Top-Down Algorithms for Constructing Structured DNNF: Theoretical and Practical Implications
نویسندگان
چکیده
We introduce a top-down compilation algorithm for constructing structured DNNF for any Boolean function. With appropriate restrictions, the algorithm can produce various subsets of DNNF such as deterministic DNNF and OBDD. We derive a size upper bound for structured DNNF based on this algorithm and use the result to generalize similar upper bounds known for several Boolean functions in the case of OBDD. We then discuss two realizations of the algorithm that work on CNF formulas. We show that these algorithms have time and space complexities that are exponential in the treewidth and the dual treewidth of the input.
منابع مشابه
A Lower Bound on the Size of Decomposable Negation Normal Form
We consider in this paper the size of a Decomposable Negation Normal Form (DNNF) that respects a given vtree (known as structured DNNF). This representation of propositional knowledge bases was introduced recently and shown to include OBDD as a special case (an OBDD variable ordering is a special type of vtree). We provide a lower bound on the size of any structured DNNF and discuss three parti...
متن کاملImprovement of the Exploration of the Search Space of a Top-Down Algorithm: Theoretical and Experimental Results
We study here concept learning from instances described as attribute-value lists in the frame of Top-Down induction algorithms. The goal of this work is to use known or unknown logical implications which are true on the instances in order to improve the exploration of a search space. We base our work on a lattice formalization (a lattice of instances and a lattice of terms) to show how one can ...
متن کاملOn the Role of Canonicity in Bottom-up Knowledge Compilation
We consider the problem of bottom-up compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boolean operators (usually called an Apply function). While such a polytime Apply function is known to exist for certain languages (e.g., OBDDs) and not exist for others (e.g., DNNF), its existence for certain languages remains...
متن کاملPattern Languages in Interaction Design
Now that individual patterns for Interaction Design have started to appear, the issue of structuring collections of patterns into Pattern Languages becomes relevant, both from a theoretical and a practical perspective. In this paper, we investigate how Pattern Languages in Interaction Design can be structured in a meaningful and practical way. A top-down approach is taken where patterns for Int...
متن کاملAn Improved Decision-DNNF Compiler
We present and evaluate a new compiler, called D4, targeting the Decision-DNNF language. As the state-of-the-art compilers C2D and Dsharp targeting the same language, D4 is a top-down treesearch algorithm exploring the space of propositional interpretations. D4 is based on the same ingredients as those considered in C2D and Dsharp (mainly, disjoint component analysis, conflict analysis and non-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010