2016/11/21 by Mikaël Mayer, Mayer, Mikaël, Jad Hamza +1
Computer Science · #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #cs.FL
paper · pdf · doi:10.48550/arxiv.1611.06703
arxiv created 2016/11/21 · arxiv updated 2016/11/22
A test set for a formal language (set of strings) L is a subset T of L such that for any two string homomorphisms f and g defined on L, if the restrictions of f and g on T are identical functions, then f and g are identical on the entire L. Previously, it was shown that there are context-free grammars for which smallest test sets are cubic in the size of the grammar, which gives a lower bound on tests set size. Existing upper bounds were higher degree polynomials; we here give the first algorithm to compute test sets of cubic size for all context-free grammars, settling the gap between the upper and lower bound.