A pumping lemma for DLI-languages Original Research Article

Stratified linear sets play a central role in the theory of bounded context-free languages, developed by Ginsburg (The Mathematical Theory of Context-Free Languages, McGraw-Hill, New York, 1966). The “Flip-Flop Lemma,” (Pure Math. Appl. Ser. A 6(2) (1995) 203), states, that the vector-set{(e0,…,em−1)∈Nm | δ0e0+⋯+δm−1em−1≠0},where δi∈{−1,0,1}, for i=0,…,m−1, and N denotes the set of non-negative integers, is a stratified semilinear set, i.e., a finite union of stratified linear sets. In this paper, we generalize the statement of the lemma giving a necessary and sufficient condition for a DLI-set (i.e., for a vector-set Defined by Linear Inequalities) to be stratified semilinear.