A Lower Bound for the Pigeonhole Principle in Tree-like Resolution by Asymmetric Prover-Delayer GamesI
نویسندگان
چکیده
In this note we show that the asymmetric Prover-Delayer game developed in [BGL10] for Parameterized Resolution is also applicable to other tree-like proof systems. In particular, we use this asymmetric Prover-Delayer game to show a lower bound of the form 2 logn) for the pigeonhole principle in tree-like Resolution. This gives a new and simpler proof of the same lower bound established by Iwama and Miyazaki [IM99] and Dantchev and Riis [DR01].
منابع مشابه
A lower bound for the pigeonhole principle in tree-like Resolution by asymmetric Prover-Delayer games
In this note we show that the asymmetric Prover-Delayer game developed in (ECCC, TR10–059) for Parameterized Resolution is also applicable to other treelike proof systems. In particular, we use this asymmetric Prover-Delayer to show a lower bound of the form 2Ω(n logn) for the pigeonhole principle in tree-like Resolution. This gives a new and simpler proof of the same lower bound established by...
متن کاملA Characterization of Tree-Like Resolution SizeI
We explain an asymmetric Prover-Delayer game which precisely characterizes proof size in tree-like Resolution. This game was previously described in a parameterized complexity context to show lower bounds for parameterized formulas [BGL13] and for the classical pigeonhole principle [BGL10]. The main point of this note is to show that the asymmetric game in fact characterizes tree-like Resolutio...
متن کاملA characterization of tree-like Resolution size
We explain an asymmetric Prover-Delayer game which precisely characterizes proof size in treelike Resolution. This game was previously described in a parameterized complexity context to show lower bounds for parameterized formulas [BGL11] and for the classical pigeonhole principle [BGL10]. The main point of this note is to show that the asymmetric game in fact characterizes tree-like Resolution...
متن کاملThe Strength of Parameterized Tree-like Resolution
We examine the proof-theoretic strength of parameterized tree-like resolution—a proof system for the coW[2]complete set of parameterized tautologies. Parameterized resolution and, moreover, a general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider (FOCS’07). In that paper, Dantchev et al. show a complexity gap in parameterized tree-like resolution fo...
متن کاملA Parameterized Complexity of DPLL Search Procedures
We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the runni...
متن کامل