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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
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
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
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. ...
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
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 ...
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
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
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
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
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
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
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)). ...
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 ...
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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