# VDHLA: Variable Depth Hybrid Learning Automaton and Its Application to Defense Against the Selfish Mining Attack in Bitcoin

arXiv: https://arxiv.org/abs/2302.12096 · HTML: https://mlsanity.com/paper/2302.12096/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 15 Feb 2023.

## Builds on (most cited first, 9 of 9)

- [On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators](https://mlsanity.com/paper/2007.14268/) (2020)
- [On the Convergence of Tsetlin Machines for the XOR Operator](https://mlsanity.com/paper/2101.02547/) (2021)
- [Tsetlin Machine Embedding: Representing Words Using Logical Expressions](https://mlsanity.com/paper/2301.00709/) (2023)
- [A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks](https://mlsanity.com/paper/1805.02707/) (2018)
- [When Blockchain Meets AI: Optimal Mining Strategy Achieved By Machine Learning](https://mlsanity.com/paper/1911.12942/) (2019)
- [Majority is not Enough: Bitcoin Mining is Vulnerable](https://mlsanity.com/paper/1311.0243/) (2013)
- [The Miner's Dilemma](https://mlsanity.com/paper/1411.7099/) (2014)
- [Nik Defense: An Artificial Intelligence Based Defense Mechanism against Selfish Mining in Bitcoin](https://mlsanity.com/paper/2301.11463/) (2023)
- [On the Equivalence of the Weighted Tsetlin Machine and the Perceptron](https://mlsanity.com/paper/2212.13634/) (2022)

## Built on by (most cited first, 1 of 1)

- [New intelligent defense systems to reduce the risks of Selfish Mining and Double-Spending attacks using Learning Automata](https://mlsanity.com/paper/2307.00529/) (2023)

## Abstract (arXiv)

Learning Automaton (LA) is an adaptive self-organized model that improves its action-selection through interaction with an unknown environment. LA with finite action set can be classified into two main categories: fixed and variable structure. Furthermore, variable action-set learning automaton (VASLA) is one of the main subsets of variable structure learning automaton. In this paper, we propose VDHLA, a novel hybrid learning automaton model, which is a combination of fixed structure and variable action set learning automaton. In the proposed model, variable action set learning automaton can increase, decrease, or leave unchanged the depth of fixed structure learning automaton during the action switching phase. In addition, the depth of the proposed model can change in a symmetric (SVDHLA) or asymmetric (AVDHLA) manner. To the best of our knowledge, it is the first hybrid model that intelligently changes the depth of fixed structure learning automaton. Several computer simulations are conducted to study the performance of the proposed model with respect to the total number of rewards and action switching in stationary and non-stationary environments. The proposed model is compared with FSLA and VSLA. In order to determine the performance of the proposed model in a practical application, the selfish mining attack which threatens the incentive-compatibility of a proof-of-work based blockchain environment is considered. The proposed model is applied to defend against the selfish mining attack in Bitcoin and compared with the tie-breaking mechanism, which is a well-known defense. Simulation results in all environments have shown the superiority of the proposed model.