LIMITED AUTOMATA AND REGULAR LANGUAGES

2014 ◽  
Vol 25 (07) ◽  
pp. 897-916 ◽  
Author(s):  
GIOVANNI PIGHIZZINI ◽  
ANDREA PISONI
Keyword(s):  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Finite State Automata ◽  
Turing Machines ◽  
Double Exponential ◽  
Finite State ◽  
A Cell ◽  
Fixed Constant ◽  
The One ◽  
Context Free

Limited automata are one-tape Turing machines that are allowed to rewrite the content of any tape cell only in the first d visits, for a fixed constant d. In the case d = 1, namely, when a rewriting is possible only during the first visit to a cell, these models have the same power of finite state automata. We prove state upper and lower bounds for the conversion of 1-limited automata into finite state automata. In particular, we prove a double exponential state gap between nondeterministic 1-limited automata and one-way deterministic finite automata. The gap reduces to a single exponential in the case of deterministic 1-limited automata. This also implies an exponential state gap between nondeterministic and deterministic 1-limited automata. Another consequence is that 1-limited automata can have less states than equivalent two-way nondeterministic finite automata. We show that this is true even if we restrict to the case of the one-letter input alphabet. For each d ≥ 2, d-limited automata are known to characterize the class of context-free languages. Using the Chomsky-Schützenberger representation for contextfree languages, we present a new conversion from context-free languages into 2-limited automata.

scholarly journals THE ROLES OF ADVICE TO ONE-TAPE LINEAR-TIME TURING MACHINES AND FINITE AUTOMATA

2010 ◽  
Vol 21 (06) ◽  
pp. 941-962 ◽  
Author(s):  
TOMOYUKI YAMAKAMI
Keyword(s):  
Computational Models ◽  
Linear Time ◽  
Finite Automata ◽  
Probability Distributions ◽  
Finite State Automata ◽  
Turing Machines ◽  
Computational Power ◽  
Finite State

We discuss the power and limitation of various "advice," when it is given particularly to weak computational models of one-tape linear-time Turing machines and one-way finite (state) automata. Of various advice types, we consider deterministically-chosen advice (not necessarily algorithmically determined) and randomly-chosen advice (according to certain probability distributions). In particular, we show that certain weak machines can be significantly enhanced in computational power when randomized advice is provided in place of deterministic advice.

Preface

1997 ◽  
Vol 11 (07) ◽  
pp. 1023-1024
Author(s):  
Serge Miguet ◽  
Annick Montanvert ◽  
P. S. P. Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

Investigations on Automata and Languages Over a Unary Alphabet

2015 ◽  
Vol 26 (07) ◽  
pp. 827-850 ◽  
Author(s):  
Giovanni Pighizzini
Keyword(s):  
Computational Models ◽  
The State ◽  
Space Complexity ◽  
Finite State Automata ◽  
Probabilistic Automata ◽  
Letter Alphabet ◽  
Finite State ◽  
Context Free ◽  
Pushdown Automata

The investigation of automata and languages defined over a one letter alphabet shows interesting differences with respect to the case of alphabets with at least two letters. Probably, the oldest example emphasizing one of these differences is the collapse of the classes of regular and context-free languages in the unary case (Ginsburg and Rice, 1962). Many differences have been proved concerning the state costs of the simulations between different variants of unary finite state automata (Chrobak, 1986, Mereghetti and Pighizzini, 2001). We present an overview of these results. Because important connections with fundamental questions in space complexity, we give emphasis to unary two-way automata. Furthermore, we discuss unary versions of other computational models, as probabilistic automata, one-way and two-way pushdown automata, even extended with auxiliary workspace, and multi-head automata.

scholarly journals Penerapan Finite State Automata Pada Vending Machine Penjual Obat Non Resep Dokter Dan Keperluan Medis

2021 ◽  
Vol 9 (2) ◽  
pp. 08-14
Author(s):  
Eko Supriyanto ◽  
Angga Ardiansyah ◽  
Frieyadie Frieyadie ◽  
Sri Rahayu ◽  
Windu Gata
Keyword(s):  
Finite Automata ◽  
Finite State Automata ◽  
Deterministic Finite Automata ◽  
Finite State

Kebutuhan obat non resep dokter dan keperluan medis menjadi salah satu kebutuhan yang sangat penting untuk dipenuhi dengan mudah,cepat, tepat, dan aman bagi masyarakat saat ini, beragamnya pilihan  obat yang dijual   mengharuskan masyarakat mampu memilih dengan cermat dan tepat dalam membeli obat sesuai dengan kebutuhan penyakit yang dialami,informasi tentang kandungan, aturan pakai dan efek samping dari obat juga sangat penting untuk diketahui masyarakat guna memaksimalkan maanfaat dari obat yang dikonsumsi. Sistem penjualan obat yang tersedia saat ini adalah dengan penjualan langsung di apotek, toko kelontong dan secara daring yang memiliki keterbatasan dalam sebaran ketersedian toko dan waktu pelayanan yang terbatas. Penelitian ini bertujuan untuk memberikan alternatif sistem penjualan obat non resep dokter dan keperluan medis dengan memanfaatkan perkembangan teknologi vending machine (VM) menggunakan  finite state automata (FSA model Non-deterministic Finite Automata (NFA)). Dengan kelebihan penjualan menggunakan VM yang dapat diletakan dimana saja dan dapat beroperasi kapan saja membuat penjualan dengan sistem ini dapat tersedia kapanpun dan dimanapun untuk memenuhi kebutuhan obat dan keperluan medis bagi masyarakat yang mendesak dengan mudah,cepat, tepat, dan aman. Metode yang diterapkan dalam Penerapan FSA pada VM Penjual Obat Non Resep Dokter dan Keperluan Medis ini antara lain Finite State Automata VM Obat Non Resep Dokter dan Keperluan Medis, Perancangan Sistem VM Obat Non Resep Dokter dan Keperluan Medis,dan Desain VM Obat Non Resep Dokter dan Keperluan Medis. Berdasarkan perancangan FSA VM diatas, dihasilkan VM Penjual Obat Non Resep Dokter dan Keperluan Medis yang dapat diletakan dimana saja dan tersedia kapan saja, sehingga dapat disimpulkan penggunaan finite state automata (FSA) model Non-deterministic Finite Automata (NFA) dapat dimanfaatkan dalam pembuatan VM Penjual Obat Non Resep Dokter dan Keperluan Medis dengan menyediakan menu pilihan metode pembayaran tunai dan non tunai, kebutuhan akan obat dan keperluan medis yang mendesak bagi masyarakat dapat terpenuhi dengan mudah, cepat, tepat dan aman.

scholarly journals Mobile Learning Application for Language and Automata Theory using Android-based

2020 ◽  
Vol 5 (2) ◽  
pp. 176
Author(s):  
Maulana Muhamad Sulaiman ◽  
Romi Andrianto ◽  
Muhamad Arief Yulianto
Keyword(s):  
Mobile Learning ◽  
Finite Automata ◽  
Automata Theory ◽  
Finite State Automata ◽  
Design Development ◽  
Study Program ◽  
Deterministic Finite Automata ◽  
Implementation Evaluation ◽  
Finite State ◽  
Evaluation Of Learning

The language and automata theory are which required course must implemented by college student in informatic engineering study program. In this course, there are finite state automata (FSA) and deterministic finite automata (DFA) which are important materials in language and automata theory. This material requires more understanding of mathematical logic from students to determine an input which can be accepted or rejected in an abstract machine system. The assist students  to understand the material, it is need to develop the learning media for mobile learning applications for language  and automata theory on finite state automata (FSA) and deterministic finite automata (DFA) based on android as an evaluation of learning media for students. And the development of this learning media use the ADDIE development model (analysis, design, development, implementation, evaluation) to  design language and automata theory applications learning so can be support the learning process for students and then assist lecturer to explain the material more dynamic and applicative.

EFFICIENT DETECTORS AND CONSTRUCTORS FOR SIMPLE LANGUAGES

1991 ◽  
Vol 02 (03) ◽  
pp. 183-205 ◽  
Author(s):  
Dung T. Huynh
Keyword(s):  
Finite Automata ◽  
Boolean Circuits ◽  
Turing Machines ◽  
Constant Depth ◽  
Pushdown Automaton ◽  
Polynomial Size ◽  
Regular Sets ◽  
Context Free ◽  
Pushdown Automata ◽  
Nondeterministic Logspace

In this paper, we investigate the complexity of computing the detector, constructor and lexicographic constructor functions for a given language. The following classes of languages will be considered: (1) context-free languages, (2) regular sets, (3) languages accepted by one-way nondeterministic auxiliary pushdown automata, (4) languages accepted by one-way nondeterministic logspace-bounded Turing machines, (5) two-way deterministic pushdown automaton languages, (6) languages accepted by uniform families of constant-depth polynomial-size Boolean circuits, and (7) languages accepted by multihead finite automata. We show that for the classes (1)–(4), efficient detectors, constructors and lexicographic constructors exist, whereas for (5)– (7) polynomial-time computable detectors, constructors and lexicographic constructors exist iff there are no sparse sets in NP−P (or equivalently, E=NE). Our results provide sharp boundaries between classes of languages which have efficient detectors, constructors and classes of languages for which efficient detectors and constructors do not appear to exist.

FINITE AUTOMATA AND DIGITAL IMAGES

2000 ◽  
Vol 14 (04) ◽  
pp. 501-524 ◽  
Author(s):  
S. V. RAMASUBRAMANIAN ◽  
KAMALA KRITHIVASAN
Keyword(s):  
Normal Forms ◽  
Digital Images ◽  
Finite Automata ◽  
Finite State Automata ◽  
3D Object ◽  
3D Objects ◽  
Finite State

In this paper, we initially consider representation of 2D black–white images and 3D objects using finite state automata. We describe transformation of scaling on the 2D image by an operation on the FSA. We also give constructions for getting the projections of a 3D object on to coordinate planes and for reconstructing the 3D object from its projections. We define minimization of nondeterministic FSAs and give an O(e2) (e is the number of edges in the FSA) algorithm for minimization of NFAs. Later, we define a WFA and describe various properties of WFA. We define four normal forms of WFA and show how a WFA can be normalized into any of these forms. We show the equivalence of WFAs with ∊ edges and ∊-free WFAs. Then, we define minimization of WFAs and present an algorithm to minimize a WFA.

Set Automata

2016 ◽  
Vol 27 (02) ◽  
pp. 187-214 ◽  
Author(s):  
Martin Kutrib ◽  
Andreas Malcher ◽  
Matthias Wendlandt
Keyword(s):  
Finite Automata ◽  
Point Of View ◽  
Storage Medium ◽  
Deterministic Finite Automaton ◽  
Closure Properties ◽  
Language Class ◽  
Trade Offs ◽  
Double Exponential ◽  
Order Of Magnitude ◽  
Context Free

We consider the model of deterministic set automata which are basically deterministic finite automata equipped with a set as an additional storage medium. The basic operations on the set are the insertion of elements, the removing of elements, and the test whether an element is in the set. We investigate the computational power of deterministic set automata and compare the language class accepted with the context-free languages and classes of languages accepted by queue automata. As result the incomparability to all classes considered is obtained. Furthermore, we examine the closure properties under several operations. Then we show that deterministic set automata may be an interesting model from a practical point of view by proving that their regularity problem as well as the problems of emptiness, finiteness, infiniteness, and universality are decidable. Finally, the descriptional complexity of deterministic and nondeterministic set automata is investigated. A conversion procedure that turns a deterministic set automaton accepting a regular language into a deterministic finite automaton is developed which leads to a double exponential upper bound. This bound is proved to be tight in the order of magnitude by presenting also a double exponential lower bound. In contrast to these recursive bounds we obtain non-recursive trade-offs when nondeterministic set automata are considered.

scholarly journals DETERMINISTIC PUSHDOWN AUTOMATA AND UNARY LANGUAGES

2009 ◽  
Vol 20 (04) ◽  
pp. 629-645 ◽  
Author(s):  
GIOVANNI PIGHIZZINI
Keyword(s):  
Finite Automata ◽  
Point Of View ◽  
Deterministic Finite Automaton ◽  
Pushdown Automaton ◽  
Nondeterministic Automaton ◽  
Letter Alphabet ◽  
Finite State ◽  
Unary Languages ◽  
Context Free ◽  
Pushdown Automata

The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, its cost cannot be reduced even if it is performed by a two-way nondeterministic automaton. We also prove that there are unary languages for which deterministic pushdown automata cannot be exponentially more succinct than finite automata. In order to state this result, we investigate the conversion of deterministic pushdown automata into context-free grammars. We prove that in the unary case the number of variables in the resulting grammar is strictly smaller than the number of variables needed in the case of nonunary alphabets.

scholarly journals A String Diagrammatic Axiomatisation of Finite-State Automata

2021 ◽  
pp. 469-489
Author(s):  
Robin Piedeleu ◽  
Fabio Zanasi
Keyword(s):  
Graphical Representation ◽  
Equational Theory ◽  
Finite State Automata ◽  
Regular Expressions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Finite State ◽  
The One ◽  
Language Equivalence ◽  
Usual State

AbstractWe develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite— a result which is provably impossible for the one-dimensional syntax of regular expressions. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks.

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