Related papers: Connecting Knowledge Compilation Classes and Width…
Several query evaluation tasks can be done via knowledge compilation: the query result is compiled as a lineage circuit from which the answer can be determined. For such tasks, it is important to leverage some width parameters of the…
We generalize many results concerning the tractability of SAT and #SAT on bounded treewidth CNF-formula in the context of Quantified Boolean Formulas (QBF). To this end, we start by studying the notion of width for OBDD and observe that the…
We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width…
The evaluation of a query over a probabilistic database boils down to computing the probability of a suitable Boolean function, the lineage of the query over the database. The method of query compilation approaches the task in two stages:…
Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be…
Knowledge compilation studies the trade-off between succinctness and efficiency of different representation languages. For many languages, there are known strong lower bounds on the representation size, but recent work shows that, for some…
We introduce Tree Decision Diagrams (TDD) as a model for Boolean functions that generalizes OBDD. They can be seen as a restriction of structured d-DNNF; that is, d-DNNF that respect a vtree $T$. We show that TDDs enjoy the same…
Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…
In this paper we study the role of cliquewidth in succinct representation of Boolean functions. Our main statement is the following: Let $Z$ be a Boolean circuit having cliquewidth $k$. Then there is another circuit $Z^*$ computing the same…
We study the problem of enumerating the satisfying assignments for circuit classes from knowledge compilation, where assignments are ranked in a specific order. In particular, we show how this problem can be used to efficiently perform…
We show new limits on the efficiency of using current techniques to make exact probabilistic inference for large classes of natural problems. In particular we show new lower bounds on knowledge compilation to SDD and DNNF forms. We give…
Decision \textsc{dnnf} (a.k.a. $\wedge_d$-\textsc{fbdd}) is an important special case of Decomposable Negation Normal Form (\textsc{dnnf}), a landmark knowledge compilation model. Like other known \textsc{dnnf} restrictions, Decision…
In this paper we show that a CNF cannot be compiled into an Ordered Binary Decision Diagram (OBDD) of fixed-parameter size parameterized by the primal graph treewidth of the CNF. Thus we provide a parameterized separation between OBDDs and…
In this paper we study complexity of an extension of ordered binary decision diagrams (OBDDs) called $c$-OBDDs on CNFs of bounded (primal graph) treewidth. In particular, we show that for each $k$ there is a class of CNFs of treewidth $k…
Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision…
Propositional model counting (#SAT) can be solved efficiently when the input formula is in deterministic decomposable negation normal form (d-DNNF). Translating an arbitrary formula into a representation that allows inference tasks, such as…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation…
We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations…
We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly $\pm 1$, and the resulting models are typically equivalent to networks whose nonzero weights are also $\pm 1$. The method…