Abstract
We describe four complete and recursively enumerable formal systems S 0, D 0, H 0, B 0 . Each one of them proves the decidability of some equivalence problem for some class of automata: namely the language equivalence problem for simple automata, the language equivalence problem for deterministic pushdown automata, the function equivalence problem for deterministic pushdown transducers with outputs in an abelian group, the bisimulation equivalence problem for loop-free pushdown automata.
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