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Page 8079 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
The second main result is a lower bound for the order and weight of perceptrons separating Boolean matrices having at least one value | in each row from such matrices where a great portion of rows contain  ...  fully compressed matching for deterministic automata is NP-complete.  ... 

Page 2806 of Mathematical Reviews Vol. , Issue 91E [page]

1991 Mathematical Reviews  
Wechsung (Jena) 91e:68053 68Q15 03D05 03D15 Grandjean, Etienne (F-CAEN-1) A nontrivial lower bound for an NP problem on automata. SIAM J. Comput. 19 (1990), no. 3, 438-451.  ...  This paper deals with one of the most challenging problems in com- plexity theory—to prove a nontrivial lower bound on the determin- istic time complexity of an NP-complete problem. W. J. Paul, N.  ... 

Page 4076 of Mathematical Reviews Vol. , Issue 80J [page]

1980 Mathematical Reviews  
The author reports upper and lower bounds on the complexity of some classes of iterations. No proofs are given. {For the entire collection see MR 80a:65012.} Verbeek, R.; Weihrauch, K.  ...  Author’s summary: “This article gives a necessary and a sufficient condition for the existence of an Eden configuration in one-dimen- sional cellular automata.” Butler, Jon T.  ... 

Page 4764 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
We present some normal forms for minimal NFAs over a unary alphabet and present an application to lower bounds on the size complexity of an NFA.  ...  We introduce bicomplexes as an algebraic tool for de- scribing these automata and develop a simple homology theory for higher-dimensional automata.  ... 

Page 2418 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
They conclude with the conjecture that any effective lower bound argument for a complexity class can be turned into an efficient distinguishing algorithm which proves that this class cannot contain PRFGs  ...  Toronto, ON) On the complexity of intersecting finite state automata and NL versus NP.  ... 

Page 6032 of Mathematical Reviews Vol. , Issue 88k [page]

1988 Mathematical Reviews  
Summary: “We prove a O(loglogn) (i.e., matching upper and lower) bound on the complexity of the union-split-find problem, a variant of the union-find problem.  ...  [Alt, Helmut] (D-FUB) A lower bound for the complexity of the union-split-find problem. Automata, languages and programming (Karlsruhe, 1987), 479-488, Lecture Notes in Comput.  ... 

Page 2946 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
In particular, lower bounds on this ratio for so-called on-line algorithms are derived.  ...  This algorithm nearly achieves the lower bound of the problem for this architecture.  ... 

A random NP-complete problem for inversion of 2D cellular automata [chapter]

Bruno Durand
1995 Lecture Notes in Computer Science  
In order to prove this result, we introduce a polynomial reduction from problems concerning finite tilings into problems concerning cellular automata.  ...  Then we add to tile sets and cellular automata probability functions and we prove that these problems are not only co-NP-complete, but co-RNPcomplete too.  ...  If a tiling contains at least one nonblank tile, then it is called nontrivial. A finite tiling is an almost everywhere bZunk tiling of the plane.  ... 
doi:10.1007/3-540-59042-0_65 fatcat:s3ochhl2cnfjlgxinez7ej4jmi

A Random NP-complete problem for inversion of 2D cellular automata

Bruno Durand
1995 Theoretical Computer Science  
In order to prove this result, we introduce a polynomial reduction from problems concerning finite tilings into problems concerning cellular automata.  ...  Then we add to tile sets and cellular automata probability functions and we prove that these problems are not only co-NP-complete, but co-RNPcomplete too.  ...  If a tiling contains at least one nonblank tile, then it is called nontrivial. A finite tiling is an almost everywhere bZunk tiling of the plane.  ... 
doi:10.1016/0304-3975(94)00293-r fatcat:r7iga3hcejcmnej3uiutj4pzxe

Page 8174 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
A PSPACE lower bound for BPA and NP lower bound for BPP were demonstrated by Stribrna. Mayr recently achieved a result, saying that weak bisimilarity for BPP is T1f- hard.  ...  Finally, we show how the technique for proving a co-NP lower bound for weak bisimilarity of BPA can be applied to strong bisimilarity of BPP.”  ... 

Page 1296 of Mathematical Reviews Vol. 54, Issue 4 [page]

1977 Mathematical Reviews  
Jan van Leeuwen (State College, Penn) Kedem, Zvi M. 9151 Combining dimensionality and rate of growth arguments for establishing lower bounds on the number of multiplications.  ...  From the author’s introduction: “In this paper we describe a new method for establishing lower bounds for the number of multi- plications and divisions required to compute rational functions,” {For the  ... 

Approximating Minimum Reset Sequences [chapter]

Michael Gerbush, Brent Heeringa
2011 Lecture Notes in Computer Science  
This improves the previous best lower bound which showed that it was NP-hard to approximate the MRS on binary alphabets to within any constant factor.  ...  Both these problems are known to be hard to approximate, although at present, SET COVER has a slightly stronger lower bound.  ...  Acknowledgements The authors wish to thank the anonymous reviewers for their helpful comments. This material is based upon work supported by the National Science Foundation under Grant No. 0812514  ... 
doi:10.1007/978-3-642-18098-9_17 fatcat:p2qgcn5l7febjmqlo763kxqd6a

Page 545 of Mathematical Reviews Vol. , Issue 90A [page]

1990 Mathematical Reviews  
However, nontrivial lower bounds for natural NP-complete problems have proved elusive.  ...  This paper provides nontrivial lower and upper bounds on the complexity of a new model-theoretic NP-complete set, SAT2:?(N). The set SAT2?  ... 

Page 512 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
This paper is devoted to the development of methods for proving lower bounds on the amount of computational resources needed to solve specific computing problems.  ...  In this paper the authors deal with the problem of proving exponential lower bounds on the size of depth-3 threshold circuits computing a specific Boolean function.  ... 

Digraph complexity measures and applications in formal language theory

Hermann Gruber
2012 Discrete Mathematics & Theoretical Computer Science  
Notwithstanding, we provide both a polynomial-time approximation algorithm and an exponential-time exact algorithm for this problem.  ...  Namely, the star height problem for bideterministic languages is NP-complete, and this holds already for binary alphabets.  ...  Acknowledgements The author would like to thank Markus Holzer for carefully reading an earlier draft of this paper, and for providing some valuable suggestions.  ... 
doi:10.46298/dmtcs.583 fatcat:ahnrjumydvfbnpnoebvctmwnwa
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