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

1995
*
Lecture Notes in Computer Science
*

In order to prove this result, we introduce

doi:10.1007/3-540-59042-0_65
fatcat:s3ochhl2cnfjlgxinez7ej4jmi
*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. ...##
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A Random NP-complete problem for inversion of 2D cellular automata

1995
*
Theoretical Computer Science
*

In order to prove this result, we introduce

doi:10.1016/0304-3975(94)00293-r
fatcat:r7iga3hcejcmnej3uiutj4pzxe
*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. ...##
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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.” ...

##
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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 ...##
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Approximating Minimum Reset Sequences
[chapter]

2011
*
Lecture Notes in Computer Science
*

This improves the previous best

doi:10.1007/978-3-642-18098-9_17
fatcat:p2qgcn5l7febjmqlo763kxqd6a
*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 ...##
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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? ...##
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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. ...##
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Digraph complexity measures and applications in formal language theory

2012
*
Discrete Mathematics & Theoretical Computer Science
*

Notwithstanding, we provide both

doi:10.46298/dmtcs.583
fatcat:ahnrjumydvfbnpnoebvctmwnwa
*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. ...
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