State Grammars with Stores
State grammars are context-free grammars where the productions have states associated with them, and can only be applied to a nonterminal if the current state matches the state in the production. Once states are added to grammars, it is natural to add various stores, similar to machine models. With such extensions, productions can only be applied if both the state and the value read from each store matches between the current sentential form and the production. Here, generative capacity results are presented for different derivation modes, with and without additional stores. In particular, with the standard derivation relation, it is shown that adding reversal-bounded counters does not increase the capacity, and states are enough. Also, state grammars with reversal-bounded counters that operate using leftmost derivations are shown to coincide with languages accepted by one-way machines with a pushdown and reversal-bounded counters, and these are surprisingly shown to be strictly weaker than state grammars with the standard derivation relation (and no counters). Complexity results of some decision problems involving state grammars with counters are also studied.
KeywordsGrammars Reversal-bounded counters Automata models Matrix grammars
- 10.Ibarra, O.H.: Grammatical characterizations of NPDAs and VPDAs with counters. In: Han, Y.S., Salomaa, K. (eds.) 21st International Conference on Implementation and Application of Automata, CIAA 2016, Seoul, South Korea. Lecture Notes in Computer Science, vol. 9705, p. 11 (2016). Invited abstract, journal version submittedGoogle Scholar
- 16.Stiebe, R.: Slender matrix languages, pp. 375–385. World Scientific (2000)Google Scholar