Formal Models of Bitcoin Contracts: A Survey

Abstract

Although Bitcoin is mostly used as a decentralized application to transfer cryptocurrency, over the last 10 years there have been several studies on how to exploit Bitcoin to execute smart contracts. These are computer protocols which allow users to exchange bitcoins according to complex pre-agreed rules. Some of these studies introduce formal models of Bitcoin contracts, which specify their behavior in non-ambiguous terms, in some cases providing tools to automatically verify relevant contract properties. In this paper, we survey the formal models proposed in the scientific literature, comparing their expressiveness and applicability in the wild.

Analysis of a Consensus Protocol for Extending Consistent Subchains on the Bitcoin Blockchain

“…The cryptocurrencies scenario has provided a first concrete example of this intuition, since in this context, actors operate in a decentralized way, in order both to create and transfer crypto-assets [22]. Indeed, the blockchain and its protocol can enforce the contract execution, since each transaction is traceable and irreversible.…”

A Survey of Smart Contract Formal Specification and Verification

“…By now, a multitude of surveys addressing smart contract analysis has been published. These include a review of security vulnerabilities [24,96,144,174,213], verification approaches and tools [53,57,69,73,77,149,161,163,216], formal specification and modeling techniques [33,110,182], and languages for smart contract development [101,159]. We found several pieces of work discussing common design patterns of smart contracts [207,208,210,212], as well as studies of smart contract platforms and practical applications [25,32,201,205].…”

“…Singh et al [182] analyzed 35 research works on formal verification and specification techniques as well as languages for smart contracts, together with the issues and vulnerabilities they address. Bartoletti et al [33] compared five formal modeling techniques for Bitcoin smart contracts based on their expressiveness, usability, and suitability for verification. Furthermore, Ladleif and Weske [121] proposed a framework for evaluating formal modeling tools with respect to their capability to model a legal smart contract, and assessed eight visual tools for smart contracts modeling using this framework.…”

Is it Possible to Verify if a Transaction is Spendable?

“…The Bitcoin protocol and its Script language permit the design of different forms of smart contracts, and currently we have a variety of pre-designed contracts, and several formal models to understand the correctness of contracts, their semantics or their power [see e.g. (Bartoletti and Zunino, 2019)]. However, there are still lower-level complexity questions that remain unanswered about Script.…”

“…A comprehensive description of different formalizations and extensions of Script can be found in (Bartoletti and Zunino, 2018). These works have focused on proposing executable semantics of Script, and some extensions of it, and on enabling the formal verification of some properties of protocols defined in this language (Andrychowicz et al, 2014;O'Connor, 2017;Atzei et al, 2018b;Atzei et al, 2018a;Bartoletti and Zunino, 2019;Singh et al, 2020). In this sense, our definition of Script follows a different direction, guided by the need to study the unlockability problem, which, to the best of our knowledge, has not been considered in previous works.…”