Showing papers on "Pushdown automaton published in 1970"

The parsing for general phrase-structure grammars

Abstract: Pushdown automata serve as a base for the description of four basic parsing techniques for general phrase-structure grammars (Chomsky O-type grammars).

Probabilistic tree automata and context free languages

Abstract: A notion of a probabilistic tree automaton is defined and a condition is given under which it is equivalent to a usual tree automaton. A theorem about context free languages is stated.

An algorithm for the construction of bounded-context parsers

Abstract: An algorithm is described which accepts an arbitrary context-free grammar and constructs a bounded-context parser for it whenever such a parser exists. In the first part of the paper the definition of a context-free grammar and the working of a bounded-context parser are recalled. The notion of reduction class for a context-free grammar is then introduced and its connection with the structure of a bounded-context parser is indicated. Next, pushdown automata which generate the different reduction classes of a context-free grammar are defined. Finally, the algorithm is described; it essentially carries out an exhaustive study of all possible runs of the pushdown automata generating the reduction classes. In the second part, the utility of the algorithm is discussed in the light of the experience gained from its use in compiler design. The algorithm is claimed to be particularly useful in the simultaneous design of a language and a compiler for it.

R70-21 Time and Tape Complexity of Pushdown Automaton Languages

Abstract: This paper is concerned with the recognition of words which are contained in languages defined by pushdown store machines. Such languages exhibit many of the syntactic properties of algorithmic programming languages. Thus the recognition problem for languages generated by pushdown store machines is related to compilation of programming languages.

Translation equations

Abstract: Input limited transduction expressions, or translation equations, are used to describe the syntax and left-context sensitive semantics for context-free languages. A formal procedure is given for deriving from a set of translation equations the specifications for a pushdown translator. The translator consists of Mealy form finite-state automata interacting by means of a pushdown stack. Within the framework described, string recognition and parsing may be treated as special cases of the translation problem.

Events which are not representable by a probabilistic automaton

Abstract: (finite) state set w and n are the initial and final vectors respectIvely over the states and (A(o)} are the transltlon matrices corresixmd-ing to the letters o ~. If x = Ol...o k~ E* then A(x) is the matrix A(x) = A(el)... A(a k) and pA(x) is the wc~-function with domain ~* and real values in the interval [0,i]: pA(x) = IA{x),. Let X be a real 0 <_ • I, n ati or sta s the uage (set of words or eye.t) T(A,A)-{x;x e Z', pA(x) > A}. Sunh a lance will be called probab~llstlo. Problem: Is there art language L which is not probabilistlc? Bukha~ev (1965) has given an example of such a lan~m~e over a single letter alphabet. Unforturately, he did not prove his example (which is quite ccmpllcated, belng defined on the basis of four arbitrary primitive recursive functions). We have not been able to prove Bukharaev's result, nor have we succeeded in establishing contact with him (directly or indirectly) and, to the best of our knowledge nobody else in the West kr~ws how to prove that result (see e.g. Salcmea (1968) who needed that result in order to establish scme relation between time variant events and prob-abilistlc evemts). Note that, when looking for a language as above, one must take into cor~ideration that there may be different automata defining-8

On the computational power of some machines with pushdown-like storage

Abstract: The computational power of 2-way pushdown automata with m additional counters (called mC-PDA) is investigated It is shown that any multi-tape Turingmachine (with a two-way input tape) which accepts within time T(n), where n is the input length, can be simulated by a 3C-PDA whose counters are bounded by T(n) and that any such Turing machine can also be simulated by a 2C-PDA whose counters are bounded by T(n)2 A number of other results relating the power of 1C-PDA and that of other types of machines are also obtained

Decomposition of simple goal-seeking automata☆

Abstract: A simple automaton model for goal-seeking and adaptive systems is given. It is shown that under certain conditions a goal-seeking automaton can be decomposed, by applying the structural theory of automata, into serial and parallel connections of simpler goal-seeking automata such that in the serial decomposition the goal of the tail automaton depends on the goal of the front automaton. Thus, a complex goal-seeking automaton may be reduced into a simpler automaton which is similar in structure to the “multi-level multi-goal systems” discussed by Mesarovic ( 1 ).

R70-23 Multi-Tape and Multi-Head Pushdown Automata

Abstract: Two of the three authors who did the first extensive work on 2-way pushdown automata [1] consider multitape and multihead extensions of 1-way and 2-way deterministic and nondeterministic pushdown automata (PDA).