Making $\textsf{IP}=\textsf{PSPACE}$ Practical: Efficient Interactive Protocols for BDD Algorithms

TL;DR

This paper demonstrates how interactive protocols, traditionally theoretical, can be practically implemented using BDDs to certify the correctness of automated reasoning tools, specifically for counting solutions in QBF instances.

Contribution

It introduces a practical interactive protocol for P using BDDs, bridging the gap between theoretical PSPACE protocols and real-world automated reasoning applications.

Findings

Proposed an interactive protocol for P with minimal overhead.

Implemented the protocol in the LIC certifying tool.

Achieved competitive performance with state-of-the-art QBF-solvers.

Abstract

We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all $\textsf{PSPACE}$ problems. The verifier of a protocol checks the prover's answer to a problem instance in probabilistic polynomial time, with polynomially many bits of communication, and with exponentially small probability of error. (The prover may need exponential time.) Existing interactive protocols are not used in practice because their provers use naive algorithms, inefficient even for small instances, that are incompatible with practical implementations of automated reasoning. We bridge the gap between theory and practice by means of an interactive protocol whose prover uses BDDs. We consider the problem of counting the number of assignments to a QBF instance ($\#\textrm{CP}$), which has a natural BDD-based algorithm. We give an interactive protocol for $\#\textrm{CP}$ whose prover is implemented on top of an extended BDD library. The prover has only a linear overhead in computation time over the natural algorithm. We have implemented our protocol in $\textsf{blic}$, a certifying tool for $\#\textrm{CP}$. Experiments on standard QBF benchmarks show that $\textsf{blic}$ is competitive with state-of-the-art QBF-solvers. The run time of the verifier is negligible. While loss of absolute certainty can be concerning, the error probability in our experiments is at most $10^{-10}$ and reduces to $10^{-10k}$ by repeating the verification $k$ times.