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

Philippe Chapdelaine, Etienne Grandjean
2006 arXiv   pre-print
recognized by 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  ... 
arXiv:cs/0606058v1 fatcat:u2gygpnrhncidgbgsgufijykue

The emptiness problem for intersections of regular languages [chapter]

Klaus-Jörn Lange, Peter Rossmanith
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.  ... 
doi:10.1007/3-540-55808-x_33 fatcat:z4zqgw3ckbewbkbichpwyqu3re

Alternation Trading Proofs and Their Limitations [chapter]

Sam Buss
2013 Lecture Notes in Computer Science  
Alternation trading proofs are motivated by the goal of separating NP from 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.  ... 
doi:10.1007/978-3-642-40313-2_1 fatcat:ax6jhreugbhr3otle5s64l2gou

Page 4568 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
This new approach to ‘sublineartime 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.  ... 

Time-space lower bounds for satisfiability

Lance Fortnow, Richard Lipton, Dieter van Melkebeek, Anastasios Viglas
2005 Journal of the ACM  
Our 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.  ... 
doi:10.1145/1101821.1101822 fatcat:thy577mqmne6xcpufkwvhqi7ee

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  ... 

Nonuniform complexity classes specified by lower and upper bounds

José L. Balcázar, Joaquim Gabarró
1989 RAIRO - Theoretical Informatics and Applications  
ACKNOWLEDGEMENT The authors wish to thank an anoniinous référée for pointing out some ntistakes 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.  ... 
doi:10.1051/ita/1989230201771 fatcat:ms4n6iq2inaa3dzwgkclmduk3u

A Survey of Lower Bounds for Satisfiability and Related Problems

Dieter van Melkebeek
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  ... 
doi:10.1561/0400000012 fatcat:vsdohimqr5a5zlbat3l37uwdem

Time–Space Tradeoffs for SAT on Nonuniform Machines

Iannis Tourlakis
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.  ... 
doi:10.1006/jcss.2001.1767 fatcat:lmusmuoedfhtdetal3y7gejopm

An improved time-space lower bound for tautologies

Scott Diehl, Dieter van Melkebeek, Ryan Williams
2010 Journal of combinatorial optimization  
a 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.  ... 
doi:10.1007/s10878-009-9286-x fatcat:a5uvcnupdfahblwqqexbxeitve

An Improved Time-Space Lower Bound for Tautologies [chapter]

Scott Diehl, Dieter van Melkebeek, Ryan Williams
2009 Lecture Notes in Computer Science  
a 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.  ... 
doi:10.1007/978-3-642-02882-3_43 fatcat:wf6u5phizbg6bifoh4hsstsk2a

A Sublinear Space, Polynomial Time Algorithm for Directed s-t Connectivity

Greg Barnes, Jonathan F. Buss, Walter L. Ruzzo, Baruch Schieber
1998 SIAM journal on computing (Print)  
We present the rst known deterministic 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.  ... 
doi:10.1137/s0097539793283151 fatcat:f7ly3z6rq5candqcioi4cjwuki

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)).  ... 

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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