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The Descriptive Complexity of the Deterministic Exponential Time Hierarchy

Cibele Matos Freire, Ana Teresa Martins
2011 Electronical Notes in Theoretical Computer Science  
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  
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

J. Hartmanis
1990 Theoretical Computer Science  
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]

Kamil Khadiev, Aliya Khadieva
2017 arXiv   pre-print
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  
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  
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]

Ronald V. BOOK, Osamu WATANABE
1993 Current Trends in Theoretical Computer Science  
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]

Zhenjian Lu, Igor C. Oliveira, Rahul Santhanam
2021 arXiv   pre-print
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

Zhenjian Lu, Igor C. Oliveira, Rahul Santhanam
2021 Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing  
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

J. Hartmanis, N. Immerman, V. Sewelson
1985 Information and Control  
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

Hugo Volger
1984 Mémoires de la Société mathématique de France  
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

Gary L. Peterson
1980 21st Annual Symposium on Foundations of Computer Science (sfcs 1980)  
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  
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  
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

Markus Holzer, Martin Kutrib, Andreas Malcher
2011 Theoretical Computer Science  
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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