Showing papers on "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: There are languages which can be recognized by a deterministic (k + 1)-headed oneway finite automaton but which cannot be recognizing by a k-headed one-way (deterministic or non-Deterministic) finite Automaton.
Abstract: : There are languages which can be recognized by a deterministic (k+1)-headed one-way finite automaton but which cannot be recognized by a k-headed one-way (deterministic or non-deterministic) finite automaton. Furthermore, there is a language accepted by a k-headed nondeterministic finite automaton which is accepted by no k-headed deterministic finite automaton. (Author)
128 citations
16 Oct 1978
TL;DR: It is shown that alternating pushdown automata are strictly more powerful than nondeterministic pushdown Automata and the number of alternations allowed during computations.
Abstract: Alternation is a generalization of nondeterminism in which existential and universal quantitiers can alternate during the course of a computation, whereas in a nondeterministic computation there are only existential quantifiers. Alternating Turing machines are defined and shown to accept precisely the recursively enumerable sets. Complexity classes of languages accepted by time(space-) bounded alternating Turing machines are characterized in terms of complexity classes of languages accepted by space(time-) bounded deterministic Turing machines. In particular, alternating polynomial time is equivalent to deterministic polynomial space and alternating polynomial space is equivalent to deterministic 'exponential time. Subrecursive quantifier hierarchies are defined in terms of timeor space-bounded alternating Tufing machines by bounding the number of alternations allowed during computations. Alternating finite-state automata are defined and shown to accept only regular languages, although, in general, 2 2 states are necessary and sufficient to simulate a k-state alternating finite automaton deterministically. Finally, it is shown that alternating pushdown automata are strictly more powerful than nondeterministic pushdown automata.
83 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: It is shown that the inequivalence problem for macro grammars generating finite languages is hard for nondeterministic double exponential time, and that the ''nonemptiness of complement'' problem for unambiguous regular expressions is in NP, which implies that unambiguousregular expressions are ''easier'' than general regular expressions (unless NP is equal to PSPACE).
Abstract: This thesis analyzes the descriptional power of finite automata, regular expressions, pushdown automata, and certain generalized models of macro grammars. For finite automata and pushdown automata the emphasis is on ambiguity. It is shown that ambiguous nondeterminism allows more succinct definitions than unambiguous nondeterminism which in turn allows more succinct definitions than determinism. The succinctness gain is nonrecursive for pda's and nonpolynomial for finite automata. The succinctness of regular expressions and macro grammars is measured in terms of complexity theory. It is shown that the inequivalence problem for Ol macro grammars generating finite languages is hard for nondeterministic double exponential time, and that the ''nonemptiness of complement'' problem for unambiguous regular expressions is in NP. This implies that unambiguous regular expressions are ''easier'' than general regular expressions (unless NP is equal to PSPACE).
54 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: Using a linear-time algorithm for solving single-origin graph shortest distance problems, it is shown how to correct a string of length n into the language accepted by a counter automaton in time proportional to $n^2 $ on a RAM with unit operation cost function.
Abstract: Correction of a string x into a language L is the problem of finding a string $y \in L$ to which x can be edited at least cost. The edit operations considered here are single-character deletions, single-character insertions, and single-character substitutions, each at an independent cost that does not depend on context. Employing a linear-time algorithm for solving single-origin graph shortest distance problems, it is shown how to correct a string of length n into the language accepted by a counter automaton in time proportional to $n^2 $ on a RAM with unit operation cost function. The algorithm is uniform over counter automata and edit cost functions; and it is shown how the correction time depends on the size of the automaton, the nature of the cost function, and the correction cost itself. For less general cases, potentially faster algorithms are described, including a linear-time algorithm for the case that very little correction is necessary and that the automaton’s counter activity is determined by ...
25 citations
10 citations
TL;DR: If a language is accepted by a deterministic (nondeterministic) one-way stack automaton then it is the image under a nonerasing homomorphism of a language accepted by the deterministic Turing machine that operates within space log n.
8 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
17 Jul 1978
TL;DR: It is shown that a simple deterministic grammar can be constructed which covers the simple chain grammar and a new type of parse is introduced which differs from the left and right parses which are common for the usual one pass no back-tracking parsing algorithms.
Abstract: A method is presented for obtaining a simple deterministic pushdown transducer which acts as a parser for simple chain grammars. It is shown that a simple deterministic grammar can be constructed which covers the simple chain grammar. To obtain both the simple deterministic pushdown transducer and the cover result, a new type of parse is introduced which differs from the left and right parses which are common for the usual one pass no back-tracking parsing algorithms. For the simple chain grammars this parse, the so-called left part parse, follows from a simple left part property which is satisfied by the grammatical trees of simple chain grammars.
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.
TL;DR: The application of digital stochastic computing techniques to the hardware implementation of a modified-estimating automaton is considered and experimental results are presented for the automaton operating in stationary Stochastic environments.
Abstract: The application of digital stochastic computing techniques to the hardware implementation of a modified-estimating automaton is considered. Experimental results are presented for the automaton operating in stationary stochastic environments.
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TL;DR: The characterization of the sets of words accepted by finite linear automata is presented for these two classes of automata: a nilpotent linear automaton and a nonsingularlinear automaton.
Abstract: The purpose of this paper is to give a characterization of the sets of words accepted by finite linear automata. Since every linear automaton is isomorphic to a parallel product of a nilpotent linear automaton and a nonsingular linear automaton, our characterization is presented for these two classes of automata.