## Lower bounds on the complexity of recognizing SAT by Turing machines (0)

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Venue: | Information Processing Letters |

Citations: | 6 - 1 self |

### BibTeX

@INPROCEEDINGS{Santhanam_lowerbounds,

author = {Rahul Santhanam},

title = {Lower bounds on the complexity of recognizing SAT by Turing machines},

booktitle = {Information Processing Letters},

year = {},

pages = {2001}

}

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### Abstract

this paper are strengthenings of the results in [4] and [9] for Turing machines. The results in [4] and [9] hold for SAT but our results hold for 2-SAT also, since the formulae we reduce the language L to belong to 2-SAT. Therefore our techniques are less promising if the ultimate goal is to prove that SAT does not belong to P, since it is known that 2-SAT belongs to P. Moreover we obtain the same lower bounds for NTMs as for DTMs, which indicates that our techniques may not be useful in separating nondeterministic time and deterministic time

### Citations

40 |
The recognition problem for the set of perfect squares
- Cobham
- 1966
(Show Context)
Citation Context ... Such methods have been used extensively to prove lower bounds or tradeos on restricted models - for example, in [3], [6], [8] and [11]. An early result of this kind was the tradeo proved by Cobham [1=-=-=-] for the acceptance of languages on Turing machines. Cobham's examples worked only for Turing machines with one read-write 1 head per tape; tradeos for Turing machines with multiple (but constant) re... |

25 | On the complexity of SAT
- Lipton, Viglas
- 1999
(Show Context)
Citation Context ...a deterministic Turing machine. In fact, Fortnow proved that SAT cannot be solved in quasilinear time and space O(n 1 ) on a deterministic Turing machine, for any > 0. Recently, Lipton and Viglas [9], using techniques of Kannan [7], have improved the tradeos in [4]. For example, they show that SAT cannot be accepted by a TM that uses time O(n p 2 ) and polylogarithmic space, for any constant ... |

23 | Nondeterministic polynomial time versus nondeterministic logarithmic space: Time-space tradeoffs for satisfiability
- Fortnow
- 1997
(Show Context)
Citation Context ...nguage by a Turing machine. Since SAT is NP-complete, proving superpolynomial lower bounds on time would imply P 6= NP . Thesrst non-trivial time-space tradeos for SAT were proved by Fortnow in 1997 [=-=4]. Her-=-e, \nontrivial " refers to any result that implies SAT cannot be solved simultaneously in linear time and constant space on a deterministic Turing machine. In fact, Fortnow proved that SAT cannot... |

14 |
Nearly-linear time
- Gurevich, Shelah
- 1989
(Show Context)
Citation Context ... NT IME(n polylog(n)), a result that follows from the facts that SAT can be accepted in n polylog(n) time on a NRAM and that there is an ecient simulation of NRAMs by NTMs, due to Gurevich and Shelah =-=[5]. Thu-=-s a \natural" language, i.e a language such that ecient reductions from it to SAT exist, will also 6 be in NT IME(n polylog(n)). Proving a superlinear lower bound on the acceptance time for such ... |

12 | Two time-space tradeoffs for element distinctness - Karchmer - 1986 |

9 |
A nearly optimal time-space lower bound for directed stconnectivity on the NNJAG model
- Edmonds, Poon
- 1995
(Show Context)
Citation Context ...ly known time-space tradeos for specic languages proved using combinatorial methods. Such methods have been used extensively to prove lower bounds or tradeos on restricted models - for example, in [3], [6], [8] and [11]. An early result of this kind was the tradeo proved by Cobham [1] for the acceptance of languages on Turing machines. Cobham's examples worked only for Turing machines with one re... |

7 |
Nondeterministic linear-time tasks may require substantially nonlinear deterministic time in the case of sublinear work space
- Gurevich, Shelah
- 1990
(Show Context)
Citation Context ...own time-space tradeos for specic languages proved using combinatorial methods. Such methods have been used extensively to prove lower bounds or tradeos on restricted models - for example, in [3], [6], [8] and [11]. An early result of this kind was the tradeo proved by Cobham [1] for the acceptance of languages on Turing machines. Cobham's examples worked only for Turing machines with one read-wr... |

6 | A time-space tradeoff for language recognition - Duris, Galil - 1984 |

4 | A time-space tradeo for language recognition - Duris, Galil - 1984 |

3 |
separating nondeterminism from determinism
- Towards
- 1984
(Show Context)
Citation Context ...In fact, Fortnow proved that SAT cannot be solved in quasilinear time and space O(n 1 ) on a deterministic Turing machine, for any > 0. Recently, Lipton and Viglas [9], using techniques of Kannan [7], have improved the tradeos in [4]. For example, they show that SAT cannot be accepted by a TM that uses time O(n p 2 ) and polylogarithmic space, for any constant > 0. Both [4] and [9] use gener... |

3 |
E.Szemeredi and W.Trotter. On determinism versus nondeterminism and related problems
- Paul
- 1983
(Show Context)
Citation Context ..." n and the function that lower bounds the acceptance time. Thus far, the best result of this kind that is known is that DT IME(n) 6= NT IME(n), which is due to Paul, Pippenger, Szemeredi and Tro=-=tter [10]-=-. 6 Acknowledgments I thank my advisor, Janos Simon, for his constant support and encouragement. The ideas in this paper originated from discussions with him. I thank Dieter Van Melkebeek for his help... |

2 | time-space tradeoff for element distinctness - Near-optimal - 1994 |

1 |
Two time-space tradeos for element distinctness
- Karchmer
- 1986
(Show Context)
Citation Context ...ime-space tradeos for specic languages proved using combinatorial methods. Such methods have been used extensively to prove lower bounds or tradeos on restricted models - for example, in [3], [6], [8] and [11]. An early result of this kind was the tradeo proved by Cobham [1] for the acceptance of languages on Turing machines. Cobham's examples worked only for Turing machines with one read-write 1... |

1 |
time-space tradeo for element distinctness
- Near-optimal
- 1994
(Show Context)
Citation Context ...e tradeos for specic languages proved using combinatorial methods. Such methods have been used extensively to prove lower bounds or tradeos on restricted models - for example, in [3], [6], [8] and [11=-=-=-]. An early result of this kind was the tradeo proved by Cobham [1] for the acceptance of languages on Turing machines. Cobham's examples worked only for Turing machines with one read-write 1 head per... |