scholarly journals A multi‐step finite‐state automaton for arbitrarily deterministic Tsetlin Machine learning

2021 ◽  
Author(s):  
Kuruge Darshana Abeyrathna ◽  
Ole‐Christoffer Granmo ◽  
Rishad Shafik ◽  
Lei Jiao ◽  
Adrian Wheeldon ◽  
...  
Keyword(s):  
Machine Learning ◽  
Finite State Automaton ◽  
Finite State

scholarly journals Non Homogeneous Rough Finite State Automaton

2021 ◽  
Vol 11 (2) ◽  
pp. 629-641
Author(s):  
B. Praba ◽  
R. Saranya
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Dynamical Behaviour ◽  
Finite State Automaton ◽  
Finite State Automata ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Finite State ◽  
Transition Map

Objective: The study of finite state automaton is an essential tool in machine learning and artificial intelligence. The class of rough finite state automaton captures the uncertainty using the rough transition map. The need to generalize this concept arises to adhere the dynamical behaviour of the system. Hence this paper focuses on defining non-homogeneous rough finite state automaton. Methodology: With the aid of Rough finite state automata we define the concept of non-homogeneous rough finite state automata. Findings: Non homogeneous Rough Finite State Automata (NRFSA) Mt is defined by a tuple (Q,Σ,δt,q0 (t),F(t)) The dynamical behaviour of any system can be expressed in terms of an information system at time t. This leads us to define non-homogeneous rough finite state automaton. For each time ‘t’ we generate lower approximation rough finite state automaton Mt_ and the upper approximation rough finite state automaton Mt- and the defined concepts are elaborated with suitable examples. The ordered pair , Mt=(M(t)-,M(t)-) is called as the non-homogeneous rough finite state automaton. Conclusion: Over all our study reveals the characterization of the system which changes its behaviour dynamically over a time ‘t’. Novelty: The novelty of the proposed article is that it clearly immense the system behaviour over a time ‘t’. Using this concept the possible and the definite transitions in the system can be calculated in any given time ‘t’.

scholarly journals A Novel Multi-step Finite-State Automaton for Arbitrarily Deterministic Tsetlin Machine Learning

2020 ◽  
pp. 108-122
Author(s):  
K. Darshana Abeyrathna ◽  
Ole-Christoffer Granmo ◽  
Rishad Shafik ◽  
Alex Yakovlev ◽  
Adrian Wheeldon ◽  
...  
Keyword(s):  
Machine Learning ◽  
Finite State Automaton ◽  
Finite State

scholarly journals Combable functions, quasimorphisms, and the central limit theorem

2009 ◽  
Vol 30 (5) ◽  
pp. 1343-1369 ◽  
Author(s):  
DANNY CALEGARI ◽  
KOJI FUJIWARA
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Word Length ◽  
Hyperbolic Groups ◽  
Finite State Automaton ◽  
List Type ◽  
Generating Sets ◽  
Finite State ◽  
Word Hyperbolic Groups

AbstractA function on a discrete group is weakly combable if its discrete derivative with respect to a combing can be calculated by a finite-state automaton. A weakly combable function is bicombable if it is Lipschitz in both the left- and right-invariant word metrics. Examples of bicombable functions on word-hyperbolic groups include:(1)homomorphisms to ℤ;(2)word length with respect to a finite generating set;(3)most known explicit constructions of quasimorphisms (e.g. the Epstein–Fujiwara counting quasimorphisms).We show that bicombable functions on word-hyperbolic groups satisfy acentral limit theorem: if$\overline {\phi }_n$is the value of ϕ on a random element of word lengthn(in a certain sense), there areEandσfor which there is convergence in the sense of distribution$n^{-1/2}(\overline {\phi }_n - nE) \to N(0,\sigma )$, whereN(0,σ) denotes the normal distribution with standard deviationσ. As a corollary, we show that ifS1andS2are any two finite generating sets forG, there is an algebraic numberλ1,2depending onS1andS2such that almost every word of lengthnin theS1metric has word lengthn⋅λ1,2in theS2metric, with error of size$O(\sqrt {n})$.

scholarly journals Model Checking Temporal Logic Formulas Using Sticker Automata

2017 ◽  
Vol 2017 ◽  
pp. 1-33 ◽  
Author(s):  
Weijun Zhu ◽  
Changwei Feng ◽  
Huanmei Wu
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Complex Problem ◽  
Finite State Automaton ◽  
Dna Molecules ◽  
Single Stranded Dna ◽  
Finite State ◽  
Input Strings ◽  
Logic Model Checking ◽  
The Given

As an important complex problem, the temporal logic model checking problem is still far from being fully resolved under the circumstance of DNA computing, especially Computation Tree Logic (CTL), Interval Temporal Logic (ITL), and Projection Temporal Logic (PTL), because there is still a lack of approaches for DNA model checking. To address this challenge, a model checking method is proposed for checking the basic formulas in the above three temporal logic types with DNA molecules. First, one-type single-stranded DNA molecules are employed to encode the Finite State Automaton (FSA) model of the given basic formula so that a sticker automaton is obtained. On the other hand, other single-stranded DNA molecules are employed to encode the given system model so that the input strings of the sticker automaton are obtained. Next, a series of biochemical reactions are conducted between the above two types of single-stranded DNA molecules. It can then be decided whether the system satisfies the formula or not. As a result, we have developed a DNA-based approach for checking all the basic formulas of CTL, ITL, and PTL. The simulated results demonstrate the effectiveness of the new method.

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