What is meaning of the term "language"? I don't have much formal background, and I could not find a suitable explanation for this after searching on Google/Wikipedia.

What is the meaning of the term "language" as used in cryptographic protocols?

Sample sentence from a recent paper:


  Every language in BQP admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical(and quantum) polynomial-time verifiers.
The concept of language has been systematized. For example here you can become familiar with this in an accessible way.

In the article you are reading the language has such meaning:

Wikipedia BQP:


  A language L is in BQP if and only  if and only if and only if there exists a polynomial-time uniform family of quantum circuits   $\{Q_n:n \in \mathbb{N}\}$, such that
  
  
  For all $n \in \mathbb{N}$, ''Qn'' takes ''n'' qubits as input and outputs 1 bit
  For all ''x'' in ''L'', $\mathrm{Pr}(Q_{|x|}(x)=1)\geq \tfrac{2}{3}$
  For all ''x'' not in ''L'', $\mathrm{Pr}(Q_{|x|}(x)=0)\geq  \tfrac{2}{3}$
  
  
  Alternatively, one can define BQP in terms of quantum Turing machines. A language L is in BQP if and only if there exists a polynomial quantum Turing machine that accepts L with an error probability of at most 1/3 for all instances.