A Census of Finite Automata

1965 ◽  
Vol 17 ◽  
pp. 100-113 ◽  
Author(s):  
Michael A. Harrison
Keyword(s):  
Finite Number ◽  
Finite Automaton ◽  
Unsolved Problem ◽  
Internal State ◽  
Finite Automata ◽  
Input Sequence ◽  
Equivalence Classes ◽  
Focused Attention ◽  
Internal States ◽  
Output Tape

A finite automaton may be thought of as a possible abstraction of a digital computer. Imagine a tape or sequence of letters from some alphabet being fed into a device with a finite number of internal states. When the device is in a particular state and receives an input letter, the system passes to another internal state and prints a letter on an output tape. This operation is continued until the entire input sequence has been processed.Both Harary (6) and Ginsburg (4) have focused attention on the previously unsolved problem of counting the number of equivalence classes of finite automata. In the present paper, this problem is solved completely by proving a variety of theorems about the enumeration of functions.

The undecidability of the Turing machine immortality problem

1966 ◽  
Vol 31 (2) ◽  
pp. 219-234 ◽  
Author(s):  
Philip K. Hooper
Keyword(s):  
Finite Number ◽  
Turing Machine ◽  
Internal State ◽  
Finite Alphabet ◽  
Infinite Words ◽  
Internal States

A Turing Machine (TM) is an abstract, synchronous, deterministic computer with a finite number of internal states. It operates on the set of infinite words, or tapes, over some finite alphabet, scanning exactly one symbol of the tape at a time. (Only a 2-symbol alphabet, consisting of “0” and “|”, will be considered here, and the scanned symbol of a tape will be distinguished by an underscore.) depending upon its internal state and the symbol under scan, it can perform one or more of the following operations: replace the scanned symbol with a new symbol, focus its attention on an adjacent square, and transfer control to a new state.

ON THE REGULARITY OF SETS OF MULTI-ACCEPTED STRINGS OF A NON-DETERMINISTIC FINITE AUTOMATON

2009 ◽  
Vol 02 (04) ◽  
pp. 717-726
Author(s):  
L. K. Waters ◽  
J. K. Grieshop
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Equivalence Classes ◽  
Deterministic Finite Automaton ◽  
Finite Sets ◽  
Nondeterministic Finite Automata ◽  
Labeling Approach ◽  
Acceptance Levels ◽  
Labeling Method

In this paper we establish the regularity of various sets of multi-accepted strings of nondeterministic finite automata. Regularity follows from the existence of accepting automata constructed by introducing a vector labeling method which generalizes the subset labeling approach. In each set the acceptance levels of the strings correspond to finite sets of additive equivalence classes of non-negative integers.

Impaired discrimination of a subanesthetic dose of ketamine in a maternal immune activation model of schizophrenia risk

2021 ◽  
pp. 026988112110297
Author(s):  
Wayne Meighan ◽  
Thomas W Elston ◽  
David Bilkey ◽  
Ryan D Ward
Keyword(s):  
Animal Models ◽  
Drug Discrimination ◽  
Immune Activation ◽  
Internal State ◽  
Nmda Receptor Antagonist ◽  
Activation Model ◽  
Data Link ◽  
Maternal Immune Activation ◽  
Internal States ◽  
Reliable Methods

Background: Animal models of psychiatric diseases suffer from a lack of reliable methods for accurate assessment of subjective internal states in nonhumans. This gap makes translation of results from animal models to patients particularly challenging. Aims/methods: Here, we used the drug-discrimination paradigm to allow rats that model a risk factor for schizophrenia (maternal immune activation, MIA) to report on the subjective internal state produced by a subanesthetic dose of the N-methyl-D-aspartate (NMDA) receptor antagonist ketamine. Results/outcomes: The MIA rats’ discrimination of ketamine was impaired relative to controls, both in the total number of rats that acquired and the asymptotic level of discrimination accuracy. This deficit was not due to a general inability to learn to discriminate an internal drug cue or internal state generally, as MIA rats were unimpaired in the learning and acquisition of a morphine drug discrimination and were as sensitive to the internal state of satiety as controls. Furthermore, the deficit was not due to a decreased sensitivity to the physiological effects of ketamine, as MIA rats showed increased ketamine-induced locomotor activity. Finally, impaired discrimination of ketamine was only seen at subanesthetic doses which functionally correspond to psychotomimetic doses in humans. Conclusion: These data link changes in NMDA responses to the MIA model. Furthermore, they confirm the utility of the drug-discrimination paradigm for future inquiries into the subjective internal state produced in models of schizophrenia and other developmental diseases.

A Fast 3-D Visualization Methodology Using Characteristic Views of Objects

1998 ◽  
Vol 08 (01) ◽  
pp. 97-114 ◽  
Author(s):  
Soochan Hwang ◽  
Sang-Young Cho ◽  
Taehyung Wang ◽  
Phillip C.-Y. Sheu
Keyword(s):  
Finite Number ◽  
Real Time ◽  
Time Complexity ◽  
Object Oriented ◽  
Equivalence Classes ◽  
Visualization Method ◽  
Tree Algorithm ◽  
Projected Image ◽  
Characteristic Views ◽  
Run Time

This paper describes a 3-D visualization method based on the concept of characteristic views (CVs). The idea of characteristic views was derived based on the observation that the infinite possible views of a 3-D object can be grouped into a finite number of equivalence classes so that within each class all the views are isomorphic in the sense that they have the same line-junction graphs. To visualize the changes of scenes in real time, the BSP tree algorithm is known to be efficient in a static environment in which the viewpoint can be changed easily. However, if a scene consists of many objects and each object consists of many polygons, the time complexity involved in traversing a BSP tree increases rapidly so that the original BSP tree algorithm may not be efficient. The method proposed in this paper is object-oriented in the sense that, for all viewpoints, at the preprocessing stage the ordering for displaying the objects is determined. At run time, the objects are displayed based on a pre-calculated ordering according to the viewpoint. In addition, a CV is used as a basic 2-D projected image of a 3-D object.

scholarly journals Autonomous Decision-Making While Drilling

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 969
Author(s):  
Eric Cayeux ◽  
Benoît Daireaux ◽  
Adrian Ambrus ◽  
Rodica Mihai ◽  
Liv Carlsen
Keyword(s):  
Decision Making ◽  
Internal State ◽  
Drilling Process ◽  
Autonomous Decision ◽  
Internal States ◽  
Markov Decision ◽  
Drilling Operations ◽  
Drilling System ◽  
Drilling Conditions ◽  
Erratic Behavior

The drilling process is complex because unexpected situations may occur at any time. Furthermore, the drilling system is extremely long and slender, therefore prone to vibrations and often being dominated by long transient periods. Adding the fact that measurements are not well distributed along the drilling system, with the majority of real-time measurements only available at the top side and having only access to very sparse data from downhole, the drilling process is poorly observed therefore making it difficult to use standard control methods. Therefore, to achieve completely autonomous drilling operations, it is necessary to utilize a method that is capable of estimating the internal state of the drilling system from parsimonious information while being able to make decisions that will keep the operation safe but effective. A solution enabling autonomous decision-making while drilling has been developed. It relies on an optimization of the time to reach the section total depth (TD). The estimated time to reach the section TD is decomposed into the effective time spent in conducting the drilling operation and the likely time lost to solve unexpected drilling events. This optimization problem is solved by using a Markov decision process method. Several example scenarios have been run in a virtual rig environment to test the validity of the concept. It is found that the system is capable to adapt itself to various drilling conditions, as for example being aggressive when the operation runs smoothly and the estimated uncertainty of the internal states is low, but also more cautious when the downhole drilling conditions deteriorate or when observations tend to indicate more erratic behavior, which is often observed prior to a drilling event.

Membership Problem for Two-Dimensional General Row Jumping Finite Automata

2020 ◽  
Vol 31 (04) ◽  
pp. 527-538
Author(s):  
Grzegorz Madejski ◽  
Andrzej Szepietowski
Keyword(s):  
Computational Model ◽  
Turing Machine ◽  
Finite Automaton ◽  
Finite Automata ◽  
The Other ◽  
Membership Problem ◽  
Two Dimensional ◽  
Np Complete ◽  
Nondeterministic Turing Machine ◽  
Membership Problems

Two-dimensional general row jumping finite automata were recently introduced as an interesting computational model for accepting two-dimensional languages. These automata are nondeterministic. They guess an order in which rows of the input array are read and they jump to the next row only after reading all symbols in the previous row. In each row, they choose, also nondeterministically, an order in which segments of the row are read. In this paper, we study the membership problem for these automata. We show that each general row jumping finite automaton can be simulated by a nondeterministic Turing machine with space bounded by the logarithm. This means that the fixed membership problems for such automata are in NL, and so in P. On the other hand, we show that the uniform membership problem is NP-complete.

MAGIC NUMBERS FOR SYMMETRIC DIFFERENCE NFAS

2005 ◽  
Vol 16 (05) ◽  
pp. 1027-1038 ◽  
Author(s):  
LYNETTE VAN ZIJL
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Symmetric Difference ◽  
Magic Numbers ◽  
Deterministic Finite Automaton ◽  
Nondeterministic Finite Automata ◽  
Binary Case ◽  
Nondeterministic Finite Automaton

Iwama et al. showed that there exists an n-state binary nondeterministic finite automaton such that its equivalent minimal deterministic finite automaton has exactly 2n - α states, for all n ≥ 7 and 5 ≤ α ≤ 2n-2, subject to certain coprimality conditions. We investigate the same question for both unary and binary symmetric difference nondeterministic finite automata. In the binary case, we show that for any n ≥ 4, there is an n-state symmetric difference nondeterministic finite automaton for which the equivalent minimal deterministic finite automaton has 2n - 1 + 2k - 1 - 1 states, for 2 < k ≤ n - 1. In the unary case, we consider a large practical subclass of unary symmetric difference nondeterministic finite automata: for all n ≥ 2, we argue that there are many values of α such that there is no n-state unary symmetric difference nondeterministic finite automaton with an equivalent minimal deterministic finite automaton with 2n - α states, where 0 < α < 2n - 1. For each n ≥ 2, we quantify such values of α precisely.

DETERMINATIONS OF WEIGHTED FINITE AUTOMATA OVER COMMUTATIVE IDEMPOTENT MF-SEMIRINGS

2012 ◽  
Vol 22 (03) ◽  
pp. 1250020
Author(s):  
YONG HE ◽  
GONGCAI XIN ◽  
ZHIXI WANG
Keyword(s):  
Finite Automaton ◽  
Finite Dimension ◽  
Finite Automata ◽  
Commutative Semiring ◽  
Special Cases ◽  
Weighted Finite Automata

The semirings admitting maximal factorizations of any finite dimension are called MF-semirings. We first show that a commutative semiring K is an MF-semiring if and only if K admits a maximal factorization of dimension n ≥ 2, and if and only if K is a multiplicatively cancellative semiring satisfying the g.c.d. condition. And then, by using above result, we prove that a weighted finite automaton [Formula: see text] over a commutative idempotent MF-semiring has a determination if [Formula: see text] has the victory property and twins property. Also, some special cases are considered.

STATE COMPLEXITY OF ADDITIVE WEIGHTED FINITE AUTOMATA

2007 ◽  
Vol 18 (06) ◽  
pp. 1407-1416 ◽  
Author(s):  
KAI SALOMAA ◽  
PAUL SCHOFIELD
Keyword(s):  
Upper Bound ◽  
Finite Automaton ◽  
Regular Language ◽  
Finite Automata ◽  
The State ◽  
Deterministic Finite Automata ◽  
State Complexity ◽  
Weighted Finite Automata

It is known that the neighborhood of a regular language with respect to an additive distance is regular. We introduce an additive weighted finite automaton model that provides a conceptually simple way to reprove this result. We consider the state complexity of converting additive weighted finite automata to deterministic finite automata. As our main result we establish a tight upper bound for the state complexity of the conversion.

scholarly journals Multiple asymptotics of kinetic equations with internal states

2020 ◽  
Vol 30 (06) ◽  
pp. 1041-1073
Author(s):  
Benoit Perthame ◽  
Weiran Sun ◽  
Min Tang ◽  
Shugo Yasuda
Keyword(s):  
Kinetic Equation ◽  
Equilibrium Equation ◽  
Internal State ◽  
Kinetic Equations ◽  
Chemical Stimulus ◽  
Adaptation Time ◽  
Macroscopic Models ◽  
Internal States ◽  
New Type ◽  
Run And Tumble

The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However, the relation between the tumbling rate and the internal state of bacteria is poorly understood. This study aims at deriving macroscopic models as limits of the mesoscopic kinetic equation in different regimes. In particular, we are interested in the roles of the stiffness of the response and the adaptation time in the kinetic equation. Depending on the asymptotics chosen both the standard Keller–Segel equation and the flux-limited Keller–Segel (FLKS) equation can appear. An interesting mathematical issue arises with a new type of equilibrium equation leading to solution with singularities.

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