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On CNF formulas irredundant with respect to unit clause propagation
Two CNF formulas are called ucp-equivalent, if they behave in the same way with respect to the unit clause propagation (UCP).
Bounds on the size of PC and URC formulas
Besides of this, we prove that the sizes of any two irredundant PC formulas for the same function differ at most by a factor polynomial in the number of the variables and present an example of a function demonstrating that a similar statement is not true for URC formulas.
Propagation complete encodings of smooth DNNF theories
Building on these encodings we generalize the result of (Abio et al. 2016) on a propagation complete encoding of decision diagrams and present a propagation complete encoding of a DNNF and its generalization for variables with finite domains.
Backdoor Decomposable Monotone Circuits and their Propagation Complete Encodings
We describe a compilation language of backdoor decomposable monotone circuits (BDMCs) which generalizes several concepts appearing in the literature, e. g. DNNFs and backdoor trees.
