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Lower bounds and complete problems in nondeterministic linear time and sublinear space complexity classes
[article]

2006
*
arXiv
*
pre-print

recognized by

arXiv:cs/0606058v1
fatcat:u2gygpnrhncidgbgsgufijykue
*nondeterministic*RAMs*in**linear**time**and**sublinear**space*. ... them a*class*of*problems*, which are*complete**in*these*classes*,*and*as a consequence of such a precise result*and*of some recent separation theorems using diagonalization, prove*time*-*space**lower**bounds*... + x, y) mod n g 1 (i) : [n] × [n] → [c] (x, y) → g(*in*+x,y) n Ú g(nx 1 + x 0 , y) = n · g 1 (x 1 ) (x 0 , y) + g 0 (x 1 ) (x 0 , y)º Ï ÒÓØ Ø Ø Ø Ø Ö Ø ÓÒ Ú Ö Ð ¸Ø Ø × y = T¸ × ÒÓØ ÑÓ ...##
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The emptiness problem for intersections of regular languages
[chapter]

1992
*
Lecture Notes in Computer Science
*

*In*this way we get

*complete*

*problems*for

*nondeterministic*

*space*-

*bounded*

*and*timespace-

*bounded*

*complexity*

*classes*. ... Further on, we get close relations to

*nondeterministic*

*sublinear*

*time*

*classes*

*and*to

*classes*which are dened by

*bounding*the number of

*nondeterministic*steps. ... 5

*and*6, always leads to DSPACE(log n)-

*complete*(resp. ...

##
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Alternation Trading Proofs and Their Limitations
[chapter]

2013
*
Lecture Notes in Computer Science
*

Alternation trading proofs are motivated by the goal of separating NP from

doi:10.1007/978-3-642-40313-2_1
fatcat:ax6jhreugbhr3otle5s64l2gou
*complexity**classes*such as Logspace or NL; they have been used to give super-*linear*runtime*bounds*for deterministic*and*conondeterministic ...*sublinear**space*algorithms which solve the Satisfiability*problem*. ...*and**sublinear**space*computational*classes*. ...##
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Page 4568 of Mathematical Reviews Vol. , Issue 98G
[page]

1998
*
Mathematical Reviews
*

This new approach to ‘

*sublinear*’*time**complexity*is a natural counterpart to*sublinear**space**complexity*. ... Now we succeed*in*separating small randomized*time**classes*for multi-tape 2-way Turing machines. Surprisingly, these ‘small’*bounds*are of type n+ f(n) with f(m) not exceeding*linear*functions. ...##
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Time-space lower bounds for satisfiability

2005
*
Journal of the ACM
*

Our

doi:10.1145/1101821.1101822
fatcat:thy577mqmne6xcpufkwvhqi7ee
*lower**bounds*apply to*nondeterministic**linear**time**and*almost all natural NP-*complete**problems*known. ...*In*fact, they even apply to the*class*of languages that can be solved on a*nondeterministic*machine*in**linear**time**and**space*n 1/c . Our proofs follow the paradigm of indirect diagonalization. ... Acknowledgments DvM would like to thank Rahul Santhanam, Madhu Sudan,*and*Iannis Tourlakis for discussions about the topic of this paper*and*/or comments on earlier drafts. ...##
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Page 335 of Mathematical Reviews Vol. , Issue 83a
[page]

1983
*
Mathematical Reviews
*

We also show that AAGAP(S(n)) is

*in*NTISP(poly, S(n)), i.e., the*class*of*problems*solvable by*nondeterministic*algorithms*in*polynomial*time**and*simultaneous S(n)*space*. ... Author’s summary: “The boundary between the*class*P (*problems*solvable*in*polynomial*time*)*and*the*class*of NP-*complete**problems*(probably not solvable*in*polynomial*time*) is investigated*in*the area of ...##
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Nonuniform complexity classes specified by lower and upper bounds

1989
*
RAIRO - Theoretical Informatics and Applications
*

ACKNOWLEDGEMENT The authors wish to thank an anoniinous référée for pointing out some ntistakes

doi:10.1051/ita/1989230201771
fatcat:ms4n6iq2inaa3dzwgkclmduk3u
*and*suggesting several iniprovements of the présentation. ... EXPONENTIAL*LOWER**BOUNDS**In*this section we characterize the*classes*defined by exponential Iower*bounds*on the nonuniform*complexity*of the languages. ... Computational models are finite automata, pushdown automata,*and**time*or*space**bounded*Turing machines,*in*their respective deterministic or*nondeterministic*versions. ...##
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A Survey of Lower Bounds for Satisfiability and Related Problems

2006
*
Foundations and Trends® in Theoretical Computer Science
*

*In*this article we survey the known

*lower*

*bounds*for the

*time*

*and*

*space*

*complexity*of satisfiability

*and*closely related

*problems*on deterministic, randomized,

*and*quantum models with random access. ... It is widely believed to be intractable,

*and*yet till recently even a

*linear*-

*time*, logarithmic-

*space*algorithm for satisfiability was not ruled out. ...

*and*discussions that shaped my understanding of the subject, Scott Diehl

*and*Madhu Sudan for helpful comments,

*and*-last but not least -Tom Watson for his very careful proofreading

*and*excellent suggestions ...

##
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Time–Space Tradeoffs for SAT on Nonuniform Machines

2001
*
Journal of computer and system sciences (Print)
*

*Lower*

*bounds*for computing SAT on random access

*nondeterministic*Turing machines taking

*sublinear*advice are also obtained. ... are generalized

*and*combined with an argument for diagonalizing over machines taking n bits of advice on inputs of length n to obtain the first nontrivial

*time*-

*space*

*lower*

*bounds*for SAT on nonuniform ... INTRODUCTION A central

*problem*

*in*

*complexity*theory is to determine the relationship between P

*and*NP. ...

##
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An improved time-space lower bound for tautologies

2010
*
Journal of combinatorial optimization
*

a

doi:10.1007/s10878-009-9286-x
fatcat:a5uvcnupdfahblwqqexbxeitve
*nondeterministic*algorithm that runs*in**time*n d*and**space*n e . ...*In*particular, for every d < 3 √ 4 there exists a positive e such that tautologies cannot be decided by a*nondeterministic*algorithm that runs*in**time*n d*and**space*n e . ... Acknowledgements The authors would like to thank an anonymous referee for a very careful reading of the manuscript*and*for helpful suggestions. ...##
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An Improved Time-Space Lower Bound for Tautologies
[chapter]

2009
*
Lecture Notes in Computer Science
*

a

doi:10.1007/978-3-642-02882-3_43
fatcat:wf6u5phizbg6bifoh4hsstsk2a
*nondeterministic*algorithm that runs*in**time*n d*and**space*n e . ...*In*particular, for every d < 3 √ 4 there exists a positive e such that tautologies cannot be decided by a*nondeterministic*algorithm that runs*in**time*n d*and**space*n e . ... Acknowledgements The authors would like to thank an anonymous referee for a very careful reading of the manuscript*and*for helpful suggestions. ...##
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A Sublinear Space, Polynomial Time Algorithm for Directed s-t Connectivity

1998
*
SIAM journal on computing (Print)
*

We present the rst known deterministic

doi:10.1137/s0097539793283151
fatcat:f7ly3z6rq5candqcioi4cjwuki
*sublinear**space*, polynomial*time*algorithm for directed s-t connectivity. ... For n-vertex graphs, our algorithm can use as little as n=2 2( p log n)*space*while still running*in*polynomial*time*. ... Acknowledgements Allan Borodin pointed us toward the short paths*problem*. Uri Feige helped nd the minimum*space**bound*. ...##
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Page 2945 of Mathematical Reviews Vol. , Issue 95e
[page]

1995
*
Mathematical Reviews
*

One of the hardest

*problems*of*complexity*theory is to prove nontrivial*lower**bounds*on fundamental*complexity*measures for concrete computing*problems*. ... We give an algorithm that is*sublinear**time*O((n/m)k log, m) when the text is random*and*k is*bounded*by the threshold m/(log, m+ O(1)). ...##
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Page 2218 of Mathematical Reviews Vol. , Issue 92d
[page]

1992
*
Mathematical Reviews
*

deterministic

*time**in*the case of*sublinear*work*space*. ...*In*particular, a form of the clique*problem*is defined,*and*it is proved that (1) a*nondeterministic*log-*space*Turing machine solves the*problem**in**linear**time*, but (2) no deterministic machine (*in*a very ...##
###
Page 1257 of Mathematical Reviews Vol. , Issue 86c
[page]

1986
*
Mathematical Reviews
*

We prove that every deterministic language has a

*linear**lower**bound**in*pushdown*complexity*. We study*sublinear**bounds*. ... The*space**complexity*S(n) of these ma- chines is characterized*in*terms of the*complexity*of deterministic Turing machines, with*time**bounds*doubly exponential*in*S(n). ...
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