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Bounded-width polynomial-size branching programs recognize exactly those languages in NC1

David A. Barrington
1989 Journal of computer and system sciences (Print)  
As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly non-uniform NC 1 .  ...  We show that any language recognized by an NC 1 circuit (fan-in 2, depth O(logn)) can be recognized by a particular type of width 5 polynomial-size branching program.  ...  As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly non-uniform NC 1 .  ... 
doi:10.1016/0022-0000(89)90037-8 fatcat:uorbc2viwngnhms7kzcerquium

Bounded-width polynomial-size branching programs recognize exactly those languages in NC1

D A Barrington
1986 Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86  
As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly non-uniform NC 1 .  ...  We show that any language recognized by an NC 1 circuit (fan-in 2, depth O(logn)) can be recognized by a particular type of width 5 polynomial-size branching program.  ...  As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly non-uniform NC 1 .  ... 
doi:10.1145/12130.12131 dblp:conf/stoc/Barrington86 fatcat:h5wnfosbozhxpiv5iwz6vg7zn4

Extensions to Barrington's M-program model

François Bédard, François Lemieux, Pierre McKenzie
1993 Theoretical Computer Science  
McKenzie, Extensions to Barrington's M-program model, Theoretical Computer Science 107 (1993) 31-61.  ...  For their part, programs over monoids growing with the input size should be viewed as an intermediate step between bounded-width and arbitrary width polynomial-order branching programs (describing NC'  ...  One such restriction of particular interest to us is the polynomial-length, bounded-width branching program [6, 9] .  ... 
doi:10.1016/0304-3975(93)90253-p fatcat:6eqxzd7vbzffrgtgxfd7nogztu

On uniformity within NC1

David A. Mix Barrington, Neil Immerman, Howard Straubing
1990 Journal of computer and system sciences (Print)  
In order to study circuit complexity classes within NC' in a uniform setting, we need a uniformity condition which is more restrictive than those in common use.  ...  Finally, we investigate a parallel notion of uniformity, still more restrictive, based on the regular languages.  ...  In addition we would like to thank the two anonymous referees for their comments, which have greatly improved the presentation.  ... 
doi:10.1016/0022-0000(90)90022-d fatcat:zdlwqu25tnh6rbht7wd264jfe4

Regular languages in NC1

David A. Mix Barrington, Kevin Compton, Howard Straubing, Denis Thérien
1992 Journal of computer and system sciences (Print)  
Using recent lower-bound results of Razborov and Smolensky, we obtain similar characterizations of the family of regular languages recognized by constant-depth circuit families that include unbounded fan-in  ...  We also obtain logical characterizations for the class of all languages recognized by nonuniform circuit families in which mod m gates (where m is not necessarily prime) are permitted.  ...  In Section 7 we use Lemma 2 and Barrington's results [2] on branching programs of bounded width to show that any regular language whose syntactic monoid contains a nonsolvable group is complete for NC  ... 
doi:10.1016/0022-0000(92)90014-a fatcat:ty7dnkixh5arhkhul52ibdfiee

Evaluating Matrix Circuits [article]

Daniel König, Markus Lohrey
2015 arXiv   pre-print
The best upper bound for this problem is coRP, which is shown by a reduction to polynomial identity testing.  ...  In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in DET⊆NC^2.  ...  Bounded-width polynomial-size branching programs recognize exactly those languages in NC1 . Journal of Computer and System Sciences, 38:150–164, 1989. 8. D. A. M. Barrington and D. Thérien.  ... 
arXiv:1502.03540v1 fatcat:excfkcl4lfachc23nbyv6zbwma

Complexity of Regular Functions [chapter]

Eric Allender, Ian Mertz
2015 Lecture Notes in Computer Science  
We give complexity bounds for various classes of functions computed by cost register automata.  ...  To do this, we will present a nondeterministic constant-width branching program recognizing B; such branching programs recognize only sets in NC 1 [11] .  ...  By [2, Proposition 5.2], arithmetic circuits of polynomial size and algebraic degree over (Γ * , max, •) characterize exactly the complexity class OptLogCFL.  ... 
doi:10.1007/978-3-319-15579-1_35 fatcat:7b67gh6a4bdm5jxzpne3xe6qx4

The history and status of the P versus NP question

Michael Sipser
1992 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92  
There are a number of open questions in monotone complexity, for example, whether Barrington's [Ba86a] beautiful simulation of log-depth circuits by polynomial-size, width 5, branch- ing programs  ...  NP consists of those languages where membership is verijiabie in poly- nomial time.  ...  n) N Kn (or N Kn2) means, of course, simply that the number of steps vis-h-via dem Mossen Pro biereng can be reduced from IV to log IV (or (log lV)2)Such strong reductions10 do indeed occur, however, in  ... 
doi:10.1145/129712.129771 dblp:conf/stoc/Sipser92 fatcat:rcg35ekcnrejflhp4vct67qxby

Secure and scalable match: overcoming the universal circuit bottleneck using group programs

Rajesh Krishnan, Ravi Sundaram
2015 Proceedings on Privacy Enhancing Technologies  
In this paper we advance the state of the art in C-CBPS by showing how all predicate circuits in NC1 (logarithmic-depth, bounded fan-in) can be confidentially computed by a broker while guaranteeing perfect  ...  We present three protocols—UGP-Match, FSGP-Match and OFSGP-Match—based on 2-decomposable randomized encodings of group programs for circuits in NC1.  ...  In his seminal paper [6] , on the way to showing that NC 1 is computable by fixed-width branching programs, Barrington showed that any logarithmic-depth circuit can be transformed into a polynomial-length  ... 
doi:10.1515/popets-2015-0013 dblp:journals/popets/KrishnanS15 fatcat:v263drb765egtdyeyn7m3ofhqm

Heavyweight Pattern Mining in Attributed Flow Graphs

Carolina Simoes Gomes, Jose Nelson Amaral, Joerg Sander, Joran Siu, Li Ding
2014 2014 IEEE International Conference on Data Mining  
-Miyamoto Musashi, in The Book of Five Rings.  ...  If you master the principles of sword-fencing, when you freely beat one man, you beat any man in the world. The spirit of defeating a man is the same for ten million men.  ...  From the fact that CFGs have bounded tree-width and that the FCSM problem can be solved in incremental polynomial time, follows that Execution Flow Graphs representing CFGs also have bounded tree-width  ... 
doi:10.1109/icdm.2014.51 dblp:conf/icdm/GomesASSD14 fatcat:kvxyxu6mbvb73pqj4fpez6h5o4

Data Enrichment [chapter]

2017 Encyclopedia of Machine Learning and Data Mining  
Decision trees and decision lists are two popular hypothesis languages, which share quite a few similarities, but also have important differences with respect to expressivity and learnability.  ...  Abstract Dimensionality reduction in an important data pre-processing when dealing with Big Data.  ...  (Policy improvement) Choose d nC1 to satisfy d nC1 2 argmax d 2D fr d C P d v n g componentwise. If d n is in this set, then choose d nC1 D d n . 4. If d nC1 D d n , set d D d n and stop.  ... 
doi:10.1007/978-1-4899-7687-1_979 fatcat:v22x3o5iuzaa5ghwx5fvqztpg4

GIS Mashups [chapter]

Ilya Zaslavsky
2017 Encyclopedia of GIS  
Thus, in the recent past, GPs have witnessed a revival primarily due to work in  ...  GPs have a probabilistic basis that allow us to estimate variances at unsampled locations, aiding in the design of targeted sampling strategies.  ...  which they branch.  ... 
doi:10.1007/978-3-319-17885-1_530 fatcat:rrr5buo3zrevpigdtjwhewipvm

Complexity of Regular Functions Complexity of Regular Functions

Eric Allender, Ian Mertz
unpublished
We give complexity bounds for various classes of functions computed by cost register automata.  ...  To do this, we will present a nondeterministic constant-width branching program recognizing B; such branching programs recognize only sets in NC 1 [11] .  ...  By [2, Proposition 5.2], arithmetic circuits of polynomial size and algebraic degree over (Γ * , max, •) characterize exactly the complexity class OptLogCFL.  ... 
fatcat:4nzrsbppvbdj3gqeg7df4v4lz4

Descriptive complexity of circuit-based counting classes [article]

Anselm Haak, University, My
2021
The focus of research in this area is on identifying logics that can express exactly the problems in specific complexity classes.  ...  For example, problems are definable in ESO, existential second-order logic, if and only if they are in NP, the class of problems decidable in nondeterministic polynomial time.  ...  More precisely, Caussinus et al. showed that #NC 1 can be characterized in terms of counting paths in bounded width branching programs [CMTV98] and Vinay showed that #SAC 1 can be characterized in terms  ... 
doi:10.15488/11353 fatcat:q4iz3ttqsvfwtpf6gfxvvsxbga

RF Mixers [chapter]

2010 Radio Frequency Circuit Design  
ACKNOWLEDGMENT The authors wish to acknowledge the help of Terry Jamison in the analysis of the impulse response data.  ...  For example, there is no mention of distributed branch line couplers, since at 1 GHz their size would be prohibitive.  ...  The program POLY can provide the complex roots of a polynomial with complex coefficients.  ... 
doi:10.1002/9780470768020.ch11 fatcat:t332r6j2p5epjpfnsnoal3xalq
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