The state complexities of some basic operations on regular languages
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We consider the state complexity of basic concatenation operations for regular tree languages. We show that the sequential (respectively, parallel) concatenation of tree languages recognized by deterministic bottom-up automata with m and n states can be recognized by an automaton with (n+1)@?(m@?2^n+2^n^-^1)-1 (respectively, m@?2^n+2^n^-^1-1) states, and establish matching state complexity lower bounds. The bound for sequential concatenation of tree languages differs by an order of magnitude from the corresponding bound for regular string languages.