Abstract
We contrast bisimulation equivalence and language equivalence. There are two threads. First is that because bisimulation is more intensional, results in language and automata theory can be recast for bisimulation. The second thread is the contrast between definability of language equivalence and bisimulation equivalence. Bisimulation equivalence is definable as a "simple" formula in first-order logic with fixed points. We show that language equivalence is not definable as an unconditional projection of simple least fixed point.
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