scholarly journals Generic Study on n-state Mealy Automata without Cycles

2018 ◽  
Vol 1000 ◽  
pp. 012162
Author(s):  
K. Thiagarajan ◽  
P. Balasubramanian ◽  
J. Padmashree
Keyword(s):  
Mealy Automata

scholarly journals ON THE FINITENESS PROBLEM FOR AUTOMATON (SEMI)GROUPS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250052 ◽  
Author(s):  
ALI AKHAVI ◽  
INES KLIMANN ◽  
SYLVAIN LOMBARDY ◽  
JEAN MAIRESSE ◽  
MATTHIEU PICANTIN
Keyword(s):  
Decision Problem ◽  
Decision Procedure ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Mealy Automata ◽  
Necessary And Sufficient ◽  
New Criteria

This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskiĭ, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for finiteness and, for groups, an effective necessary but not sufficient condition. The efficiency of the new criteria is demonstrated by testing all Mealy automata with small stateset and alphabet. Finally, for groups, we provide a necessary and sufficient condition that does not directly lead to a decision procedure.

Numerical upper bounds on growth of automaton groups

2021 ◽  
pp. 1-33
Author(s):  
Jérémie Brieussel ◽  
Thibault Godin ◽  
Bijan Mohammadi
Keyword(s):  
Group Theory ◽  
Upper Bounds ◽  
Geometric Invariant ◽  
Finitely Generated ◽  
Grigorchuk Group ◽  
Finitely Generated Group ◽  
Intermediate Growth ◽  
Mealy Automata ◽  
Optimal Bounds ◽  
Algorithmic Procedure

The growth of a finitely generated group is an important geometric invariant which has been studied for decades. It can be either polynomial, for a well-understood class of groups, or exponential, for most groups studied by geometers, or intermediate, that is between polynomial and exponential. Despite recent spectacular progresses, the class of groups with intermediate growth remains largely mysterious. Many examples of such groups are constructed using Mealy automata. The aim of this paper is to give an algorithmic procedure to study the growth of such automaton groups, and more precisely to provide numerical upper bounds on their exponents. Our functions retrieve known optimal bounds on the famous first Grigorchuk group. They also improve known upper bounds on other automaton groups and permitted us to discover several new examples of automaton groups of intermediate growth. All the algorithms described are implemented in GAP, a language dedicated to computational group theory.

An Automatic Network Protocol State Machine Inference Method in Protocol Reverse Engineering

2014 ◽  
Vol 513-517 ◽  
pp. 2496-2501
Author(s):  
Li Hua Zhao ◽  
Xue Jia Liang ◽  
Xiang Peng ◽  
Hua Feng Kong ◽  
Mei Zhen Wang
Keyword(s):  
Network Security ◽  
Reverse Engineering ◽  
Communication Protocol ◽  
State Machine ◽  
Important Application ◽  
Network Protocol ◽  
Extended Version ◽  
Inference Method ◽  
Mealy Automata ◽  
Protocol Reverse Engineering

To infer the network protocol state machine is very useful in network security-related contexts, both in research and management. This process follows an extension of the classic Angluins L* algorithm and has achieved an extended version of some Mealy automata to represent or model a communication protocol. The algorithm has been validated by inferring the protocol state machine from SMTPFTP protocol, and tested offline algorithms for the comparison experiments. The experimental results show that this method can more accurately identify the network protocol state machine and is of the important application value.

scholarly journals THE IMITATION MODEL OF BURSTY AND BATCH DATA PACKET FLOW

2006 ◽  
Vol 12 (4) ◽  
pp. 360-366
Author(s):  
Aušra Žvironienė ◽  
Zenonas Navickas ◽  
Ramutis Rindzevičius
Keyword(s):  
Data Packet ◽  
Imitation Model ◽  
Mealy Automata ◽  
Batch Data

The imitation model of bursty and batch data packet flow is presented in this paper. The proposed imitation model was created using the convolution of Moore and Mealy automata.

scholarly journals A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group

2018 ◽  
Vol 29 (02) ◽  
pp. 297-314
Author(s):  
Ines Klimann ◽  
Matthieu Picantin ◽  
Dmytro Savchuk
Keyword(s):  
Infinite Order ◽  
Rich Source ◽  
Burnside Groups ◽  
Mealy Automaton ◽  
Mealy Automata

The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, all such examples have been constructed as groups generated by non-reversible automata. Moreover, it was recently shown that 2-state reversible Mealy automata cannot generate infinite Burnside groups. Here we extend this result to connected 3-state reversible Mealy automata, using new original techniques. The results rely on a fine analysis of associated orbit trees and a new characterization of the existence of elements of infinite order.

scholarly journals Cascade Products of Stochastic Automata

2021 ◽  
Vol 20 ◽  
pp. 168-175
Author(s):  
Merve Nur Cakir ◽  
Mehwish Saleemi ◽  
Karl-Heinz Zimmermann
Keyword(s):  
Stochastic Automata ◽  
Mild Conditions ◽  
Mealy Automata ◽  
Moore Automata ◽  
General Stochastic

Stochastic Moore automata have in opposition to stochastic Mealy automata the same capabilities as general stochastic automata, but have the advantage that they are easier to access than their pure stochastic counterparts. Cascade decomposition of automata leads to a loop-free partitioning and in this way contributes to the analysis of automata. This paper shows that stochastic Moore automata can be decomposed into cascade products of stochastic Moore automata under mild conditions

Sign in / Sign up

Export Citation Format

Share Document