Descriptional Complexity of Union and Star on Context-Free Languages
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We investigate context-free languages with respect to the measures Prod and Symb
of descriptional complexity, which give the minimal number of productions and the
minimal total number of symbols in productions, respectively, necessary to generate
the language by context-free grammars. In particular, we consider the behaviour of
these measures with respect to operations. For a measure $K\in \{\Prod,\Symb\}$, given
natural numbers $c_1,c_2,\dots ,c_n$ and an $n$-ary operation $\tau$ on languages, we discuss the
set $g_{\tau,K}(c_1,c_2,\dots ,c_n)$ which is the range of $K(\tau(L_1,L_2,\dots , L_n))$ where, for $1\leq i\leq n$,
$L_i$ is a context-free language with $K(L_i)=c_i$. The operations under discussion are
union and Kleene closure.