Abstract
In this paper, we investigate the complexity of deciding closeness, segment equivalence and sparseness for context-free and regular languages. It will be shown that the closeness problem for context-free grammars (CFGs) is undecidable while it is PSPACE-complete for nondeterministic finite automata (NFAs) and NL-complete for deterministic finite automata (DFAs). The segment equivalence problems for CFGs and NFAs are co-NP-complete. It is NL-complete for DFAs. If encoded in binary, the segment equivalence problems for CFGs and NFAs are co-NE-complete and PSPACE-complete, respectively. The sparseness problems for NFAs and DFAs are NL-complete. We also show that the equivalence problems for CFGs and NFAs generating commutative languages are II 2 P -complete and co-NP-complete, respectively. For trim DFAs generating commutative languages the equivalence problem is in L.
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