A time lower bound for satisfiability

Dieter Van Melkebeek; Ran Raz

doi:10.1016/j.tcs.2005.09.020

A time lower bound for satisfiability

Dieter Van Melkebeek, Ran Raz

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time na for a<(d+2)/(d+1). For conondeterministic machines, we obtain a similar lower bound for any a such that a3<1+a/(d+1). The same bounds apply to almost all natural NP-complete problems known.

Original language	English (US)
Pages (from-to)	311-320
Number of pages	10
Journal	Theoretical Computer Science
Volume	348
Issue number	2-3 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.tcs.2005.09.020
State	Published - Dec 8 2005
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Keywords

Computational complexity
Lower bounds
Satisfiability

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10.1016/j.tcs.2005.09.020

Cite this

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title = "A time lower bound for satisfiability",

abstract = "We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time na for a<(d+2)/(d+1). For conondeterministic machines, we obtain a similar lower bound for any a such that a3<1+a/(d+1). The same bounds apply to almost all natural NP-complete problems known.",

keywords = "Computational complexity, Lower bounds, Satisfiability",

author = "{Van Melkebeek}, Dieter and Ran Raz",

note = "Funding Information: A preliminary version of this paper appeared in the Proceedings of the 31st International Colloquium on Automata, Languages and Programming. ∗Corresponding author. E-mail addresses: dieter@cs.wisc.edu (D. van Melkebeek), ran.raz@weizmann.ac.il (R. Raz) URLs: http://www.cs.wisc.edu/∼dieter (D. van Melkebeek), http://www.wisdom.weizmann.ac.il/∼ranraz (R. Raz). 1Partially supported by NSF Career award CCR-0133693.",

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doi = "10.1016/j.tcs.2005.09.020",

language = "English (US)",

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AU - Van Melkebeek, Dieter

AU - Raz, Ran

N1 - Funding Information: A preliminary version of this paper appeared in the Proceedings of the 31st International Colloquium on Automata, Languages and Programming. ∗Corresponding author. E-mail addresses: dieter@cs.wisc.edu (D. van Melkebeek), ran.raz@weizmann.ac.il (R. Raz) URLs: http://www.cs.wisc.edu/∼dieter (D. van Melkebeek), http://www.wisdom.weizmann.ac.il/∼ranraz (R. Raz). 1Partially supported by NSF Career award CCR-0133693.

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N2 - We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time na for a<(d+2)/(d+1). For conondeterministic machines, we obtain a similar lower bound for any a such that a3<1+a/(d+1). The same bounds apply to almost all natural NP-complete problems known.

AB - We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time na for a<(d+2)/(d+1). For conondeterministic machines, we obtain a similar lower bound for any a such that a3<1+a/(d+1). The same bounds apply to almost all natural NP-complete problems known.

KW - Computational complexity

KW - Lower bounds

KW - Satisfiability

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DO - 10.1016/j.tcs.2005.09.020

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JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 2-3 SPEC. ISS.

ER -

A time lower bound for satisfiability

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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