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Boundedwidth polynomialsize branching programs recognize exactly those languages
 in NC’, in “Proceedings, 18th ACM STOC
, 1986
"... We show that any language recognized by an NC ’ circuit (fanin 2, depth O(log n)) can be recognized by a width5 polynomialsize branching program. As any boundedwidth polynomialsize branching program can be simulated by an NC ’ circuit, we have that the class of languages recognized by such prog ..."
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Cited by 209 (13 self)
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We show that any language recognized by an NC ’ circuit (fanin 2, depth O(log n)) can be recognized by a width5 polynomialsize branching program. As any boundedwidth polynomialsize branching program can be simulated by an NC ’ circuit, we have that the class of languages recognized by such programs is exactly nonuniform NC’. Further, following
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
BottomUp Induction of Oblivious ReadOnce Decision Graphs
, 1994
"... . We investigate the use of oblivious, readonce decision graphs as structures for representing concepts over discrete domains, and present a bottomup, hillclimbing algorithm for inferring these structures from labelled instances. The algorithm is robust with respect to irrelevant attributes, and ..."
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Cited by 45 (8 self)
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. We investigate the use of oblivious, readonce decision graphs as structures for representing concepts over discrete domains, and present a bottomup, hillclimbing algorithm for inferring these structures from labelled instances. The algorithm is robust with respect to irrelevant attributes, and experimental results show that it performs well on problems considered difficult for symbolic induction methods, such as the Monk's problems and parity. 1 Introduction Top down induction of decision trees [25, 24, 20] has been one of the principal induction methods for symbolic, supervised learning. The tree structure, which is used for representing the hypothesized target concept, suffers from some wellknown problems, most notably the replication problem and the fragmentation problem [23]. The replication problem forces duplication of subtrees in disjunctive concepts, such as (A B) (C D); the fragmentation problem causes partitioning of the data into fragments, when a higharity attrib...
On the Complexity of Branching Programs and Decision Trees for Clique Functions
, 1988
"... Exponential lower bounds on the complexity of computing the clique functions in the Boolean decisiontree model are proved. For onetimeonly branching programs, large polynomial lower bounds are proved for kclique functions if k is fixed, and exponential lower bounds if k increases with n. Finall ..."
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Cited by 42 (5 self)
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Exponential lower bounds on the complexity of computing the clique functions in the Boolean decisiontree model are proved. For onetimeonly branching programs, large polynomial lower bounds are proved for kclique functions if k is fixed, and exponential lower bounds if k increases with n. Finally, the hierarchy of the classes BP&‘) of all sequences of Boolean functions that may be computed by dtimes only branching programs of polynomial size is introduced. It is shown constructively that BP,(P) is a proper subset of BP#).
A TimeSpace Tradeoff for Sorting on NonOblivious Machines
, 1981
"... This paper adopts the latter strategy in order to pursue the complexity of sorting ..."
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Cited by 24 (2 self)
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This paper adopts the latter strategy in order to pursue the complexity of sorting
On the Power of Randomized Branching Programs
 IN PROCEEDINGS OF THE ICALP'96, LECTURE NOTES IN COMPUTER SCIENCE
, 1996
"... We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit function fn for which we prove that: 1) f n can be computed by polynomial size randomized readonce ordered branching program with a small onesided ..."
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Cited by 19 (9 self)
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We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit function fn for which we prove that: 1) f n can be computed by polynomial size randomized readonce ordered branching program with a small onesided error; 2) fn cannot be computed in polynomial size by deterministic readonce branching programs; 3) fn cannot be computed in polynomial size by deterministic read ktimes ordered branching program for k = o(n= log n) (the required deterministic size is exp \Gamma\Omega \Gamma n k \Delta\Delta ).
Neither Reading Few Bits Twice nor Reading Illegaly Helps Much
 Discrete Appl. Math
, 1996
"... We first consider socalled (1; +s)branching programs in which along every consistent path at most s variables are tested more than once. We prove that any such program computing a characteristic function of a linear code C has size at least 2\Omega\Gamma2/1 , where d 1 and d 2 are the minim ..."
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Cited by 19 (7 self)
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We first consider socalled (1; +s)branching programs in which along every consistent path at most s variables are tested more than once. We prove that any such program computing a characteristic function of a linear code C has size at least 2\Omega\Gamma2/1 , where d 1 and d 2 are the minimal distances of C and its dual C : We apply this criterion to explicit linear codes and obtain a superpolynomial lower bound for s = o(n= log n): Then we introduce a natural generalization of readktimes and (1; +s) branching programs that we call semantic branching programs. These programs correspond to corrupting Turing machines which, unlike eraser machines, are allowed to read input bits even illegally, i.e. in excess of their quota on multiple readings, but in that case they receive in response an unpredictably corrupted value. We generalize the abovementioned bound to the semantic case, and also prove exponential lower bounds for semantic readonce nondeterministic branching programs.
Two Lower Bounds for Branching Programs
, 1986
"... . The first result concerns branching programs having width (log n) O(1) . We give an \Omega\Gamma n log n= log log n) lower bound for the size of such branching programs computing almost any symmetric Boolean function and in particular the following explicit function: "the sum of the input vari ..."
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Cited by 19 (1 self)
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. The first result concerns branching programs having width (log n) O(1) . We give an \Omega\Gamma n log n= log log n) lower bound for the size of such branching programs computing almost any symmetric Boolean function and in particular the following explicit function: "the sum of the input variables is a quadratic residue mod p" where p is any given prime between n 1=4 and n 1=3 . This is a strengthening of previous nonlinear lower bounds obtained by Chandra, Furst, Lipton and by Pudl'ak. We mention that by iterating our method the result can be further strengthened to \Omega\Gamma n log n). The second result is a C n lower bound for readonceonly branching programs computing an explicit Boolean function. For n = \Gamma v 2 \Delta , the function computes the parity of the number of triangles in a graph on v vertices. This improves previous exp(c p n) lower bounds for other graph functions by Wegener and Z'ak. The result implies a linear lower bound for the space comp...
Complexity Theoretical Results for Randomized Branching Programs
, 1998
"... This work is settled in the area of complexity theory for restricted variants of branching programs. Today, branching programs can be considered one of the standard nonuniform models of computation. One reason for their popularity is that they allow to describe computations in an intuitively straigh ..."
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Cited by 9 (8 self)
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This work is settled in the area of complexity theory for restricted variants of branching programs. Today, branching programs can be considered one of the standard nonuniform models of computation. One reason for their popularity is that they allow to describe computations in an intuitively straightforward way and promise to be easier to analyze than the traditional models. In complexity theory, we are mainly interested in upper and lower bounds on the size of branching programs. Although proving superpolynomial lower bounds on the size of general branching programs still remains a challenging open problem, there has been considerable success in the study of lower bound techniques for various restricted variants, most notably perhaps readonce branching programs and OBDDs (ordered binary decision diagrams). Surprisingly, OBDDs have also turned out to be extremely useful in practical applications as a data structure for Boolean functions. So far, research has concentrated on determinis...
On the Power of Randomized Ordered Branching Programs
, 1997
"... We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit boolean function fn : f0; 1g n ! f0; 1g for which we prove that: 1) fn can be computed by polynomial size randomized readonce ordered branching progr ..."
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Cited by 6 (1 self)
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We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit boolean function fn : f0; 1g n ! f0; 1g for which we prove that: 1) fn can be computed by polynomial size randomized readonce ordered branching program with a small onesided error; 2) fn cannot be computed in polynomial size by nondeterministic ordered read A ktimes branching program for k = o(n= log n) (any nondeterministic ordered read A ktimes branching program that computes function fn has the size no less than 2 (n\Gamma1)=(2k\Gamma1) ). By read A ktimes branching program we define branching program with the property: no input variable appears more than k times on any consistent accepting computation path in the program. 1 Preliminaries and definitions Different models of branching program introduced in [18, 19], has been studied extensively in the last decade (see [25]). A survey of known lower bounds for different...