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45
TimeSpace Tradeoffs for Branching Programs
, 1999
"... We obtain the first nontrivial timespace tradeoff lower bound for functions f : {0, 1}^n → {0, 1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε)n, for some constant ε > 0 ..."
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Cited by 44 (2 self)
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We obtain the first nontrivial timespace tradeoff lower bound for functions f : {0, 1}^n → {0, 1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε)n, for some constant ε > 0. We also give the first separation result between the syntactic and semantic readk models [BRS93] for k > 1 by showing that polynomialsize semantic readtwice branching programs can compute functions that require exponential size on any syntactic readk branching program. We also show...
Making Nondeterminism Unambiguous
, 1997
"... We show that in the context of nonuniform complexity, nondeterministic logarithmic space bounded computation can be made unambiguous. An analogous result holds for the class of problems reducible to contextfree languages. In terms of complexity classes, this can be stated as: NL/poly = UL/poly Lo ..."
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Cited by 37 (10 self)
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We show that in the context of nonuniform complexity, nondeterministic logarithmic space bounded computation can be made unambiguous. An analogous result holds for the class of problems reducible to contextfree languages. In terms of complexity classes, this can be stated as: NL/poly = UL/poly LogCFL/poly = UAuxPDA(log n; n O(1) )/poly
Readonce branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus
 in: Proceedings of the 29th ACM Symposium on Theory of Computing
, 1997
"... We investigate readonce branching programs for the following search problem: given a Boolean m n matrix with m>n, nd either an allzero row, or two 1's in some column. Our primary motivation is that this models regular resolution proofs of the pigeonhole principle PHP m n, and that for m>n 2 no low ..."
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Cited by 34 (9 self)
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We investigate readonce branching programs for the following search problem: given a Boolean m n matrix with m>n, nd either an allzero row, or two 1's in some column. Our primary motivation is that this models regular resolution proofs of the pigeonhole principle PHP m n, and that for m>n 2 no lower bounds are known for the length of such proofs. We prove exponential lower bounds (for arbitrarily large m!) if we further restrict this model by requiring the branching program either
Complexity of Restricted and Unrestricted Models of Molecular Computation
 DNA Based Computers 1, volume 27 of DIMACS
, 1995
"... In [Li1] and [Ad2] a formal model for molecular computing was proposed, which makes focused use of affinity purification. The use of PCR was suggested to expand the range of feasible computations, resulting in a second model. In this note, we give a precise characterization of these two models in te ..."
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Cited by 32 (4 self)
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In [Li1] and [Ad2] a formal model for molecular computing was proposed, which makes focused use of affinity purification. The use of PCR was suggested to expand the range of feasible computations, resulting in a second model. In this note, we give a precise characterization of these two models in terms of recognized computational complexity classes, namely branching programs (BP) and nondeterministic branching programs (NBP) respectively. This allows us to give upper and lower bounds on the complexity of desired computations. Examples are given of computable and uncomputable problems, given limited time. 1 Introduction Molecular computation, as introduced by [Ad1], provides a new approach to solving combinatorial inverse problems, where we are interested in computing f \Gamma1 (1) for nbit strings x and boolean function f . Instances of NPcomplete problems can be expressed in this form; for example 3SAT. Adleman's technique involves using individual DNA strands to represent poten...
Symmetric Logspace is Closed Under Complement
 CHICAGO JOURNAL OF THEORETICAL COMPUTER SCIENCE
, 1994
"... We present a Logspace, manyone reduction from the undirected stconnectivity problem to its complement. This shows that SL = co  SL. ..."
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Cited by 26 (1 self)
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We present a Logspace, manyone reduction from the undirected stconnectivity problem to its complement. This shows that SL = co  SL.
Searching Constant Width Mazes Captures the ACĀ° Hierarchy
 In Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
, 1997
"... We show that searching a width /' maze is complete for II, i.e., for the /"th level of the AC hierarchy. Equivalently, stconnectivity for width /' grid graphs is complete for II. As an application, we show that there is a data structure solving dynamic stconnectivity for constant width grid gr ..."
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Cited by 22 (4 self)
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We show that searching a width /' maze is complete for II, i.e., for the /"th level of the AC hierarchy. Equivalently, stconnectivity for width /' grid graphs is complete for II. As an application, we show that there is a data structure solving dynamic stconnectivity for constant width grid graphs with time bound O (log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools.
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.
A Lower Bound for Randomized ReadkTimes Branching Programs
 Electr. Coll. on Comp. Compl
, 1997
"... In this paper, we are concerned with randomized OBDDs and randomized readktimes branching programs. We present an example of a Boolean function which has polynomial size randomized OBDDs with small, onesided error, but only nondeterministic readonce branching programs of exponential size. Further ..."
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Cited by 15 (8 self)
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In this paper, we are concerned with randomized OBDDs and randomized readktimes branching programs. We present an example of a Boolean function which has polynomial size randomized OBDDs with small, onesided error, but only nondeterministic readonce branching programs of exponential size. Furthermore, we discuss a lower bound technique for randomized OBDDs with twosided error and prove an exponential lower bound of this type. Our main result is an exponential lower bound for randomized readktimes branching programs with twosided error. 1 Introduction Branching programs are a theoretically and practically interesting data structure for the representation of Boolean functions. In complexity theory, among other problems, lower bounds for the size of branching programs for explicitly defined functions and the relations of the various branching program models are investigated. A branching program (BP) on the variable set fx 1 ; : : : ; x n g is a directed acyclic graph with one sour...
On Arithmetic Branching Programs
 IN PROC. OF THE 13TH ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY
, 1998
"... The model of arithmetic branching programs is an algebraic model of computation generalizing the model of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs, a model introduced by Pudl'ak ..."
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Cited by 13 (0 self)
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The model of arithmetic branching programs is an algebraic model of computation generalizing the model of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs, a model introduced by Pudl'ak and Sgall [20]. Using this equivalence we prove that dependency programs are closed under conjunction over every field, answering an open problem of [20]. Furthermore, we show that span programs, an algebraic model of computation introduced by Karchmer and Wigderson [16], are at least as strong as arithmetic programs; every arithmetic program can be simulated by a span program of size not more than twice the size of the arithmetic program. Using the above results we give a new proof that NL/poly ` \PhiL/poly, first proved by Wigderson [25]. Our simulation of NL/poly is more efficient, and it holds for logspace counting classes over every field.