Linearity is polynomially decidable for realtime pushdown store automata

S.A. Greibach
1979 Information and Control  
i If M is a realtime deterministic pushdown store acceptor, the language L(M) accepted by M by final state and empty store is linear context-free if and only if a certain grammar obtained from M is linear context-free. Hence, it is polynomially decidable for realtime deterministic pushdown store automata M whether L(M) is linear context-free. If M is a realtime deterministic pushdown store acceptor and L(M) is linear context-free, we can construct a realtime single turn deterministic pushdown
more » ... ore automaton _~r with L(M) = L(~I). Hence "L(M) ~ L" is decidable for M a realtime deterministic pushdown store acceptor and L the language accepted by final state by a single turn deterministic pushdown store acceptor. Many decision problems for deterministic pushdown store automata have remained open since they were first studied (Ginsburg and Greibach, 1966). The most notable is the equivalence problem; this problem has been shown equivalent to the equivalence problem for monadic recursion schemes (Friedman, 1977a) and various subeases have been solved (McNaughtonOyamaguchi et al., 1978). There are also the "containment" problems of the following nature: for a class of languages c~ which does not include all deterministic context-free languages and a deterministic pushdown store automaton M, is the language accepted by M a member of ¢C ? The strongest result on those lines was obtained by Stearns (1967) and the timing of the algorithm improved by Valian t (1975): it is decidable whether a deterministic pushdown store automaton accepts a regular set. Some containment problems are also equivalent to problems on schemes: the containment problem with respect to the class of simple languages is equivalent to the problem of determining whether or not a monadic recursion scheme has a strongly equivalent
doi:10.1016/s0019-9958(79)90134-7 fatcat:p6k4foitfvfmpa47aighxiuacy