A grammatical approach to the LBA problem
In this paper, the degree of non-regulation for programmed grammars is introduced, as the largest number of elements in success or in failure fields. We show that this measure can be restricted to two without loss of generative capacity. Moreover, we present interrelations between the lba problem on the one hand and the relationship between the families of languages described by λ-free programmed grammars with degree of non-regulation one and two on the other hand. Especially, in case of accepting programmed grammars with monotone core rules and leftmost derivations this relationship exactly characterizes the lba problem.
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