Definability for model counting

Improving Model Counting by Leveraging Definability

We present a new preprocessing technique for propositional model counting. This technique leverages definability, i.e., the ability to determine that some gates are implied by the input formula ⌃. Such gates can be exploited to simplify ⌃ without modifying its number of models. Unlike previous techniques based on gate detection and replacement, gates do not need to be made explicit in our appro...

Logical Definability of Counting Functions

The relationship between counting functions and logical expressibility is explored. The most well studied class of counting functions is #P, which consists of the functions counting the accepting computation paths of a nondeterministic polynomial-time Turing machine. For a logic L, #L is the class of functions on nite structures counting the tuples (T ; c) satisfying a given formula (T ; c) in ...

Inductive Definability with Counting on Finite Structures

3 Definability and a Nonlinear Sigma Model

The concept of definability of physics fields is introduced and a set-theoretical foundation is proposed. In this foundation, we obtain a scale invariant nonlinear sigma model and then show that quantization of the model is necessary and sufficient for definability. We also obtain com-pactification of the spatial dimensions effectively and show its equivalence to quantization. We look to provid...

Algorithms for Propositional Model Counting

We present algorithms for the propositional model counting problem #SAT. The algorithms utilize tree decompositions of certain graphs associated with the given CNF formula; in particular we consider primal, dual, and incidence graphs. We describe the algorithms coherently for a direct comparison and with sufficient detail for making an actual implementation reasonably easy. We discuss several a...