Showing papers on "Pushdown automaton published in 1968"
TL;DR: This paper considers languages defined by pushdown store systems and investigates how much time and memory is needed in order to de- termine whether an arbitrary input sentence belongs or does not belong to some language in this class.
Abstract: A n algorithm is presented which will determine whether any string w in Z*, of length n, is contained in a language L C Z* defined by a two-way nondeterministic pushdown automaton, This algorithm re- quires time n 3 when implemented on a random access computer. It re- quires n 4 time and n 2 tape when implemented on a multitape Turing machine. If the pushdown automaton is deterministic, the algorithm re- quires n ~ time on a random access computer and n 2 log n time on a mul- titape Turing machine. I. INTRODUCTION A pushdown store is a list in which information can be accessed only on a last-in first-out principle of operation. The use of pushdown stores is an important technique in the construction of compilers and other language processing devices. Of particular interest from both practical and theoretical considera- tions is how the time and memory required to process a language is func- tionally related to the length of the input sentence under consideration. In this paper we consider languages defined by pushdown store systems and we investigate how much time and memory is needed in order to de- termine whether an arbitrary input sentence belongs or does not belong to some language in this class. To obtain analytical results, a pushdown automaton (PDA for short) will be used as the model of a pushdown store system. There are four types of pushdown automaton depending on whether the automaton is deterministic or nondeterministie and whether it moves one or two ways on the input. We will use the following abbreviations for pushd0wn au- * Currently at Cornell University, Ithaca, New York. 186
95 citations
TL;DR: The closure, characterization, and decision properties of the sets definable by these automata are iavestigated and the relationship between these sets and some well known families of languages is established.
Abstract: This paper considers multi-tape and multi-head extensions of various models of pushdown automata. One-way and two-way deterministic and nondeterministic multi-tape and multi-head pushdown automata are introduced and studied. The closure, characterization, and decision properties of the sets definable by these automata are iavestigated and the relationship between these sets and some well known families of languages is established.
71 citations
TL;DR: It is shown that the linearly bounded automaton can accept the set of primes, and it is conjectured that no automaton whose memory grows less rapidly can recognize the setof primes.
Abstract: A study of the problem of recognizing the set of primes by automata is presented. A simple algebraic condition is derived which shows that neither the set of primes nor any infinite subset of the set of primes can be accepted by a pushdown or finite automaton.In view of this result an interesting open problem is to determine the “weakest” automaton which can accept the set of primes. It is shown that the linearly bounded automaton can accept the set of primes, and it is conjectured that no automaton whose memory grows less rapidly can recognize the set of primes. One of the results shows that if this conjecture is true, it cannot be proved by the use of arguments about the distribution of primes, as described by the Prime Number Theorem. Some relations are established between two classical conjectures in number theory and the minimal rate of memory growth of automata which can recognize the set of primes.
45 citations
TL;DR: A device is presented which has its memory organized as a linear list, a type of storage equivalent to having two pushdown stores, and the nondeterministic automaton which results when the input is read one-way and the device operates in real-time.
Abstract: A device is presented which has its memory organized as a linear list, a type of storage equivalent to having two pushdown stores. Attention is then focused on the nondeterministic automaton (called an lsa) which results when the input is read one-way and the device operates in real-time. The set of words (called a language) accepted by an lsa is extensively studied. In particular, several characterizations and closure properties of languages are given.
25 citations
TL;DR: It is shown that a nondeterministic stack automation with a one-way input tape can be simulated by a deterministic linear bounded automaton.
Abstract: A stack automaton is a pushdown automaton that can read the interior of its pushdown list without altering it. It is shown that a nondeterministic stack automation with a one-way input tape can be simulated by a deterministic linear bounded automaton. Hence, each nondeterministic one-way stack language is context sensitive.
19 citations
TL;DR: The deterministic stack automaton with a one-way input (dsa) is considered and it is shown that if L is a language accepted by a dsa and R is a regular set, then L/R={w| for some x in R, wx is in L}.
19 citations
15 Oct 1968
TL;DR: It is shown that there exists an infinite hierarchy of syntax directed translations in terms of the number of variables allowed on the right side of productions of the underlying context free grammar.
Abstract: This paper is a compendium of recent results obtained in the area of syntax directed translations. It is shown that there exists an infinite hierarchy of syntax directed translations in terms of the number of variables allowed on the right side of productions of the underlying context free grammar. An automaton for the formal specification of translations, called a pushdown assembler, is introduced. A k-register pushdown assembler is a pushdown automaton which has k passive registers associated with each level on the pushdown tape. Each register can hold a string of output symbols, and when a level is erased, the contents of the registers are concatenated together and passed to the level below. Two types of pushdown assembler are considered. One model, called the type A pushdown assembler or A-machine, can write output strings into empty registers at the top level only. The other model, the B-machine, can concatenate arbitrarily many output strings to the left or right of the present contents of a register at the top level. The A-machines provide an exact characterization for the syntax directed translations. The B-machines define a new larger class of translations having many properties possessed by the syntax directed translations. In addition, we show that a B-machine with one register per level is equivalent to an A-machine with two registers per level.
7 citations
15 Oct 1968
TL;DR: The quasi-real-time one- way stack languages are not a full AFL but are a proper subAFL of the one-way stack languages, which properly include the stack languages.
Abstract: A checking automaton is equivalent to a one-way nonerasing stack automaton which, once it enters its stack, never again writes on its stack. The checking automaton languages (cal) form a full AFL closed under substitution. If L ⊆ a* is an infinite cal, then L contains an infinite regular set. Consequently, there are one-way nonerasing stack languages (such as (an2|n≥1|)) which are not cal. Let L be the family of one-way stack languages and let L1 be a subAFL of L. L is closed under substitution into L1 if and only if L1 is contained in the family of context-free languages. L is closed under substitution by L1 if and only if L1 is a family of cal. Hence, the one-way stack languages are not closed under substitution. The one-way nested stack languages properly include the stack languages. The family of quasi-real-time one-way stack languages is not closed under substitution by cal. Thus the quasi-real-time one-way stack languages are not a full AFL but are a proper subAFL of the one-way stack languages. Let LN be the family of one-way nonerasing stack languages, and let L1 be a subAFL. Then LN is closed under substitution into L1 if and only if L1 is a family of regular sets. Hence LN is a proper subfamily of L.
3 citations
2 citations
01 Jan 1968
TL;DR: This paper considers languages which can be defined by pushdown store systems and investigates how the time and memory required to process a language is functionally related to the length of the input sentence under consideration.
Abstract: A pushdown store is a list in which information can be accessed only on a last-in first-out principle of operation. The use of pushdown stores is an important technique in the construction of compilers and other language-processing devices. Of particular interest from both practical and theoretical considerations is how the time and memory required to process a language is functionally related to the length of the input sentence under consideration. In this paper we consider languages which can be defined by pushdown store systems. To obtain quantitative results, a two-way (off-line) nondeterministic pushdown automaton (2N PDA, for short) is used as an analytical model of a pushdown store system, and the two-way deterministic push-down automaton (2D PDA, for short) is also considered as a special case.
01 Jan 1968
TL;DR: In the course of studying context-free languages, work has been done toward the construction of push-down acceptors, and a pushdown acceptor model is considered to be efficient in the following two aspects; it should be simple and clear in its structure and operation, and be an effective tool for syntactic analysis of its corresponding context- free language.
Abstract: In the course of studying context-free languages, work has been done toward the construction of push-down acceptors.1 The motivation of constructing a pushdown acceptor for a specified context-free language is twofold; to decide whether a given string belongs to this language and to facilitate the syntactic analysis of this language. A pushdown store acceptor is, in a general sense, a finite automaton with exactly one pushdown store of potentially infinite depth. There can be many ways to formalize pushdown acceptors.2 The main concern is then to find an efficient pushdown acceptor model. A pushdown acceptor model is considered to be efficient in the following two aspects; it should be simple and clear in its structure and operation, it should be an effective tool for syntactic analysis of its corresponding context-free language.
01 Jul 1968
TL;DR: In this article, a straightforward algorithm for converting context free grammars into pushdown-store automata is presented. But this algorithm is not suitable for pushdown store automata.
Abstract: Straightforward algorithm for converting context free grammars into pushdown-store automata