Equivalence problem

In theoretical computer science and formal language theory, the equivalence problem is the question of determining, given two representations of formal languages, whether they denote the same formal language.

The complexity and decidability of this decision problem depends upon the type of representation under consideration. For instance, in the case of finite-state automata, equivalence is decidable, and the problem is PSPACE-complete, whereas it is undecidable for pushdown automata, context-free grammars, etc.