Complexity Considerations, cSAT problem lower bound

被引:0
|
作者
Hofman, Radoslaw [1 ]
机构
[1] Poznan Univ Econ, Dept Informat Syst, Poznan, Poland
关键词
complexity class; P vs NP; Boolean Algebra; First Order Theory; First Order Predicate Calculus;
D O I
暂无
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This article considers lower bound understood as worst case minimal amount of time required to calculate problem result for cSAT (Counted Boolean Satisfiability Problem). It uses observation that Boolean Algebra is complete First Order Theory where every sentence is decidable. Lower bound of this decidability is defined and shown. This article shows that deterministic calculation model built of finite number of machines (algorithms), oracles, axioms or predicates is incapable of solving considered NP-complete problem when its instance grows to infinity. This is direct proof that P and NP complexity classes differ and oracle capable of solving NP-complete problems in polynomial time must consist of infinite number of objects (must be nondeterministic). Corollary of this paper clears complexity hierarchy: P < NP
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页码:451 / 458
页数:8
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