Knowledge Compilation for Quantification in Alternating Automata

2026-05-03

AI Summary

Existing approaches to handling universal quantification based on nondeterministic Büchi automata rely on complementation, which incurs high computational costs. This work proposes a knowledge compilation method tailored to alternating safety automata, introducing for the first time a normal form that supports efficient existential and universal quantifier projection. By structurally transforming the transition function using binary decision diagrams (BDDs), the method eliminates the need for complementation and enables stepwise elimination of quantifier sequences. A prototype implementation demonstrates substantial performance gains over state-of-the-art techniques on QPTL satisfiability benchmarks, confirming both the feasibility and superiority of the proposed approach.

Abstract

We present a knowledge compilation approach for existential and universal quantification in alternating automata. Knowledge compilation transforms formulas into normal forms with special properties that enable efficient answering of questions of interest. For Boolean formulas, several normal forms that have proven effective for existential/universal quantification, and even for functional synthesis, have been studied in the literature. For infinite word automata, quantification is a fundamental operation in verification tasks such as QPTL satisfiability checking and HyperLTL model checking. Existing algorithms rely on nondeterministic infinite word automata, where existential projection can be efficiently performed state-wise, but universal projection requires complementation. Complementing nondeterministic infinite word automata, however, is expensive in practice, making existing algorithms infeasible for automata in practice. Towards addressing this problem, we propose novel knowledge compilation techniques for existential and universal quantification on alternating safety automata. Our approach compiles alternating automata into normal forms where projection can be applied uniformly and efficiently to each state's transition function. Using the compilations for each type of quantification, we can effectively eliminate a sequence of alternating quantifiers in formulas without complementation. Our BDD-based prototype demonstrates the practical effectiveness of our algorithms on a suite of QPTL satisfiability benchmarks.

Problem

• alternating automata
• universal quantification
• complementation
• knowledge compilation
• infinite word automata

Innovation

• knowledge compilation
• alternating automata
• quantification
• projection
• safety automata