Turing completeness is the noun form of Turing complete, the entry that explains the concept and its role in blockchain design. This page explains the term as it appears in comparisons of smart contract platforms.
A system has Turing completeness if it can simulate a Turing machine, the abstract model of computation described by the mathematician Alan Turing in 1936. In practice, this means it can carry out any calculation that any computer can, provided it has enough time and memory, because it supports features such as conditional logic, loops and storage. Most everyday programming languages are Turing complete.
In crypto, the term is mainly used to contrast blockchains. Bitcoin's scripting language was deliberately kept limited, without general loops, to reduce the risk of bugs and attacks. Ethereum was designed around the Ethereum Virtual Machine, which is described as quasi-Turing complete, so that developers can write smart contracts of any complexity in languages such as Solidity. Because a program can in principle run forever, and no general method can predict whether it will stop, Ethereum caps every computation with gas, which makes each step cost a fee and halts code when the fee runs out.
The two forms of the term are used interchangeably. Critics note that greater expressiveness also widens the room for coding errors, a lesson drawn from smart contract hacks.