Boolean expression diagrams

Andersen, Henrik Reif; Hulgaard, Henrik

doi:10.1109/lics.1997.614938

Cited by 36 publications

(16 citation statements)

References 19 publications

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“…In order to reduce the soundness argument to more standard first-order terminology, we will recall that each constrained clause has a reading as a first-order formula using formulation (1). Then we establish that each clause added by conflict resolution are implied by the formula existing formula F. We also need to establish that all clauses that are used to annotate literals in the context are consequences of F. The Conflict rule creates an initial conflict clause C · Θ using a formula that already occurs in F. This clause is modified using the conflict resolution rules.…”

Section: Inference Rulesmentioning

confidence: 99%

“…We used reduced ordered BDDs in our evaluation of the calculus, but this is by no means the only possible representation. We may for instance delay forming canonical decision diagrams until it is required for evaluating (non-emptiness) queries (a technique used for Boolean Expression Diagrams [1]). It would also be illustrative to investigate how DPLL(SX ) applies to finite model finding and general first-order problems.…”

Section: Extensionsmentioning

confidence: 99%

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Deciding Effectively Propositional Logic Using DPLL and Substitution Sets

2009

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We introduce a DPLL calculus that is a decision procedure for the Bernays-Schönfinkel class, also known as EPR. Our calculus allows combining techniques for efficient propositional search with data-structures, such as Binary Decision Diagrams, that can efficiently and succinctly encode finite sets of substitutions and operations on these. In the calculus, clauses comprise of a sequence of literals together with a finite set of substitutions; truth assignments are also represented using substitution sets. The calculus works directly at the level of sets, and admits performing simultaneous constraint propagation and decisions, resulting in potentially exponential speedups over existing approaches.

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Section: Inference Rulesmentioning

confidence: 99%

Section: Extensionsmentioning

confidence: 99%

Deciding Effectively Propositional Logic Using DPLL and Substitution Sets

2009

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“…There are several extensions for the basic BDD's. For instance, in Boolean Expression Diagrams [1] there are three node types instead of the two presented above: a terminal node has a value 0 or 1, a variable node has a Boolean variable and operator node has a Boolean operator. Observe that the variable and operator nodes correspond the non-terminal nodes in the basic BDD description.…”

Section: Complexity Of Assignment Statementsmentioning

confidence: 99%

“…That is, it gives rather pessimistic results with larger number of input arguments, comparing to the size results obtained with BDD's [1]. Therefore, we adopted properties from the graph based approach presented with BDD's [9], [10].…”

Section: Complexity Of Assignment Statementsmentioning

confidence: 99%

Power Aware System Refinement

Tuominen

Westerlund

Plosila

2008

Electronic Notes in Theoretical Computer Science

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We propose a formal, power aware refinement of systems. The proposed approach lays its foundation to the traditional refinement calculus of Action Systems and its direct extension, time wise refinement method. The adaptation provides well-founded mathematical basis for the systems modeled with the Timed Action Systems formalism. In the refinement of an abstract system into more concrete one a designer must that show conditions of both functional and temporal properties, and furthermore, power related issues are satisfied.

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“…DDs for theories other than propositional logic have been studied extensively since the early 90's, capitalizing on the great success of BDDs and numerous BDD optimizations. Among these, we do not cover DDs -such as Binary Moment Diagrams (BMDs) [5], Algebraic Decision Diagrams (ADDs) [2], and Boolean Expression Diagrams (BEDs) [1] -which are restricted to variables with finite domains. Thus, the most relevant structures to LDDs are those that label the nodes with linear predicates over the reals.…”

Section: Introductionmentioning

confidence: 99%

Decision diagrams for linear arithmetic

Chaki

Gurfinkel

Strichman

2009

2009 Formal Methods in Computer-Aided Design

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Boolean manipulation and existential quantification of numeric variables from linear arithmetic (LA) formulas is at the core of many program analysis and software model checking techniques (e.g., predicate abstraction). We present a new data structure, Linear Decision Diagrams (LDDs), to represent formulas in LA and its fragments, which has certain properties that make it efficient for such tasks. LDDs can be seen as an extension of Difference Decision Diagrams (DDDs) to full LA. Beyond this extension, we make three key contributions. First, we extend sifting-based dynamic variable ordering (DVO) from BDDs to LDDs. Second, we develop, implement, and evaluate several algorithms for existential quantification. Third, we implement LDDs inside CUDD, a state-of-the-art BDD package, and evaluate them on a large benchmark consisting of 850 functions derived from the source code of 25 open source programs. Overall, our experiments indicate that LDDs are an effective data structure for program analysis tasks.

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Boolean expression diagrams

Cited by 36 publications

References 19 publications

Deciding Effectively Propositional Logic Using DPLL and Substitution Sets

Deciding Effectively Propositional Logic Using DPLL and Substitution Sets

Power Aware System Refinement

Decision diagrams for linear arithmetic

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