In the present work, we study the propositional proof complexity. First, we prove an exponential lower bound on the complexity of resolution applying directly Razborov's approximation method, which was previously used only for bounds on the size of monotone circuits. Next, we use the approximation method for a new proof of an exponential lower bound on the complexity of random resolution refutations. That should have further applications in separating some theories in bounded arithmetic. In both cases, we use a problem from the graph theory called Broken Mosquito Screens. Finally, we state a conjecture that the approximation method is applicable even for stronger propositional proof systems, for example Cutting Plane Proofs. Powered by TCPDF (www.tcpdf.org)
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:321397 |
| Date | January 2013 |
| Creators | Peterová, Alena |
| Contributors | Pudlák, Pavel, Krajíček, Jan |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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