Showing papers on "Deterministic pushdown automaton published in 1978"
TL;DR: A tape hardest deterministic context-free language is described and the best upper bound known on the tape complexity of (deterministic) context- free languages is (log(n) 2).
Abstract: Let DSPACE(L(n)) denote the family of languages recognized by deterministic L(n)-tape bounded Turmg machines The pnnopal result described m this paper is the equivalence of the following statements (l) The determtmsttc context-free language L~ 2) (described m the paper) is m DSPACE(Iog(n)) (2) The simple LL(I) languages are m DSPACE(tog(n)) (3) The simple precedence languages are in DSPACE(Iog(n)). (4) DSPACE(Iog(n)) is identical to the famdy of languages recogmzed by deterministic two-way multlhead pushdown automata m polynomml tmae These results are obtained by constructing a determlmstlc context-free language L~ 2~ which is log(n)-complete for the family of determlmstlc context-free languages In other words, a tape hardest deterministic context-free language is described The best upper bound known on the tape complexity of (deterministic) context-free languages is (log(n)) 2
249 citations
TL;DR: Algebraic characterizations are obtained for each of the classes of ω-DCFL's, showing certain decision problems, generally undecidable, to be decidable within some of these classes.
56 citations
01 Jan 1978
TL;DR: This paper shows that unless the use of such parameterized definitions is restricted, new (unparameterized) types may be defined which more closely resemble deterministic context-free languages.
Abstract: It has long been known that recursively defined types in a highly typed language such as Algol 68 or Pascal may be tested for structural equivalence by the same algorithm that compares finite automata [5,11]. Several authors (for example, [3,8,9,16]) have proposed that classes of types be simultaneously defined by the use of parameterized type definitions, such asType list(x) = record val:x; next:↑list(x) end .This paper shows that unless the use of such parameterized definitions is restricted, new (unparameterized) types may be defined which more closely resemble deterministic context-free languages. In fact, the equivalence problem for such types becomes as hard as the (currently unsolved) deterministic pushdown automaton equivalence problem. Several restrictions on type definitions are considered which allow known equivalence algorithms to be applied.
42 citations
TL;DR: It is proved that there is an algorithm for deciding whether two deterministic stateless pushdown automata are equivalent and it is shown that equivalence can be tested in double-exponential time.
Abstract: It is proved that there is an algorithm for deciding whether two deterministic stateless pushdown automata are equivalent. It is shown that equivalence can be tested in double-exponential time.
28 citations
TL;DR: It is shown that such questtons as acceptance of the empty set, eqmvalence, and so on are retractable even for these relatively simple programs.
Abstract: In an earlier paper (JACM, 1976) we studied the computational complexity of a number of questions of both programming and theoretical interest (eg 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)
18 citations
14 citations
10 citations
TL;DR: It is shown that all the members of two distinct subclasses of deterministic context-free languages are recognizable in O(log n) tape complexity on off-line deterministic Turing machines.
Abstract: The tape complexity of context-free languages is investigated. It is shown that all the members of two distinct subclasses of deterministic context-free languages are recognizable in O(log n) tape complexity on off-line deterministic Turing machines.
9 citations
TL;DR: It is shown that the equivalence problem for non-singular automata is reducible to the problem of deciding whether or not a deterministic pushdown automaton is non- Singular.
7 citations
TL;DR: Classes of source languages which can be mapped by a deterministic pushdown transduction into a given object language (while their complement is mapped into the complement of the object language) are studied and the inverse DPDA transductions of the Dyck sets are studied.
17 Jul 1978
TL;DR: These results are based on the observation that the "triple construction" for converting a pushdown automaton into a context-free grammar is optimal.
Abstract: In pushdown automata, states can sometimes do more than stack symbols. More precisely, reducing the state set by a factor of k may require an increase in the stack alphabet by a factor of k2. These results are based on the observation that the "triple construction" for converting a pushdown automaton into a context-free grammar is optimal.
TL;DR: An algorithm is presented for converting a deterministic pushdown automaton (dpda) of size n into an equivalent dpda that always halts, which operates in linear time on a random access machine, and in time $O(n^2 )$ on a multi-tape Turing machine.
Abstract: An algorithm is presented for converting a deterministic pushdown automaton (dpda) of size n into an equivalent dpda that always halts. The dpda produced is of size $O(n)$. The algorithm operates in linear time on a random access machine (but may require the allocation of $O(n^2 )$ storage), and in time $O(n^2 )$ on a multi-tape Turing machine. Related results on polynomial time algorithms for dpda equivalence problems and for two-way pushdown automata language recognition problems are discussed.