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The Descriptive Complexity of the Deterministic Exponential Time Hierarchy
2011
Electronical Notes in Theoretical Computer Science
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each level of the deterministic exponential time hierarchy. ...
In Descriptive Complexity, we investigate the use of logics to characterize computational complexity classes. ...
Our central result is that HO i (LFP) captures the (i − 1)-EXP complexity class, for i ≥ 2. Hence, we characterized all levels of the Deterministic Exponential Time Hierarchy. ...
doi:10.1016/j.entcs.2011.03.006
fatcat:5z6vjfygvnafdjw5yd7idllj7m
Page 3781 of Mathematical Reviews Vol. , Issue 88g
[page]
1988
Mathematical Reviews
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polynomial, exponential, etc., time-bounded deterministic, nondeterministic, x? ...
M. (2-GORSU) On the relation between the complexity of the description of a set and the complexity of a problem of the minimization of a linear form on it. ...
New developments in structural complexity theory
1990
Theoretical Computer Science
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The Query Hierarchy is defined in terms of the number of queries a p-time machine can make to SAT (or any NP complete problem). pArlmt is the set of languages accepted by deterministic polynomial time ...
Major complexity chsses 8ad biirarcbks We recall some definitions. Let P and NP denote the sets of languages accepted in deterministic and nondeterministic polynomial time, respectively. ...
Time booDded eompaltaGaEs The last few years have been a very exciting and successful time in the development of structural complexity theory. ...
doi:10.1016/0304-3975(90)90191-j
fatcat:b32wvwbx4jcw3jmuinbslhk2ii
Reordering Method and Hierarchies for Quantum and Classical Ordered Binary Decision Diagrams
[article]
2017
arXiv
pre-print
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It is restricted version of read-once Quantum Branching Programs, with respect to "width" complexity. It is known that maximal complexity gap between deterministic and quantum model is exponential. ...
Using this result we prove the width hierarchy for complexity classes of Boolean functions for quantum OBDDs. ...
We thank Alexander Vasiliev and Aida Gainutdinova from Kazan Federal University and Andris Ambainis from University of Latvia for their helpful comments and discussions. ...
arXiv:1703.00242v2
fatcat:5wpazzeaynbfjltapz2hgkdttm
Page 8079 of Mathematical Reviews Vol. , Issue 98M
[page]
1998
Mathematical Reviews
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The length of the text 7 [resp. pattern P] may grow exponentially with respect to its description size ||7 || =n [resp. ||P || = m]. ...
From the summary: “We consider the complexity of some pattern- matching problems for two-dimensional images which are highly compressed using finite deterministic and weighted automata as small descriptions ...
Page 2852 of Mathematical Reviews Vol. , Issue 94e
[page]
1994
Mathematical Reviews
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The description represents a flattened object, whose size can be exponential in the size of the description. ...
We also present a simulation of an alternating pointer machine of time complexity ¢ by a deterministic pointer machine of mass complexity O(t/ log t).”
94e:68075 68Q25 68M15
Rosenkrantz, Daniel J. (1-SUNYA-C ...
A View of Structural Complexity Theory
[chapter]
1993
Current Trends in Theoretical Computer Science
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Acknowledgments Preparation of this paper was supported in part by the National Science Foundation under grant CCR86-11980 and CCR89-13584. ...
Informally, the Kolmogorov complexity of a finite string is the length of the shortest program that will generate the string; intuitively, it is a measure of the amount of descriptive information that ...
Now consider any set L in DEXT(S); that is, some deterministic exponential-time oracle machine M accepts L relative to S. ...
doi:10.1142/9789812794499_0034
dblp:series/wsscs/Book093
fatcat:jcrj2u7caveejeojt6w6ouzqvq
Pseudodeterministic Algorithms and the Structure of Probabilistic Time
[article]
2021
arXiv
pre-print
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We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of 𝖡𝖯𝖳𝖨𝖬𝖤: proving hierarchy theorems and showing the existence of complete problems ...
We establish an equivalence between pseudodeterministic construction of strings of large 𝗋𝖪𝗍 complexity (Oliveira, ICALP 2019) and the existence of strong hierarchy theorems for probabilistic time. ...
We are also grateful to Lijie Chen for sharing comments about a preliminary version of the paper that helped us to improve the presentation. ...
arXiv:2103.08539v1
fatcat:t344sx34orgormjvstk3l3n2l4
Pseudodeterministic algorithms and the structure of probabilistic time
2021
Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
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We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of BPTIME: proving hierarchy theorems and showing the existence of complete problems. ...
This offers an exponential improvement over the running time of previous results, and shows that infinitely many primes have succinct and efficient representations. * ...
Acknowledgements The first two authors received support from the Royal Society University Research Fellowship URF\R1\191059. ...
doi:10.1145/3406325.3451085
fatcat:yqh6zf42y5akrflgxvwvianpmm
Sparse sets in NP-P: EXPTIME versus NEXPTIME
1985
Information and Control
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and nondeterministic time-bounded complexity classes. ...
This paper investigates the structural properties of sets in NP-P and shows that the computational difficulty of lower density sets in NP depends explicitly on the relations between higher deterministic ...
The original search for the upward separation method was stimulated by Kurtz's relativization result (Kurtz, 1985) obtaining during the AMS Summer Institute on Recursive Function Theory at Cornell University ...
doi:10.1016/s0019-9958(85)80004-8
fatcat:2spxuego3nbxzo5sgphlt6o45i
The role of rudimentary relations in complexity theory
1984
Mémoires de la Société mathématique de France
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Extending these results we obtain a chain of hierarchies for the iterated exponential time levels , whose union is the class ERUD , the exponential analogue of RUD . ...
A chain of exponential time hierarchies
7. Two logspace hierarchies
8. The theories of bounded concatenation
9. Conclusion
10. ...
doi:10.24033/msmf.311
fatcat:iwoj6vbr25e4nlgdmbgc76y6ly
Succinct representation random strings, and complexity classes
1980
21st Annual Symposium on Foundations of Computer Science (sfcs 1980)
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These measures are used to indicate the inherent information (or "randomness") of a string, but with respect to time and space complexity classes. ...
A genera] paradigm for relating measures of succinctness of representation and complexity theory is presented. The measures are based on the new Private and Blindfold Alternation machines. ...
This means that any process which finds the shorter description of X must take more than exponential time. ...
doi:10.1109/sfcs.1980.42
dblp:conf/focs/Peterson80
fatcat:dil2pbffdzbhdlsuf2kuilfuti
Page 473 of Mathematical Reviews Vol. , Issue 96a
[page]
1996
Mathematical Reviews
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Summary: “We show that the EOL structural equivalence prob- lem is logspace hard for deterministic exponential time. ...
The converse reduction is well known and thus context-free structural equivalence is complete for deterministic exponential time.” ...
Page 8286 of Mathematical Reviews Vol. , Issue 2001K
[page]
2001
Mathematical Reviews
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For example, it follows that sat- isfiability for the full branching time logic CTL* can be tested in deterministic double exponential time. ...
Chapter 7 (Linguistically relevant properties) is devoted to semilinearity, the complexity of recogniz- ing contextual languages, descriptional complexity, several types of ambiguity, syntactical structures ...
Complexity of multi-head finite automata: Origins and directions
2011
Theoretical Computer Science
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Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. ...
Questions on the economics of description size were already investigated in the early days of theoretical computer science and build a cornerstone of descriptional complexity theory [39, 49, 58] . ...
Here we ask for the descriptional complexity of k-head finite automata. ...
doi:10.1016/j.tcs.2010.08.024
fatcat:yjkjor7r5rawrjijnxihcdnuve
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