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23
Wrappers For Performance Enhancement And Oblivious Decision Graphs
, 1995
"... In this doctoral dissertation, we study three basic problems in machine learning and two new hypothesis spaces with corresponding learning algorithms. The problems we investigate are: accuracy estimation, feature subset selection, and parameter tuning. The latter two problems are related and are stu ..."
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Cited by 107 (8 self)
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In this doctoral dissertation, we study three basic problems in machine learning and two new hypothesis spaces with corresponding learning algorithms. The problems we investigate are: accuracy estimation, feature subset selection, and parameter tuning. The latter two problems are related and are studied under the wrapper approach. The hypothesis spaces we investigate are: decision tables with a default majority rule (DTMs) and oblivious readonce decision graphs (OODGs).
Efficient Boolean Manipulation with OBDD's Can be Extended to FBDD's
, 1993
"... OBDD's are the stateoftheart data structure for Boolean function manipulation since basic tasks of Boolean manipulation such as testing equivalence, satisfiability, or tautology, and performing single Boolean synthesis steps can be done efficiently. In the following we show that the efficient man ..."
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Cited by 37 (0 self)
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OBDD's are the stateoftheart data structure for Boolean function manipulation since basic tasks of Boolean manipulation such as testing equivalence, satisfiability, or tautology, and performing single Boolean synthesis steps can be done efficiently. In the following we show that the efficient manipulation of OBDD's can be extended to a more general data structure, socalled FBDD's. In detail, the advantages of using FBDD's instead of OBDD's are ffl FBDD's are generally more (sometimes even exponentially more) succinct than OBDD's, ffl FBDD's provide, similarly to OBDD's, canonical representations of Boolean functions, and ffl in terms of FBDD's basic tasks of Boolean manipulation can be performed similarly efficient as in terms of OBDD's. The power of the FBDDconcept is demonstrated by showing that the verification of the benchmark circuit design for the hidden weighted bit function HWB proposed by Bryant can be carried out efficiently in terms of FBDD's while, for princip...
A Lower Bound For Integer Multiplication With ReadOnce Branching Programs
 Proceedings of the 27th STOC
, 1998
"... . We prove that readonce branching programs computing integer multiplication require size 2 ## # n) . This is the first nontrivial lower bound for multiplication on branching programs that are not oblivious. By the appropriate problem reductions, we obtain the same lower bound for other arithmeti ..."
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Cited by 34 (0 self)
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. We prove that readonce branching programs computing integer multiplication require size 2 ## # n) . This is the first nontrivial lower bound for multiplication on branching programs that are not oblivious. By the appropriate problem reductions, we obtain the same lower bound for other arithmetic functions. Key words. multiplication, readonce, branching programs, BDD, verification AMS subject classifications. 68Q05, 68Q25, 68M15 PII. S0097539795290349 1. Introduction and background. It is well known that many functions, some of them very simple, cannot be computed by readonce branching programs of polynomial size [We88, Za84, Du85, We87, BHST87, Ju88, Kr88]. Interest in whether integer multiplication can be so computed has been created by recent developments in the field of digital design and hardware verification. 1.1. Hardware verification and branching programs. The central problem of verification is to check whether a combinational hardware circuit has been correctly designe...
Frontiers of Feasible and Probabilistic Feasible Boolean Manipulation with Branching Programs
 Proc. of 10th Annual Symposium on Theoretical Aspects of Computer Science (Feb.), Lecture Notes in Computer Science 665
, 1993
"... Abstract. A central issue in the solution of many computer aided design problems is to find concise representations for circuit designs and their functional specification. Recently, a restricted type of branching programs (OBDDs) proved to be extremely useful for representing Boolean functions for v ..."
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Cited by 20 (7 self)
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Abstract. A central issue in the solution of many computer aided design problems is to find concise representations for circuit designs and their functional specification. Recently, a restricted type of branching programs (OBDDs) proved to be extremely useful for representing Boolean functions for various CAD applications [Bry92]. Unfortunatelly, many circuits of practical interest provably require OBDDrepresentations of exponential size. In the following we systematically study the question up to what extend more concise BPrepresentations can be successfully used in symbolic Boolean manipulation, too. We prove, in very general settings,  The frontier of efficient (deterministic) symbolic Boolean manipulation on the basis of BPrepresentations are readonceonly branching programs (BP1).  The frontier of efficient probabilistic manipulation with BPbased data structures are parity readonceonly branching programs (\Phi BP1). Since BP1s and \PhiBP1s are generally mor...
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 ..."
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Cited by 18 (0 self)
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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...
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...
Bounds on the OBDDSize of Integer Multiplication via Universal Hashing
, 2005
"... Bryant [5] has shown that any OBDD for the function MULn−1,n, i.e. the middle bit of the nbit multiplication, requires at least 2 n/8 nodes. In this paper a stronger lower bound of essentially 2 n/2 /61 is proven by a new technique, using a universal family of hash functions. As a consequence, one ..."
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Cited by 13 (1 self)
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Bryant [5] has shown that any OBDD for the function MULn−1,n, i.e. the middle bit of the nbit multiplication, requires at least 2 n/8 nodes. In this paper a stronger lower bound of essentially 2 n/2 /61 is proven by a new technique, using a universal family of hash functions. As a consequence, one cannot hope anymore to verify e.g. 128bit multiplication circuits using OBDDtechniques because the representation of the middle bit of such a multiplier requires more than 3 · 10 17 OBDDnodes. Further, a first nontrivial upper bound of 7/3 · 2 4n/3 for the OBDDsize of MULn−1,n is provided.
On the Size of Randomized OBDDs and ReadOnce Branching Programs for kStable Functions
 In Proc. of the 16th Ann. Symp. on Theoretical Aspects of Computer Science (STACS), LNCS 1563
, 1999
"... In this paper, a simple technique which unifies the known approaches for proving lower bound results on the size of deterministic, nondeterministic, and randomized OBDDs and kOBDDs is described. ..."
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Cited by 12 (9 self)
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In this paper, a simple technique which unifies the known approaches for proving lower bound results on the size of deterministic, nondeterministic, and randomized OBDDs and kOBDDs is described.
Symbolic Topological Sorting with OBDDs
"... We present a symbolic OBDD algorithm for topological sorting which requires O(log² V) OBDD operations. Then we analyze its true runtime for the directed grid graph and show an upper bound of O(log^4 V · log log V). This is the first true runtime analysis of a symbolic OBDD algorithm for a fun ..."
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Cited by 10 (0 self)
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We present a symbolic OBDD algorithm for topological sorting which requires O(log² V) OBDD operations. Then we analyze its true runtime for the directed grid graph and show an upper bound of O(log^4 V · log log V). This is the first true runtime analysis of a symbolic OBDD algorithm for a fundamental graph problem, and it demonstrates that one can hope that the algorithm behaves well for sufficiently structured inputs.
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...