Showing papers on "Deterministic pushdown automaton published in 1976"

A note on the succinctness of descriptions of deterministic languages

Abstract: It is shown that the relative succinctness that may be achieved by describing deterministic context-free languages by general unambiguous grammars rather than by deterministic pushdown automata is not bounded by any recursive function.

Some open problems in the theory of computation as questions about two-way deterministic pushdown automaton languages

Abstract: We considered some of the important unsolved problems in the theory of computation concerning the relationship between deterministic and nondeterministic computations, and between tape and time bounded computations. For each such problem we find an equivalent problem concerning two-way deterministic pushdown automaton languages.

On ω-sets associated with context-free languages

Abstract: New families of ω-languages (sets of infinite sequences) associated with context-free languages and pushdown automata are introduced. Their basic properties, such as inclusion relations, closure under the Boolean operations and periodicity, are studied and compared with the corresponding properties of the families of ω-languages accepted by finite automata. Moreover, a number of solvability and unsolvability results are proved. The results obtained imply that there is a definite difference between the family of ω-languages accepted by pushdown automata and the family associated with context-free languages.

On deterministic context-free languages, multihead automata, and the power of an auxiliary pushdown store

Abstract: A deterministic context-free language L0 is described which is log(n)-complete for the family of languages recognized by deterministic log(n)- tape bounded auxiliary pushdown automata in polynomial time. It follows that L0 is a “hardest” deterministic context-free language (DCFL), since all DCFL's are recognized in polynomial time by deterministic pushdown automata. L0 is, moreover, a simple precedence language and a simple LL(1) language. Thus the tape complexities of these proper subfamilies are essentially the same as the tape complexity of all DCFL's.We show that an auxiliary pushdown store does, in fact, add some power to some restricted families of log(n)-tape bounded Turing machines. The basic result is that every two-way 2k-head nondeterministic finite automation can be replaced by an equivalent two-way k-head nondeterministic pushdown automation. This indicates, also, that every 2k-head nondeterministic finite automation language can be recognized in 0(n3k) steps. Other results relate multihead automata classes with other multihead automata classes, with families recognized by log(n)-tape bounded Turing machines with restricted tape alphabets, and with time-bounded complexity classes.

On the complexity of finite, pushdown, and stack automata

Abstract: The complexity of predicates on several classes of formal languages is studied. For finite automata, pushdown automata, and several classes of stack automata, every nontrivial predicate on the languages accepted by the 1-way devices requires as much time and space as the recognition problem for any language accepted by the corresponding 2-way devices. Moreover there are nontrivial predicates on the languages accepted by the 1-way devices such that is the accepted language of some corresponding one or two head 2-way device. Thus our lower bounds are fairly tight.

Recognizing certain repetitions and reversals within strings

Abstract: Let P1 = {w e Σ*:w = wR, |w| ≫ 1} be the set of all nontrivial palindromes over Σ. In Part I, we present a linear-time on-line recognition algorithm for P1* ("palstar") on a random-access machine with addition and uniform cost criterion. We also present a lineartime on-line recognition algorithm for P12 on a multitape Turing machine and a recognition algorithm for P12 on a two-way deterministic pushdown automaton. The correctness of these algorithms is based on new "cancellation lemmas" for the languages P1* and P12. In Part II, we present real-time recognition algorithms for the languages {wxyxz e Σ*: |w|=r|x|, |y|=s|x|, |z|=t|x|} and {wxyxRz e Σ*: |w|=r|x|, |y|=s|x|, |z|=t|x|} on multitape Turing machines, for arbitrary fixed r, s, and t.

The Complexity of Finite Memory Programs with Recursion

Abstract: In an earlier paper (JACM, 1976) we studied the computational complexity of a number of questions of both programming and theoretical interest (e.g. halting, looping, equivalence) concerning the behaviour of programs written in an extremely simple programming language. These finite memory programs or fmps model the behaviour of FORTRAN-like programs with a finite memory whose size can be determined by examination of the program itself. The present paper is a continuation in which we extend the analysis to include ALGOL-like programs (called fmp^(rec) s) with the finite memory augmented by an implicit pushdown stack used to support recursion. Our major results are the following. First, we show that at least deterministic exponential time is required to determine whether a program in the basic fmpr~C model accepts a nonempty set. Then we show that a model with a limited version of call-by-name requires exponential space to determine acceptance of a nonempty set, and that a more sophisticated model with rewritable conditional formal parametershas an undecidable halting problem. The same lower bounds apply to the equivalence problem, which in contrast to the situation for the basic fmp model is not known to be decidable (since it is not known whether equivalence of deterministic pushdown automata is decidable).

Probabilistic pushdown automata

Abstract: The properties of Probabilistic Pushdown Automata (PPA) are examined. First PPA is defined, various basic properties of it are derived, and several more restrictive types are considered. Then, the families of random languages acceptable and generable by various types of PPA, as well as the families of languages acceptable and generable by various types of PPA with cut-point, are studied. The relationships among these families are also examined, and many interesting results are obtained. Among them, it is shown that the family of languages generable by PPA having uniform output length is the homomorphic closure of the family of languages acceptable by PPA.