Results 1  10
of
19
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 ..."
Abstract

Cited by 213 (14 self)
 Add to MetaCart
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 & ..."
Abstract

Cited by 190 (0 self)
 Add to MetaCart
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
Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity
, 1988
"... , Introduction and References only) Benny Chor Oded Goldreich MIT \Gamma Laboratory for Computer Science Cambridge, Massachusetts 02139 ABSTRACT \Gamma A new model for weak random physical sources is presented. The new model strictly generalizes previous models (e.g. the Santha and Vazirani model [2 ..."
Abstract

Cited by 187 (5 self)
 Add to MetaCart
, Introduction and References only) Benny Chor Oded Goldreich MIT \Gamma Laboratory for Computer Science Cambridge, Massachusetts 02139 ABSTRACT \Gamma A new model for weak random physical sources is presented. The new model strictly generalizes previous models (e.g. the Santha and Vazirani model [24]). The sources considered output strings according to probability distributions in which no single string is too probable. The new model provides a fruitful viewpoint on problems studied previously as: ffl Extracting almost perfect bits from sources of weak randomness: the question of possibility as well as the question of efficiency of such extraction schemes are addressed. ffl Probabilistic Communication Complexity: it is shown that most functions have linear communication complexity in a very strong probabilistic sense. ffl Robustness of BPP with respect to sources of weak randomness (generalizing a result of Vazirani and Vazirani [27]). The paper has appeared in SIAM Journal o...
On the Relation Between BDDs and FDDs
 INFORMATION AND COMPUTATION
, 1995
"... Data structures for Boolean functions build an essential component of design automation tools, especially in the area of logic synthesis. The state of the art data structure is the ordered binary decision diagram (OBDD), which results from general binary decision diagrams (BDDs), also called bran ..."
Abstract

Cited by 27 (12 self)
 Add to MetaCart
Data structures for Boolean functions build an essential component of design automation tools, especially in the area of logic synthesis. The state of the art data structure is the ordered binary decision diagram (OBDD), which results from general binary decision diagrams (BDDs), also called branching programs, by ordering restrictions. In the context of EXORbased logic synthesis another type of decision diagram (DD), called (ordered) functional decision diagram ((O)FDD) becomes increasingly important. We study the relation between (ordered, free) BDDs and FDDs. Both, BDDs and FDDs, result from DDs by defining the represented function in different ways. If the underlying DD is complete, the relation between both types of interpretation can be described by a Boolean transformation . This allows us to relate the FDDsize of f and the BDDsize of (f) also in the case that the corresponding DDs are free or ordered, but not (necessarily) complete. We use this property to derive...
On the Descriptive and Algorithmic Power of Parity Ordered Binary Decision Diagrams
 In Proc. of the 14th Symposium on Theoretical Aspects of Computer Science, volume 1200 of LNCS
, 1997
"... We present a data structure for Boolean functions, which we call ParityOBDDs or \Phi OBDDs, which combines the nice algorithmic properties of the wellknown ordered binary decision diagrams (OBDDs) with a considerably larger descriptive power. Beginning from an algebraic characterization of th ..."
Abstract

Cited by 19 (0 self)
 Add to MetaCart
We present a data structure for Boolean functions, which we call ParityOBDDs or \Phi OBDDs, which combines the nice algorithmic properties of the wellknown ordered binary decision diagrams (OBDDs) with a considerably larger descriptive power. Beginning from an algebraic characterization of the \PhiOBDD complexity we prove in particular that the minimization of the number of nodes, the synthesis, and the equivalence test for \PhiOBDDs, which are the fundamental operations for circuit verification, have efficient deterministic solutions. Several functions of pratical interest, i.e. the indirect storage access function, have exponential ODBBsize but are of polynomial size if \PhiOBDDs are used. Keywords: data structures for Boolean functions, BDDs, circuit verification 1 Introduction Formal circuit verification is a fundamantal task. The following approach for verification is often used (for a survey see [8] and [21]). A data structure for representing Boolean functions is...
On extracting private randomness over a public channel
 In Proc. RANDOM ’03
, 2003
"... We introduce the notion of a superstrong extractor. Given two independent weak random sources X, Y, such extractor EXT(·, ·) has the property that EXT(X, Y) is statistically random even if one is given Y. Namely, 〈Y, EXT(X, Y) 〉 ≈ 〈Y, R〉. Superstrong extractors generalize the notion of strong ext ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
We introduce the notion of a superstrong extractor. Given two independent weak random sources X, Y, such extractor EXT(·, ·) has the property that EXT(X, Y) is statistically random even if one is given Y. Namely, 〈Y, EXT(X, Y) 〉 ≈ 〈Y, R〉. Superstrong extractors generalize the notion of strong extractors [16], which assume that Y is truly random, and extractors from two weak random sources [26, 7] which only assure that EXT(X, Y) ≈ R. We show that superextractors have many natural applications to design of cryptographic systems in a setting when different parties have independent weak sources of randomness, but have to communicate over an insecure channel. For example, they allow one party to “help ” other party extract private randomness: the “helper ” simply sends Y, and the “client ” gets private randomness EXT(X, Y). In particular, it allows two parties to derive a nearly random key after initial agreement on only a weak shared key, without using ideal local randomness. We show that optimal superstrong extractors exist, which are capable of extracting all the randomness from X, as long as Y has a logarithmic amount of minentropy. This generalizes a similar result from strong extractors, and improves upon previously known bounds [7] for a weaker problem of randomness extraction from two independent random sources. We also give explicit superstrong extractors which work provided the
OKFDDs versus OBDDs and OFDDs
, 1995
"... Ordered Decision Diagrams (ODDs) as a means for the representation of Boolean functions are used in many applications in CAD. Depending on the decomposition type, various classes of ODDs have been defined, the most important being the Ordered Binary Decision Diagrams (OBDDs), the Ordered Functiona ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
Ordered Decision Diagrams (ODDs) as a means for the representation of Boolean functions are used in many applications in CAD. Depending on the decomposition type, various classes of ODDs have been defined, the most important being the Ordered Binary Decision Diagrams (OBDDs), the Ordered Functional Decision Diagrams (OFDDs) and the Ordered Kronecker Functional Decision Diagrams (OKFDDs). In this paper we clarify the computational power of OKFDDs versus OBDDs and OFDDs from a (more) theoretical point of view. We prove several exponential gaps between specific types of ODDs. Combining these results it follows that a restriction of the OKFDD concept to subclasses, such as OBDDs and OFDDs as well, results in families of functions which lose their efficient representation.
Constructing Small Sets That Are Uniform in Arithmetic Progressions
, 2002
"... this paper also satisfy (A ;N ) ..."
Readonce Projections and Formal Circuit Verification with Binary Decision Diagrams
 Proc. STACS'96
, 1995
"... Computational complexity is concerned with the complexity of solving problems and computing functions and not with the complexity of verifying circuit designs. The importance of formal circuit verification is evident. Therefore, a framework of a complexity theory for formal circuit verification with ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Computational complexity is concerned with the complexity of solving problems and computing functions and not with the complexity of verifying circuit designs. The importance of formal circuit verification is evident. Therefore, a framework of a complexity theory for formal circuit verification with binary decision diagrams is developed. This theory is based on readonce projections. For many problems it is determined whether and how they are related with respect to readonce projections. It is proved that multiplication can be reduced to squaring but squaring is not a readonce projection of multiplication. This perhaps surprising result is discussed. For most of the common binary decision diagram models of polynomial size complete problems with respect to readonce projections are described. But for the class of functions with polynomialsize free binary decision diagrams (readonce branching programs) no complete problem with respect to readonce projection exists. Supported by DF...