. Hertel, T. Pitassi, Exponential time/space speedups for resolution and the PSPACE-completeness of black-white pebbling, in: Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS '07), Oct. 2007, pp. 137-149], and also prove a couple of other theorems in the same vein. We point out two important ingredients needed for our proofs to work, and discuss some possible conclusions. Our key trick is to look at formulas of the type [email protected]?H, where G and H are over disjoint sets of variables and have very different length-space properties with respect to resolution.

[1]  Eli Ben-Sasson,et al.  Understanding Space in Resolution: Optimal Lower Bounds and Exponential Trade-offs , 2009, Electron. Colloquium Comput. Complex..

[2]  Salil P. Vadhan,et al.  Computational Complexity , 2005, Encyclopedia of Cryptography and Security.

[3]  Johan Håstad,et al.  Towards an optimal separation of space and length in resolution , 2008, Theory Comput..

[4]  Eli Ben-Sasson,et al.  Space complexity of random formulae in resolution , 2003, Random Struct. Algorithms.

[5]  Maria Luisa Bonet,et al.  Optimality of size-width tradeoffs for resolution , 2001, computational complexity.

[6]  Michael Alekhnovich,et al.  Space complexity in propositional calculus , 2000, STOC '00.

[7]  Toniann Pitassi,et al.  Exponential Time/Space Speedups for Resolution and the PSPACE-completeness of Black-White Pebbling , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[8]  Alasdair Urquhart,et al.  Formal Languages]: Mathematical Logic--mechanical theorem proving , 2022 .

[9]  Gunnar Stålmarck.  Short resolution proofs for a sequence of tricky formulas , 2009, Acta Informatica.

[10]  Maria Luisa Bonet,et al.  A study of proof search algorithms for resolution and polynomial calculus , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[11]  Eli Ben-Sasson,et al.  Short proofs are narrow—resolution made simple , 2001, JACM.

[12]  Jakob Nordström,et al.  Narrow proofs may be spacious: separating space and width in resolution , 2006, STOC '06.

[13]  Toniann Pitassi,et al.  Exponential Time/Space Speedups for Resolution and the PSPACE-completeness of Black-White Pebbling , 2007, FOCS 2007.

[14]  Eli Ben-Sasson,et al.  Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[15]  Jacobo Torán.  Lower Bounds for Space in Resolution , 1999, CSL.

[16]  Toniann Pitassi,et al.  An Exponential Time/Space Speedup For Resolution , 2007, Electron. Colloquium Comput. Complex..

[17]  Albert Atserias,et al.  A combinatorial characterization of resolution width , 2003, 18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings..

[18]  Christos H. Papadimitriou,et al.  The complexity of facets resolved , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[19]  Jakob Nordström.  Short Proofs May Be Spacious : Understanding Space in Resolution , 2008 .

[20]  Jacobo Torán,et al.  Space Bounds for Resolution , 1999, STACS.

[21]  Michael E. Saks,et al.  The Efficiency of Resolution and Davis--Putnam Procedures , 2002, SIAM J. Comput..

[22]  Toniann Pitassi,et al.  Black-White Pebbling is PSPACE-Complete , 2007, Electron. Colloquium Comput. Complex..