Graph driven BDDs — a new data structure for Boolean functions

Sieling, Detlef; Wegener, Ingo

doi:10.1016/0304-3975(94)00078-w

Cited by 87 publications

(41 citation statements)

References 7 publications

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“…Unlike OBDD, here we no longer require the same variable order on different paths. FBDD are known to be strictly more expressive than OBDD over arbitrary (nonmonotone) Boolean expressions, for example the Weighted Bit Addressing problem admits polynomial sized FBDD, but no polynomial size OBDD [5,15,23]. On the other hand, to the best of our knowledge no monotone formula was known to separate these two classes.…”

Section: Queries and Fbddmentioning

confidence: 91%

“…, Xn) = X P i=1,n X i (where X0 = 0). Bryant [5] has shown that has it has no polynomial size OBDD, while Gergov and Meinel [15] and independently Sieling and Wegener [23] have shown that WBA has a polynomial sized FBDD. More examples are given in [26].…”

Section: Query Syntacticmentioning

confidence: 99%

“…monotone, and with polynomial size DNF) that has a polynomial size FBDD but no polynomial size OBDD. Previous examples separating these classes where Weighted Bit Addressing problem (WBA) [5,15,23], and other examples given in [26], and these were not "simple". Our result also constrasts UCQ to CQ − : for the latter it follows from [20] that CQ − (OBDD) = CQ − (FBDD).…”

Section: Queries and Fbddmentioning

confidence: 99%

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Knowledge Compilation Meets Database Theory: Compiling Queries to Decision Diagrams

Jha

Suciu

2012

Theory Comput Syst

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The goal of Knowledge Compilation is to represent a Boolean expression in a format in which it can answer a range of online-queries in PTIME. The online-query of main interest to us is model counting, because of its application to query evaluation on probabilistic databases, but other online-queries can be supported as well such as testing for equivalence, testing for implication, etc. In this paper we study the following problem. Given a database query q, decide whether its lineage can be compiled efficiently into a given target language. We consider four target languages, of strictly increasing expressive power(when the size of compilation is constrained to be polynomial in the input size): Read-Once Boolean formulae, OBDD, FBDD and d-DNNF. For each target, we study the class of database queries that admit polynomial size representation: these queries can also be evaluated in PTIME over probabilistic databases. When queries are restricted to conjunctive queries without self-joins, it was known that these four classes collapse to the class of hierarchical queries, which is also the class of PTIME queries over probabilistic databases. Our main result in this paper is that, in the case of Unions of Conjunctive Queries (UCQ), these classes form a strict hierarchy. Thus, unlike conjunctive queries without self-joins, the expressive power of UCQ differs considerably w.r.t. these target compilation languages. Moreover, we give a complete characterization of the first two target languages, based on the query's syntax.

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Section: Queries and Fbddmentioning

confidence: 91%

Section: Query Syntacticmentioning

confidence: 99%

Section: Queries and Fbddmentioning

confidence: 99%

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Knowledge Compilation Meets Database Theory: Compiling Queries to Decision Diagrams

Jha

Suciu

2012

Theory Comput Syst

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“…In [9] and [16] it was observed that FBDDs can be efficiently minimized with respect to all equivalent FBDDs which read the input variables in an equivalent order. The equivalence of orders of reading the input variables is expressed by using the notion of graph orderings.…”

Section: Binary Decision Diagrams (Bdds)mentioning

confidence: 99%

“…FBDD is the abbreviation for free binary decision diagrams, a data structure for representing and manipulating Boolean function, which were introduced by Gergov and Meinel in [9] and Sieling and Wegener in [16]. Due to specific algorithmic properties, FBDDs and in particular Ordered BDDs (OBDDs), a special kind of FBDDs, became a very usefull tool in the area of automatic hardware verification (see also the paper of Bryant [4] who initiated the study of graph-based data structures for Boolean function manipulation).…”

Section: Introductionmentioning

confidence: 99%

BDD-Based Cryptanalysis of Keystream Generators

Krause

2002

Advances in Cryptology — EUROCRYPT 2002

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Abstract. Many of the keystream generators which are used in practice are LFSR-based in the sense that they produce the keystream according to a rule y = C(L(x)), where L(x) denotes an internal linear bitstream, produced by a small number of parallel linear feedback shift registers (LFSRs), and C denotes some nonlinear compression function. We present an n O(1) 2 (1−α)/(1+α)n time bounded attack, the FBDD-attack, against LFSR-based generators, which computes the secret initial state x ∈ {0, 1} n from cn consecutive keystream bits, where α denotes the rate of information, which C reveals about the internal bitstream, and c denotes some small constant. The algorithm uses Free Binary Decision Diagrams (FBDDs), a data structure for minimizing and manipulating Boolean functions. The FBDD-attack yields better bounds on the effective key length for several keystream generators of practical use, so a 0.656n bound for the self-shrinking generator, a 0.6403n bound for the A5/1 generator, used in the GSM standard, a 0.6n bound for the E0 encryption standard in the one level mode, and a 0.8823n bound for the two-level E0 generator used in the Bluetooth wireless LAN system.

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Completeness and Non-Completeness Results with Respect to Read-Once Projections

Bollig

Wegener

1998

Information and Computation

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Graph driven BDDs — a new data structure for Boolean functions

Cited by 87 publications

References 7 publications

Knowledge Compilation Meets Database Theory: Compiling Queries to Decision Diagrams

Knowledge Compilation Meets Database Theory: Compiling Queries to Decision Diagrams

BDD-Based Cryptanalysis of Keystream Generators

Completeness and Non-Completeness Results with Respect to Read-Once Projections

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