An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams

An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams

We prove an exponential lower bound on the size of proofs in the proof system operating with ordered binary decision diagrams introduced by Atserias, Kolaitis and Vardi [2]. In fact, the lower bound applies to semantic derivations operating with sets defined by OBDDs. We do not assume any particular format of proofs or ordering of variables, the hard formulas are in CNF. We utilize (somewhat in...

Exponential Lower Bounds for Refuting Random Formulas Using Ordered Binary Decision Diagrams

A propositional proof system based on ordered binary decision diagrams (OBDDs) was introduced by Atserias et al. in [AKV04]. Kraj́ıček proved exponential lower bounds for a strong variant of this system using feasible interpolation [Kra07], and Tveretina et al. proved exponential lower bounds for restricted versions of this system for refuting formulas derived from the Pigeonhole Principle [TSZ1...

Learning Ordered Binary Decision Diagrams

This note studies the learnability of ordered binary decision diagrams (obdds). We give a polynomial-time algorithm using membership and equivalence queries that nds the minimum obdd for the target respecting a given ordering. We also prove that both types of queries and the restriction to a given ordering are necessary if we want minimality in the output, unless P=NP. If learning has to occur ...

Ordered Binary Decision Diagrams and Minimal Trellises

Ordered binary decision diagrams (OBDDs) are graph-based data structures for representing Boolean functions. They have found widespread use in computer-aided design and in formal veriication of digital circuits. Minimal trellises are graphical representations of error-correcting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphi...

Ordered Binary Decision Diagrams as Knowledge-Bases