Showing papers on "Pushdown automaton published in 1988"

Formulation and control of real time discrete event processes

Abstract: A discrete-event process is modeled as a controlled state machine, in the framework of D.J. Ramadge and W.M. Wohman (1986). Their approach is extended to model a class of real-time discrete-event processes by means of a special type of automaton, called a clock automaton. The clock automaton is used for decreasing the real-time behavior of processes, controllers, and real-time specifications. >

Two applications of complementation via inductive counting

Abstract: A recent proof that nondeterministic space-bounded complexity classes are closed under complementation is used to develop two further applications of the inductive counting technique. An errorless probabilistic algorithm is given for the undirected graph s-t connectivity problem that runs in O(log n) space and polynomial expected time, and it is shown that the class LOGCFL is closed under complementation. The latter is a special case of a general result that shows closure under complementation of classes defined by semiunbounded fan-in circuits (or, equivalently, nondeterministic auxiliary pushdown automata or tree-sized bounded alternating Turing machines). As one consequence, small numbers of role switches in two-person pebbling can be eliminated. >

The complexity of ranking

Abstract: It is shown that ranking languages accepted by one-way unambiguous auxiliary pushdown automata are in NC/sup (2)/. Negative results about ranking for several classes of simple languages are proved. It is shown that C is rankable in deterministic polynomial time if P= Hash P, where C is any of the following classes of languages: (1) languages accepted by logtime-bounded nondeterministic Turing machines; (2) languages accepted by (uniform) families of unbounded fan-in circuits of constant depth and polynomial size; (3) languages accepted by two-way deterministic finite automata; (4) languages accepted by multihead deterministic finite automata; (5) languages accepted by one-way nondeterministic logspace-bounded Turing machines; and (6) finitely ambiguous linear context-free languages. >

Parallel time O (log n ) acceptance of deterministic CFLs on an exclusive-write P-RAM

Abstract: We give an algorithm for accepting a deterministic context-free language on the P-RAM, an exclusive-write, concurrent-read model of parallel computation. Whereas on inputs of length n, a deterministic push-down automaton will use time linear in n, our algorithm runs in time $O(\log n)$ on $n^3 $ processors. The algorithm is easily generalized to permit parallel simulation of any deterministic auxiliary pushdown automaton that uses space $s(n) \geqq \log n$ and time $2^{O(s(n))} $. The simulation runs in time $O(s(n))$ on $2^{O(s(n))} $ processors, and is nearly optimal, since we observe that any language accepted by a P-RAM in time $T(n)$ is accepted by a deterministic auxiliary pushdown automaton in space $T(n)$ and time $2^{O(T(n)^2 )} $.

Datalog Automata Extended Abstract

Abstract: We propose a new computational paradigm for the evaluation of recursive Datalog queries, which is based on a pushdown automaton (PDA) model. By extending to these automata a dynamic programming technique developed for PDAs in context-free parsing, we obtain a general and simple technique for constructing efficient polynomial query evaluators. Keywords: Datalog, Recursive Queries, Complete Strategies, Dynamic Programming, Polynomial Complexity.

Languages and parsing

Abstract: 1 Elements of Language Theory- 11 Mathematical Preliminaries- 12 Languages- 13 Random Access Machines- 14 Decision Problems- 15 Computational Complexity- 16 Rewriting Systems- Exercises- Bibliographic Notes- 2 Algorithms on Graphs- 21 Basic Algorithms- 22 Finding Strongly Connected Components- 23 Computing Functions Defined on Graphs- 24 Computing Relational Expressions- Exercises- Bibliographic Notes- 3 Regular Languages- 31 Regular Expressions- 32 Finite Automata- 33 Regular Grammars- 34 Deterministic Finite Automata- 35 Decision Problems on Regular Languages- 36 Applications to Lexical Analysis- Exercises- Bibliographic Notes- 4 Context-free Languages- 41 Context-free Grammars- 42 Leftmost and Rightmost Derivations- 43 Ambiguity of Grammars- 44 Useless and Nullable Symbols- 45 Canonical Two-form Grammars- 46 Derivational Complexity- 47 Context-free Language Recognition- Exercises- Bibliographic Notes- 5 Parsing- 51 Pushdown Automata- 52 Left Parsers and Right Parsers- 53 Strong LL(k) Parsing- 54 Strong LL(k) Grammars- 55 Construction of Strong LL(1) Parsers- 56 Implementation of Strong LL(1) Parsers- 57 Simple Precedence Parsing- Exercises- Bibliographic Notes- Bibliography to Volume I- Index to Volume I

Characterizing the Polynomial Hierarchy by Alternating Auxiliary Pushdown Automata

Abstract: An alternating auxiliary pushdown hierarchy is defined by extending the machine model of the Logarithmic Alternation Hierarchy by a pushdown store while keeping a polynomial time bound. Although recently it was proven by Borodin et al. that the class of languages accepted by nondeterministic logarithmic space bounded auxiliary pushdown automata with a polynomial time bound is closed under complement [Bo et al], it is shown that, surprisingly, the further levels of this alternating auxiliary pushdown hierarchy coincide level by level with the Polynomial Hierarchy. Furthermore, it is shown that PSPACE can be characterized by simultaneously logarithmic space and polynomial time bounded auxiliary pushdown automata with unbounded alternation.

Using Prolog to present abstract machines

Abstract: Introductory courses in Theory of Computation usually include a study of abstract machines such as finite state machines and Turing machines. This paper demonstrates that a neat and useful way of presenting these automata is to use a logic programming language such as Prolog, making the approach useful from a teaching point of view. Not only does a Prolog specification provide a precise definition of an automoton's behaviour, but it also gives an immediately-executable simulator. The reversible execution property of Prolog programs can make these simulators inherently more powerful than traditional simulators. The paper includes Prolog specifications for finite state machines, Turing machines, linear bounded automata, and pushdown automata.

Time varying pushdown automata

Abstract: Time varying pushdown automata (PDA) are defined and equivalence between two modes of acceptance shown. It is seen that periodically time varying pushdown automata accept exactly the class of context-free languages. Time varying generalized PDA are defined and their equivalence to terminal weighted context free grammars in GNF shown. It is shown that TVGPDA can be simulated by TVPDA. Thus TVPDA give another machine characterization of recursively enumerable sets.

An automaton decomposition for learning system environments

Abstract: A finite automaton two-component cascade decomposition is presented in which the first component has a synchronizer and the second component is a permutation automaton. The synchronizer corresponds to a primitive idempotent element e in the transition monoid M of the automaton. The state set of the second component is the range of e ; each state of the first component is an image of this range under one of the transitions in M . The transition monoid of the second component is the group eMe . as a conceptual tool, the decomposition can be used to clarify the credit assignment problems faced by learning system reward schemes in finite automaton environments.

Trading reversals for alternation

Abstract: The relation between reversals and alternation is studied in two simple models of computation: the two-counter machine with a one-way input tape whose counters make only one reversal (1-reversal 2CM) and the one-way pushdown automation whose pushdown store makes only one reversal (1-reversal PDA). It is known that nondeterministic 1-reversal 2CMs (and, more generally, 1-reversal mCMs when there are m counters, m>0) can be simulated by a log n space-bounded nondeterministic TMs, and nondeterministic 1-reversal PDAs accept exactly the linear context-free languages. When nondeterministic is generalized to alternating, it is shown that alternating 1-reversal 2CMs accept all recursively enumerable languages and that alternating 1-reversal PDAs accept exactly the languages accepted by exponential time-bonded deterministic TMs. Since deterministic 2CMs with unrestricted counters accept all recursively enumerable languages, the first results show that reversals can be traded for alternation. >

The Complexity of a Counting Finite-State Automaton

Abstract: A counting finite-state automaton is a nondeterministic finite-state automaton which, on an input over its input alphabet, (magically) writes in binary the number of accepting computations on the input. We examine the complexity of computing the counting function of an NFA, and the complexity of recognizing its range as a set of binary strings. We also consider the pumping behavior of counting finite-state automata. The class of functions computed by counting NFA's (1) includes a class of functions computed by deterministic finite-state transducers; (2) is contained in the class of functions computed by polynomially time- and linearly space-bounded Turing transducers; (3) includes a function whose range is the composite numbers.

The permutation rank of an automaton II

Abstract: This paper is a continuation of the study of the permutation rank of an automaton as was initiated in Smit [2]. The p 2 permutation r 2(A) of an automaton A is defined as the largest integer k such that (i) every subset of the state set of A consisting of k different states can be distinguished by an input; (ii) every input to A distinguishes k states of A. If x is an input string the expression “x distinguishes k states” means that k different states change to k different states which need not be the same as the original k states under the input x. The p 2 -permutation rank of a permutation automaton will always be equal to the number of states of the automaton. The semigroup of a permutation automaton is a group. It is shown that certain group properties are preserved in the semigroup of an automaton A of which r 2 (A) is restricted. The role of r 2 (A) in the semigroup of a strictly connected automaton is considered. As is in the case of Smit [2], it is shown that if r 2 (A) differs with only one from ...