Pseudo-MDPs: A Novel Framework for Efficiently Optimizing Last Revealer Seed Manipulations in Blockchains

Abstract: This study tackles the computational challenges of solving Markov Decision Processes (MDPs) for a restricted class of problems. It is motivated by the Last Revealer Attack (LRA), which undermines fairness in some Proof-of-Stake (PoS) blockchains such as Ethereum (\$400B market capitalization). We introduce pseudo-MDPs (pMDPs) a framework that naturally models such problems and propose two distinct problem reductions to standard MDPs. One problem reduction provides a novel, counter-intuitive perspective, and combining the two problem reductions enables significant improvements in dynamic programming algorithms such as value iteration. In the case of the LRA which size is parameterized by $\kappa$ (in Ethereum's case $\kappa$ = 32), we reduce the computational complexity from O(2^$\kappa$ $\kappa$^2^$\appa$+2)) to O($\kappa$^4) (per iteration). This solution also provide the usual benefits from Dynamic Programming solutions: exponentially fast convergence toward the optimal solution is guaranteed. The dual perspective also simplifies policy extraction, making the approach well-suited for resource-constrained agents who can operate with very limited memory and computation once the problem has been solved. Furthermore, we generalize those results to a broader class of MDPs, enhancing their applicability. The framework is validated through two case studies: a fictional card game and the LRA on the Ethereum random seed consensus protocol. These applications demonstrate the framework's ability to solve large-scale problems effectively while offering actionable insights into optimal strategies. This work advances the study of MDPs and contributes to understanding security vulnerabilities in blockchain systems.