Showing papers on "Pushdown automaton published in 1971"

Characterizations of Pushdown Machines in Terms of Time-Bounded Computers

Abstract: A class of machines called auxiliary pushdown machines is introduced. Several types of pushdown automata, including stack automata, are characterized in terms of these machines. The computing power of each class of machines in question is characterized in terms of time-bounded Turing machines, and corollaries are derived which answer some open questions in the field. ~

A context-free language which is not acceptable by a probabilistic automaton

Abstract: A linear context-free language which is not acceptable by a finite probabilistic automaton is given, and it is shown that the family of stochastic languages is not closed under concatenation and homomorphism.

Deterministic Pushdown Store Machines and Real-Time Computation

Abstract: A comparison is made of the computing capabilities of deterministic pushdown store machines and real-time iterative arrays of finite-state machines. The main result is that every deterministic pushdown store computation can be performed by some (multidimensional) iterative array in real-time. The latter are strictly more powerful since they can recognize the set of palindromes in real-time, which deterministic pushdown store machines cannot do even if permitted unlimited computing time. During the development of the main result, variants of pushdown store machines, the tabulator machines and the n-dimensional pushdown store machines, are introduced. By imposing a real-time constraint and letting the number of tabs and the number of dimensions vary, an infinite hierarchy of pushdown store (deterministic context-free) languages is obtained.

A Two-Way Automaton with Fewer States than Any Equivalent One-Way Automaton

Abstract: This correspondence presents an example of a two-way automaton which has significantly fewer states than any one-way automaton accepting the same set of tapes. Thus, in this particular case, memory space can be saved by using a two-way automaton. This savings in space, however, is accompanied by an increase in recognition time.

Analysis for an Effective Operation of a General Automaton: Recursive Methods Applied to a Graph Model

Abstract: With many there is a general agreement that the problems arising from large and complex systems in society are interdisciplinary in nature and that pending solutions require contributions from all concerned who are willing to view the problems in full perspective There is a need for the development of a general theory which can serve as a basis for establishing theoretical concepts fundamental to the various disciplines Such a theory could then be used directly in the modeling and studying of a specific physical system or system component In [1], we first identified a component of general system and treated it as a general automaton That work concluded with a graph model for a general automaton The natural extension presented here is the development and application of recursive methods for determining properties of these graphs that reflect the effective operation of the general automaton The recursive methods provide a means of studying a component of such a system by a computer The key r

Parallel non-deterministic bottom-up parsing

Abstract: The development of translator writing systems and extensible languages has led to a simultaneous development of more efficient and general syntax analyzers, usually for context-free (CF) syntax. Our paper describes a type of parser that can be used with reasonable efficiency for any CF grammar, even one which is ambiguous. Our parser, like most others, is based on the pushdown automaton model, and thus its generality requires it to be non-deterministic (in the automata theoretic sense). An actual implementation of a non-deterministic automaton requires that we explore every computational path that could be followed by the theoretical automaton. This can be done serially [5], following successively every computational path whenever a choice occurs. It leads to the algorithms described in [1], whose time bounds can be exponential functions of the length of the string to be parsed. We can also use a parallel implementation which consists in following “simultaneously” all the possible computational paths whenever a non-deterministic choice occurs. Then we can merge paths that have ceased to be different after a certain point. Those mergings reduce drastically the amount of computation. The best known example is the top-down algorithm described in [2]. The algorithm we describe in the first part of our paper is a basic bottom-up parser, similar to [2] in its organization. Both parsers can be shown to work within time bounds which are at most the cube of the length of the input string, and are often a linear function of it. The space bounds are at most the square of that length. The second part of our paper deals with the optimization of the basic parallel bottom-up algorithm, using the properties of weak precedence relations [3]. The various optimization techniques further reduce the amount of computation required and cause frequent occurrence of a “sparse determinism” phenomenon which allows determination of part of the parse-tree before the non-deterministic analysis is ended. These optimizations also considerably lessen the space requirements. Full details can be found in [6]. The parser is easy to generate for any CF grammar, requiring only the computation of precedence tables. It is slower than most deterministic parsers (on the order of ten times); but all examples we have tried showed it to be more efficient than any other parser having the same generality. We consider that the inefficiency of our parser is reasonable as we intend it as a research tool for the language designer rather than as a part of an industrial compiler. Languages designers, or extensible languages users, are often more preoccupied with semantics than syntax and fix the syntax of their language in a “nice” form only when they have found what kind of semantics it is to represent. So they can easily come up with ambiguous syntax [4]. Our parser parses ambiguous languages and detects ambiguities in programs, thus enabling the programmer to eliminate them.

Characterizations and extensions of pushdown translations

Abstract: A device called a pushdown assembler has been recently introduced and has been shown capable of defining exactly the syntax directed translations (SDT's). The output operation of the pushdown assembler can be extended in a natural way to obtain a more powerful device called a type B pushdown assembler (or B-machine). A B-machine can define SDT's more simply and directly than the original pushdown assembler. B-machines can also define many interesting translations which are not SDT's. In this paper the B-machine is defined and compared with the original pushdown assembler. The properties of B-machine translations are investigated and it is shown that, as with SDT's, there exists a natural infinite hierarchy of B-machine translations.

Theorems on additive automata

Abstract: Publisher Summary This chapter discusses theorems on additive automata. The theory of linear automata is well developed, and many works have appeared on this topic. To every given automaton, there belongs a unique minimal one, which is a homomorpic image of it. The minimal automaton, belonging to a linear automaton over a field K, is again a linear automaton over the same field. The chapter discusses whether the minimal automaton belonging to an additive automaton is again additive with the same operator sets. Many well-known results on linear automata can be generalized to additive automata. The chapter describes the necessary and sufficient conditions for the (H,K)-realizability of an automaton M.