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Showing papers on "Pushdown automaton published in 1986"


Book
01 Jan 1986
TL;DR: This chapter discusses models for Finite Automata Regular Expressions Context-Free Grammars Pushdown Automata Turing Machines Functions, Relations, and Translations, and properties of these models.
Abstract: Part 1 Introduction: Preliminaries Languages and Computation. Part 2 Models: Finite Automata Regular Expressions Context-Free Grammars Pushdown Automata Turing Machines Functions, Relations, and Translations. Part 3 Properties: Family Relationships Closure Properties Decision Problems. Part 4 Onward: Further Topics.

502 citations


Journal ArticleDOI
TL;DR: This work defines several pushdown machines of which the control is recursive without parameters, or even iterative, and which work on a generalized pushdown as storage, and characterize the n-fold composition of total deterministic macro tree transducers by recursive push down machines with an iterated push down as storage.

73 citations


Journal ArticleDOI
TL;DR: By viewing level- n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run-time behavior of procedures defined by recursion on higher type which makes the results of this paper interesting not only from a language theoretical point of view.
Abstract: This paper gives an automata-theoretical characterization of the OI-hierarchy ( Damm (1982) , Engelfriet and Schmidt (1977) , Wand (1975) ). This hierarchy is generated by so-called level- n grammars which are natural generalizations from context free and macro grammars in that their nonterminals are treated as functionals of higher type, i.e., they are allowed to carry up to n levels of parameters. The automata model used for this characterization is the n -iterated pushdown automaton. Its characteristic feature is the storage structure which consists of a nesting of pushdowns up to nesting depth n . The equivalence proof is given constructively, its method is illustrated using examples. By viewing level- n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run-time behavior of procedures defined by recursion on higher types which makes the results of this paper interesting not only from a language theoretical point of view.

73 citations


Journal ArticleDOI
TL;DR: It is proved that every language accepted by a two-way nondeterministic pushdown automaton can be recognized on a random access machine in O ( n 3 /log n ) time.
Abstract: We prove: 1) every language accepted by two-way nondeterministic pushdown automaton can be recognized on RAM in O(n3/log n) time; 2) every language accepted by two-way loop-free pushdown automaton can be recognized in O(n3/log2n) time; 3) every context-free language can be recognized on-line in O(n3/log2n) time. We improve the results of [1,7,4].

46 citations


Journal ArticleDOI
TL;DR: An elementary construction of a Buchi automaton with O(16 n 2 ) states which recognizes the complement of the ω-language recognized by the first one is proposed.

27 citations


Journal ArticleDOI
Ming Li1, Y. Yesha1
TL;DR: This paper answers the special case k = 2 of the open question, due to Galil and Seiferas (1983), whether a k-head one-way deterministic finite automaton can perform string-matching.

22 citations


Journal ArticleDOI
27 Oct 1986
TL;DR: The following long-standing conjecture of Harrison and Ibarra in 1968 is resolved: there are languages accepted by (k+1)-head 1-way deterministic pushdown automata ((k-DPDA) but not by k- head 1- way pushdown Automata (k-PDA), for every k.
Abstract: We resolve the following long-standing conjecture of Harrison and Ibarra in 1968 [HI, p.462]: There are languages accepted by (k+1)-head 1-way deterministic pushdown automata ((k+1)-DPDA) but not by k-head 1-way pushdown automata (k-PDA), for every k. (Partial solutions for this conjecture can be found in [M1,M2,C].) On the assumption that their conjecture holds, [HI] also derived many important consequences. Now all those consequences become theorems. For example, the class of languages accepted by k-PDA's is not closed under ∩ and complementation. Several other interesting consequences also follow: CFL ⊆∪kDPDA(k) and FA(2)⊆∪kDPDA(k), where DPDA (k)={L|L is accepted by a k-DPDA} and FA(2)={L|L is accepted by a 2-head FA). Our new proof itself is also interesting in the sense that the k+l versus k heads problems was solved by diagonalization methods [I2,M2,M3,M4,S] for stronger machines (2-way, etc). and by traditional counting arguments [S2,IK,YR,M1] for weaker machines (k-FA, k-head counter machine, etc).

18 citations


Journal ArticleDOI
Heiko Vogler1
TL;DR: In this paper, a strong connection between iterated linear control and iterated one-turn pushdown automata is established, where the innermost pushdown is unrestricted and the language class obtained by the kth step is denoted by CTRLk(ℒ).
Abstract: For a classℒ of languages, anℒ-controlled linear grammarK consists of a linear context-free grammarG and a control languageH inℒ, where the terminals ofH are interpreted as the labels of rules ofG. The language generated byK is obtained by derivations ofG such that the corresponding strings of labels of the rules applied are control strings inH. The control of linear grammars can be iterated by starting withℒ and by taking the result of thekth step as class of control languages for the (k + 1)st step. The language class obtained by thekth step is denoted by CTRLk(ℒ). Denote byℒ(S) the language class accepted by nondeterministic one-wayS automata, whereS is a storage type. We prove that for anyS, CTRLk(ℒ(S)) = ℒ(P 1t k (S)), whereP 1t k (S) is the storage type the configurations of which consist ofk-iterated one-turn pushdowns ofS-configurations. We establish a strong connection between iterated linear control and iterated one-turn pushdowns. In particular, we characterize CTRL k (ℒ CF), where ℒCF is the class of context-free languages, by iterated one-turn pushdown automata in which the innermost pushdown is unrestricted.

18 citations




Journal ArticleDOI
TL;DR: It is shown that m log m space (m2 space) is necessary and sufficient for deterministic three-way two-dimensional Turing machines to simulate deterministic (nondeterministic) three- way two- dimensional finite automata with rotated inputs.

Journal ArticleDOI
TL;DR: It is shown that a language is accepted by a 2 k -head two-way finite automaton if and only if it is acceptance by a k - head two- way pushdown automaton which makes one reversal on its stack.
Abstract: We give characterizations of multihead two-way finite automata in terms of multihead reversal-bounded pushdown automata and restricted checking stack automata. In particular, we show that a language is accepted by a 2 k -head two-way finite automaton if and only if it is accepted by a k -head two-way pushdown automaton which makes one reversal on its stack. We also show that a 2-head two-way deterministic finite automaton is equivalent to a simple type of two-way deterministic checking stack automaton. This is in contrast to a previously known result which shows that simple two-way nondeterministic checking stack automata are equivalent to nondeterministic linear bounded automata.

Journal ArticleDOI
TL;DR: Two automata models are introduced that play the same role as pushdown automata have with respect to context-free grammars and their parsing, and it is shown that these automata define the same class of string-to-value translations as attribute Grammars.
Abstract: Two automata models are introduced that play, with respect to attribute grammars and attribute-evaluation for them, the same role as pushdown automata have with respect to context-free grammars and their parsing. It is shown, in fact, that these automata define the same class of string-to-value translations as attribute grammars. Their class of tree-to-value translations seems instead to be larger than that of attribute grammars and the difference is overcome by means of (a special type of) context-free grammar interpretations. An extended model of attribute grammar is presented that is as powerful as the automata with respect to tree-to-value translations.

01 Jan 1986
TL;DR: A new two-person pebble game that abstracts the control structure of many parallel algorithms is defined and studied, and it is shown that the game model unifies in a single framework the proofs of the following three well known results of complexity theory.
Abstract: A new two-person pebble game that abstracts the control structure of many parallel algorithms is defined and studied This game extends the two-person pebble game defined by Dymond and Tompa (JCSS, Vol 30, no 2, 1985, pp 149-161) in two ways: (a) the game is played on a Boolean circuit rather than on an unlabelled graph, and takes into consideration the types of the gates in the circuit, and (b) the two players' roles are completely symmetric The new game is used to study the relationship between two natural parallel complexity classes, namely LOGCFL and AC('1) LOGCFL is the class of languages log space reducible to context-free languages AC('1) is the class of languages accepted by an alternating Turing machine in space O(log n) and alternation depth O(log n) LOGCFL is a subclass of AC('1), but it is not known whether the inclusion is proper For many problems in LOGCFL the algorithms that show their membership in that class also show their membership in AC('1) However, these algorithms do not use the full power of AC('1) computations The two-person game defined here provides a model of computation in which this perceived difference can be quantified This is done by characterizing the two classes using the same measures of resources in the game model The results so obtained not only illustrate the similarity between these two classes, but also isolate a fundamental difference between them: the recognition of languages in LOGCFL does not utilize the symmetry between the two players, whereas the recognition of languages in AC('1) does A resource that captures this difference, called role switches, is identified in the game model: languages in LOGCFL use no role switches, whereas languages in AC('1) use O(log n) role switches Thus the results indicate why the two classes may not be equal As another application of this game, it is shown that the game model unifies in a single framework the proofs of the following three well known results of complexity theory: (1) Savitch's theorem that nondeterministic space S is contained in deterministic space S('2), (2) Ruzzo's NC algorithm for context-free language recognition, and (3) Borodin and Ruzzo's simulation of simultaneous space and alternation bounded alternating Turing machines by simultaneous space and time bounded alternating Turing machines Motivated by the characterizations in terms of the game, a property called semi-unboundedness is defined for the following four models: alternating Turing machines, nondeterministic auxiliary pushdown automata, bounded fan-in Boolean circuits, and unbounded fan-in Boolean circuits This is used in obtaining new characterizations of LOGCFL on these models Three of these characterizations are in terms of the same measures of resources used to characterize AC('1) on these models, and provide supporting evidence to the belief that these two classes are not equal

Book ChapterDOI
01 Jun 1986
TL;DR: In some branches of theoretical computer science, we meet systems of equations whose solutions are obtained by a fixed-point technique, such as context-free grammars and flow-chart programs as mentioned in this paper.
Abstract: In some branches of theoretical computer science we meet systems of equations whose solutions are obtained by a fixed-point technique, a) Every context-free grammar has its system. The least solution gives the languaEes generated by nonterminals, b) Every flow chart program has its rational system. The least solution gives the unfoldment. The interpretation of the umLoldment gives the program behaviour, c)Every reeursive program has its contex-free system. The least solution gives the unfoldment. The interpretation of the um~oldment gives the program behaViOt~j

Journal ArticleDOI
TL;DR: A new type of representation of a strongly connetted group-matrix type automaton of order n on G with output or an (n, O)automaton with output is introduced.
Abstract: In this paper some results of [6] are extended for a strongly connected groupmatrix type automaton with output. A new type of representation of a strongly connetted group-matrix type automaton of order n on G with output or an (n, O)automaton with output is introduced. Using this representation we prove some important results on automorphism groups of a strongly connected (n, G)-automaton with output and also on a strongly connected abelian (n, G)-automaton with output.