Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the space complexity of refuting unsatisfiable random k-CNFs in the resolution proof system.  prove that for any large enough /spl Delta/, with high probability a random k-CNF over n variables and /spl Delta/n clauses requires resolution clause space of /spl Omega/(n/spl middot//spl Delta//sup -1+/spl epsiv//k-2-/spl epsiv//), for any 0 >/spl radic/n. This bound is nearly tight. Specifically,  show that with high probability, a random 3-CNF with /spl Delta/n clauses requires tree-like refutation size of exp(/spl Omega/(n//spl Delta//sup 1+/spl epsiv//1-/spl epsiv//)), for any 0</spl epsiv/<1/2. Our space lor bound is the consequence of three main contributions. 1.  introduce a 2-player matching game on bipartite graphs G to prove that there are no perfect matchings in G. 2.  reduce lor bounds for the clause space of a formula F in resolution to lor bounds for the complexity of the game played on the bipartite graph G(F) associated with F. 3.  prove that the complexity of the game is large whenever G is an expander graph. Finally, a simple probabilistic analysis shows that for a random formula F, with high probability G(F) is an expander.  also extend our result to the case of G-PHP, a generalization of the pigeonhole principle based on bipartite graphs G.  prove that the clause space for G-PHP can be reduced to the game complexity on G.
['Eli Ben-Sasson', 'Nicola Galesi']
I am writing a research paper on a idea Space complexity of random formulae in resolution
[{"from": "human", "value": "I am writing a research paper on a idea Space complexity of random formulae in resolution"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the space complexity of refuting unsatisfiable random k-CNFs in the resolution proof system.  prove that for any large enough /spl Delta/, with high probability a random k-CNF over n variables and /spl Delta/n clauses requires resolution clause space of /spl Omega/(n/spl middot//spl Delta//sup -1+/spl epsiv//k-2-/spl epsiv//), for any 0 >/spl radic/n. This bound is nearly tight. Specifically,  show that with high probability, a random 3-CNF with /spl Delta/n clauses requires tree-like refutation size of exp(/spl Omega/(n//spl Delta//sup 1+/spl epsiv//1-/spl epsiv//)), for any 0</spl epsiv/<1/2. Our space lor bound is the consequence of three main contributions. 1.  introduce a 2-player matching game on bipartite graphs G to prove that there are no perfect matchings in G. 2.  reduce lor bounds for the clause space of a formula F in resolution to lor bounds for the complexity of the game played on the bipartite graph G(F) associated with F. 3.  prove that the complexity of the game is large whenever G is an expander graph. Finally, a simple probabilistic analysis shows that for a random formula F, with high probability G(F) is an expander.  also extend our result to the case of G-PHP, a generalization of the pigeonhole principle based on bipartite graphs G.  prove that the clause space for G-PHP can be reduced to the game complexity on G."}]