论文信息 - Monadic Logical Definability of NP-Complete Problems

Monadic Logical Definability of NP-Complete Problems

It is well known that monadic second-order logic with linear order captures exactly regular languages. On the other hand, if addition is allowed, then J.F.Lynch has proved that existential monadic secondorder logic captures at least all the languages in NTIME(n), and then expresses some NP-complete languages (e.g. knapsack problem).

Frédéric Olive | Etienne Grandjean

[1] Etienne Grandjean,et al. A Nontrivial Lower Bound for an NP Problem on Automata , 1990, SIAM J. Comput..

[2] Phokion G. Kolaitis,et al. Logical Definability of NP Optimization Problems , 1994, Inf. Comput..

[3] Claus-Peter Schnorr. Satisfiability Is Quasilinear Complete in NQL , 1978, JACM.

[4] Erich Grädel. On the Notion of Linear Time Computability , 1990, Int. J. Found. Comput. Sci..

[5] Yuri Gurevich,et al. Toward logic tailored for computational complexity , 1984 .

[6] Moshe Y. Vardi. The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[7] Neil Immerman. Languages which capture complexity classes , 1983, STOC '83.

[8] Michael M. Richter,et al. Computation and Proof Theory , 1984 .

[9] J. Büchi. Weak Second‐Order Arithmetic and Finite Automata , 1960 .

[10] Neil Immerman,et al. Descriptive and Computational Complexity , 1989, FCT.

[11] Neil Immerman,et al. Relational Queries Computable in Polynomial Time , 1986, Inf. Control..

[12] Etienne Grandjean. A Natural NP-Complete Problem with a Nontrivial Lower Nound , 1988, SIAM J. Comput..

[13] Neil Immerman,et al. Languages that Capture Complexity Classes , 1987, SIAM J. Comput..

[14] Saharon Shelah,et al. Nearly Linear Time , 1989, Logic at Botik.

[15] Etienne Grandjean. Linear Time Algorithms and NP-Complete Problems , 1992, CSL.