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44
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 36 (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 30 (3 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 AC° 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...
Amplifying lower bounds by means of selfreducibility
 In IEEE Conference on Computational Complexity
, 2008
"... We observe that many important computational problems in NC 1 share a simple selfreducibility property. We then show that, for any problem A having this selfreducibility property, A has polynomial size TC 0 circuits if and only if it has TC 0 circuits of size n 1+ɛ for every ɛ>0 (counting the numb ..."
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Cited by 13 (4 self)
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We observe that many important computational problems in NC 1 share a simple selfreducibility property. We then show that, for any problem A having this selfreducibility property, A has polynomial size TC 0 circuits if and only if it has TC 0 circuits of size n 1+ɛ for every ɛ>0 (counting the number of wires in a circuit as the size of the circuit). As an example of what this observation yields, consider the Boolean Formula Evaluation problem (BFE), which is complete for NC 1 and has the selfreducibility property. It follows from a lower bound of Impagliazzo, Paturi, and Saks, that BFE requires depth d TC 0 circuits of size n 1+ɛd. If one were able to improve this lower bound to show that there is some constant ɛ>0 such that every TC 0 circuit family recognizing BFE has size n 1+ɛ, then it would follow that TC 0 ̸ = NC 1. We show that proving lower bounds of the form n 1+ɛ is not ruled out by the Natural Proof framework of Razborov and Rudich and hence there is currently no known barrier for separating classes such as ACC 0,TC 0 and NC 1 via existing “natural ” approaches to proving circuit lower bounds. We also show that problems with small uniform constantdepth circuits have algorithms that simultaneously have small space and time bounds. We then make use of known timespace tradeoff lower bounds to show that SAT requires uniform depth d TC 0 and AC 0 [6] circuits of size n 1+c for some constant c depending on d. 1