Flexibility and Optimization of QBF Skolem–Herbrand Certificates

Skolem and Herbrand functions are important certificates validating the truth and falsity, respectively, of quantified Boolean formulas (QBFs). They are essential in various synthesis and verification applications. Recent advancement established a linear time extraction of Skolem/Herbrand functions from QBF consensus/resolution proofs. However, the obtained functions are often excessively large and improper for practical applications. To overcome this limitation, this paper characterizes various flexibilities of QBF certificates, and exploits them for certificate simplification. Experiments show substantial reduction on QBF certificates in terms of circuit size and depth, which are of primary concerns for synthesis applications.