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Lower bounds for deterministic and nondeterministic branching programs [chapter]

Alexander A. Razborov
1991 Lecture Notes in Computer Science  
We survey lower bounds established for the complexity of computing explicitly given Boolean functions by switching-and-rectifier networks, branching programs and switching networks.  ...  Among these are monotone networks, bounded-width devices * , oblivious devices and read-k times only devices. * we will be using the word "device" to denote one of the two words "program" and "network"  ...  Section 4 is devoted to lower bounds known for monotone networks. In section 5 we consider bounded-width branching programs and switching-and-rectifier networks.  ... 
doi:10.1007/3-540-54458-5_49 fatcat:tqfisfl5uba73egddzmtaoamwu

Branching programs provide lower bounds on the areas of multilective deterministic and nondeterministic VLSI-circuits

Juraj Hromkovič, Matthias Krause, Christoph Meinel, Stephen Waack
1992 Information and Computation  
Lower bounds are derived for the sequence equality problem (SEQ) and the graph accessibility problem (GAP). 'P  ...  That is why exponential lower bounds on the width of (disjunctive) oblivious branching programs of linear depth provide lower bounds of order Sl(nlm2'), 0 <a < i, on the area of (nondeterministic) multilective  ...  It contributes a new and quite powerful method for proving lower bounds on the area A of (deterministic or nondeterministic) multilective VLSI-circuits (i.e., VLSI-circuits which are allowed to read input  ... 
doi:10.1016/0890-5401(92)90046-i fatcat:tcmnes323vhnfjbbbwkqqec7aq

Computing with Restricted Nondeterminism: The Dependence of the OBDD Size on the Number of Nondeterministic Variables [chapter]

Martin Sauerhoff
1999 Lecture Notes in Computer Science  
It is an open question whether an analogous simulation exists in the context of space-bounded computation. In this paper, a negative answer to this question is given for nondeterministic OBDDs.  ...  It is well-known that an arbitrary nondeterministic Turing machine can be simulated with polynomial overhead by a so-called guess-and-verify machine.  ...  Thanks to Ingo Wegener for proofreading and improving the upper bound of Theorem 2, to Juraj Hromkovič, Detlef Sieling, and Ingo Wegener for helpful discussions, and finally to the referees for careful  ... 
doi:10.1007/3-540-46691-6_28 fatcat:3onwga6ukbcr3cotoi6hsmjrki

Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication [chapter]

Beate Bollig
2000 Lecture Notes in Computer Science  
For that reason two restricted models of nondeterministic read-once branching programs are defined and a lower bound method is presented.  ...  Furthermore, the first exponential lower bound for integer multiplication on the size of a nondeterministic nonoblivious read-once branching program model is proven.  ...  Thanks to Detlef Sieling and Ingo Wegener for fruitful discussions and to Stefan Droste for proofreading. I also would like to thank the anonymous referees for their helpful comments.  ... 
doi:10.1007/3-540-44612-5_18 fatcat:zak2tm34vnhadf5igohiptdlue

Some Results on the Circuit Complexity of Bounded Width Circuits and Nondeterministic Circuits [article]

Hiroki Morizumi
2019 arXiv   pre-print
Actually, we prove a more generalized lower bound. Our proof outline for the lower bound also provides a satisfiability algorithm for nondeterministic bounded width circuits.  ...  This is the first separation on the power of deterministic and nondeterministic circuits for general circuits.  ...  The proof of our lower bounds is based on the size lower bound for nondeterministic syntactic read-k-times branching programs in 1993 [2] . The relation has not been known for a long time.  ... 
arXiv:1811.01347v2 fatcat:lqgvw3i2pnbfrmv5tt4cjlk6fu

Incremental Branching Programs [chapter]

Anna Gál, Michal Koucký, Pierre McKenzie
2006 Lecture Notes in Computer Science  
We show several exponential lower bounds for variants of our model although we are unable to prove any strong lower bounds for the most general variant of incremental branching programs.  ...  It remains open if incremental branching programs are as powerful as unrestricted branching programs for  ...  Theorem 6.6 n-GEN (1row) can be computed by deterministic syntactic incremental branching programs of size (n − 2) 2 + 3. Proof.  ... 
doi:10.1007/11753728_20 fatcat:vxorpj3zzrdilgrpwwmcq5jzju

Incremental Branching Programs

Anna Gál, Michal Koucký, Pierre McKenzie
2007 Theory of Computing Systems  
We show several exponential lower bounds for variants of our model although we are unable to prove any strong lower bounds for the most general variant of incremental branching programs.  ...  It remains open if incremental branching programs are as powerful as unrestricted branching programs for  ...  Theorem 6.6 n-GEN (1row) can be computed by deterministic syntactic incremental branching programs of size (n − 2) 2 + 3. Proof.  ... 
doi:10.1007/s00224-007-9049-y fatcat:iz3ywtc64rbrjbfnmlr5qu7efu

Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication

Beate Bollig
2001 RAIRO - Theoretical Informatics and Applications  
For that reason two restricted models of nondeterministic read-once branching programs are defined and a lower bound method is presented.  ...  Furthermore, the first exponential lower bound for integer multiplication on the size of a nondeterministic nonoblivious read-once branching program model is proven.  ...  Acknowledgement Thanks to Ingo Wegener for several valuable hints and fruitful discussions and to Stefan Droste for proofreading.  ... 
doi:10.1051/ita:2001113 fatcat:yjaouw2vpjboznwowlup3xyb3e

Separating complexity classes related to certain input oblivious logarithmic space-bounded Turing machines

M. Krause, Ch. Meinel, St. Waack
1992 RAIRO - Theoretical Informatics and Applications  
={ v }), conjunctive (Q={ A }), and alternating (Q={ v, A }) branching programs and logarithmic space-bounded deterministic, nondeterministic, co-nondeterministic and alternating Turing machines (Theorem  ...  . • A LOWER AND AN UPPER BOUND FOR THE SEQUENCE EQUALITY PROBLEM In the foUowing section we give an exp (Q (n)) lower bound for the sizes of oblivious disjunctive branching programs of linear length  ... 
doi:10.1051/ita/1992260403451 fatcat:xx2eppi2hvawhngwzzzkzet3qy

Separating the eraser Turing machine classes Le, NLe, co-NLe and Pe

Matthias Krause, Christoph Meinel, Stephan Waack
1991 Theoretical Computer Science  
By means of exponential lower and polynomial upper bounds for read-once-only n-branching programs we separate the logarithmic space-bounded complexity classes L" NL" co-NL, and P, for eraser Turing machines  ...  Meinel and S. Waack, Separating the eraser Turing machine classes, Theoretical Computer Science 86 (1991) 267-275.  ...  In particular we are grateful to Ingo Wegener for suggesting an important improvement of the proof of Lemma 2.1.  ... 
doi:10.1016/0304-3975(91)90021-s fatcat:4headdg2wfbyvkmxpazvkhhjqi

Branching Programs for Tree Evaluation [chapter]

Mark Braverman, Stephen Cook, Pierre McKenzie, Rahul Santhanam, Dustin Wehr
2009 Lecture Notes in Computer Science  
Both methods yield the tight bounds Θ(k 3 ) and Θ(k 5/2 ) for deterministic and nondeterministic branching programs solving F T 3 2 (k) respectively.  ...  We introduce a "state sequence" method that can match the size lower bounds on F T h d (k) obtained by the Neciporuk method and can yield slightly better (yet still subquadratic) bounds for some nonboolean  ...  The second author is grateful to Michael Taitslin for suggesting a version of the tree evaluation problem in which the nodes are labelled by fixed quasi groups (see [Tai05] ).  ... 
doi:10.1007/978-3-642-03816-7_16 fatcat:tpde7umheffuvo33tmcnbj5st4

Cumulative subject index volumes 68–71

1986 Information and Control  
analysis, 68, 105 for computing properties and functions of n-node forest stored in processor mesh, 69, 168 deterministic, applications to optimal parallel list ranking, 70, 32 network resource allocation  ...  Aggregation problems, formulation of several versions, analysis from recursion theoretic point of view, 70, 69 Algorithms for circular retrieval and k-nearest neighbor search problems, description and  ...  bases and Church-Rosser com- mutative Thue systems, 68, 196 upper, for neighbor searching, modifi- cation, 68, 105 Branching programs real-time, exponential lower bound for, 71, 87 Branching time  ... 
doi:10.1016/s0019-9958(86)80014-6 fatcat:hkligygazvcyvdgrhtvhrefpj4

Complexity Theoretical Results on Nondeterministic Graph-driven Read-Once Branching Programs

Beate Bollig
2003 RAIRO - Theoretical Informatics and Applications  
Branching programs are a well-established computation model for boolean functions, especially read-once branching programs (BP1s) have been studied intensively.  ...  Here it is proved that the consistency test is co-NP-complete for nondeterministic (parity) graph-driven BP1s. Moreover, a lower bound technique for nondeterministic graph-driven BP1s is presented.  ...  The author would like to thank Ingo Wegener for fruitful discussions on the subject of the paper.  ... 
doi:10.1051/ita:2003010 fatcat:5kwlzcpdujfqfmp5avd2uz47q4

Complexity Theoretical Results on Nondeterministic Graph-Driven Read-Once Branching Programs [chapter]

Beate Bollig
2003 Lecture Notes in Computer Science  
Branching programs are a well-established computation model for boolean functions, especially read-once branching programs (BP1s) have been studied intensively.  ...  Here it is proved that the consistency test is co-NP-complete for nondeterministic (parity) graph-driven BP1s. Moreover, a lower bound technique for nondeterministic graph-driven BP1s is presented.  ...  The author would like to thank Ingo Wegener for fruitful discussions on the subject of the paper.  ... 
doi:10.1007/3-540-36494-3_27 fatcat:72jylkrqrrcuhlckyaq52jepua

A Lower Bound Technique for Nondeterministic Graph-Driven Read-Once-Branching Programs and Its Applications [chapter]

Beate Bollig, Philipp Woelfel
2002 Lecture Notes in Computer Science  
We present a new lower bound technique for a restricted Branching Program model, namely for nondeterministic graph-driven read-once Branching Programs (g.d.-BP1s).  ...  We apply the technique in order to prove an exponential lower bound for integer multiplication for ωnondeterministic well-structured g.d.-BP1s.  ...  Acknowledgment We would like to thank Martin Sauerhoff and Ingo Wegener for fruitful discussions about the subject of this paper and helpful comments.  ... 
doi:10.1007/3-540-45687-2_10 fatcat:ehj7iq2iy5euhe66rk2xvf4zz4
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