Non Homogeneous Rough Finite State Automaton

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’.

Download Full-text

KNUTH–BENDIX FOR GROUPS WITH INFINITELY MANY RULES

International Journal of Algebra and Computation ◽

10.1142/s0218196700000352 ◽

2000 ◽

Vol 10 (05) ◽

pp. 539-589 ◽

Cited By ~ 1

Author(s):

D. B. A. EPSTEIN ◽

P. J. SANDERS

Keyword(s):

Computer Program ◽

Regular Language ◽

The Body ◽

Finite State Automaton ◽

Finite State Automata ◽

Central Feature ◽

Rapid Reduction ◽

Automatic Structures ◽

Small Constant ◽

Finite State

We introduce a new class of groups with solvable word problem, namely groups specified by a confluent set of short-lex-reducing Knuth–Bendix rules which form a regular language. This simultaneously generalizes short-lex-automatic groups and groups with a finite confluent set of short-lex-reducing rules. We describe a computer program which looks for such a set of rules in an arbitrary finitely presented group. Our main theorem is that our computer program finds the set of rules, if it exists, given enough time and space. (This is an optimistic description of our result — for the more pessimistic details, see the body of the paper.) The set of rules is embodied in a finite state automaton in two variables. A central feature of our program is an operation, which we call welding, used to combine existing rules with new rules as they are found. Welding can be defined on arbitrary finite state automata, and we investigate this operation in abstract, proving that it can be considered as a process which takes as input one regular language and outputs another regular language. In our programs we need to convert several nondeterministic finite state automata to deterministic versions accepting the same language. We show how to improve somewhat on the standard subset construction, due to special features in our case. We axiomatize these special features, in the hope that these improvements can be used in other applications. The Knuth–Bendix process normally spends most of its time in reduction, so its efficiency depends on doing reduction quickly. Standard data structures for doing this can become very large, ultimately limiting the set of presentations of groups which can be so analyzed. We are able to give a method for rapid reduction using our much smaller two variable automaton, encoding the (usually infinite) regular language of rules found so far. Time taken for reduction in a given group is a small constant times the time taken for reduction in the best schemes known (see [5]), which is not too bad since we are reducing with respect to an infinite set of rules, whereas known schemes use a finite set of rules. We hope that the method described here might lead to the computation of automatic structures in groups for which this is currently infeasible. Some proofs have been omitted from this paper in the interests of brevity. Full details are provided in [4].

Download Full-text

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

Expert Systems ◽

10.1111/exsy.12836 ◽

2021 ◽

Author(s):

Kuruge Darshana Abeyrathna ◽

Ole‐Christoffer Granmo ◽

Rishad Shafik ◽

Lei Jiao ◽

Adrian Wheeldon ◽

...

Keyword(s):

Machine Learning ◽

Finite State Automaton ◽

Finite State

Download Full-text

Applications of the finite state automata for counting restricted permutations and variations

Yugoslav journal of operations research ◽

10.2298/yjor120211023b ◽

2012 ◽

Vol 22 (2) ◽

pp. 183-198

Author(s):

Vladimir Baltic

Keyword(s):

The Other ◽

Finite State Automaton ◽

Finite State Automata ◽

Combinatorial Structures ◽

Restricted Permutations ◽

Finite State

In this paper, we use the finite state automata to count the number of restricted permutations and the number of restricted variations. For each type of restricted permutations, we construct a finite state automaton able to recognize and enumerate them. We, also, discuss how it encompasses the other known methods for enumerating permutations with restricted position, and in one case, we establish connections with some other combinatorial structures, such as subsets and compositions.

Download Full-text

A Transformation-Based Approach to Implication of GSTE Assertion Graphs

Journal of Applied Mathematics ◽

10.1155/2013/709071 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

Guowu Yang ◽

William N. N. Hung ◽

Xiaoyu Song ◽

Wensheng Guo

Keyword(s):

Model Checking ◽

Directed Graphs ◽

Classical Model ◽

Regular Languages ◽

Finite State Automaton ◽

Finite State Automata ◽

Symbolic Trajectory Evaluation ◽

Finite State ◽

Symbolic Trajectory ◽

Language Containment

Generalized symbolic trajectory evaluation (GSTE) is a model checking approach and has successfully demonstrated its powerful capacity in formal verification of VLSI systems. GSTE is an extension of symbolic trajectory evaluation (STE) to the model checking ofω-regular properties. It is an alternative to classical model checking algorithms where properties are specified as finite-state automata. In GSTE, properties are specified as assertion graphs, which are labeled directed graphs where each edge is labeled with two labeling functions: antecedent and consequent. In this paper, we show the complement relation between GSTE assertion graphs and finite-state automata with the expressiveness of regular languages andω-regular languages. We present an algorithm that transforms a GSTE assertion graph to a finite-state automaton and vice versa. By applying this algorithm, we transform the problem of GSTE assertion graphs implication to the problem of automata language containment. We demonstrate our approach with its application to verification of an FIFO circuit.

Download Full-text

Machine Learning with Explainable Artificial Intelligence Vision for Characterization of Solution Conductivity Using Optical Emission Spectroscopy of Plasma in Aqueous Solution

Plasma Processes and Polymers ◽

10.1002/ppap.202100096 ◽

2021 ◽

Author(s):

Ching‐Yu Wang ◽

Tsung‐Shun Ko ◽

Cheng‐Che Hsu

Keyword(s):

Artificial Intelligence ◽

Machine Learning ◽

Aqueous Solution ◽

Emission Spectroscopy ◽

Optical Emission Spectroscopy ◽

Optical Emission ◽

Explainable Artificial Intelligence ◽

Solution Conductivity

Download Full-text

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

Lecture Notes in Computer Science - Artificial Intelligence XXXVII ◽

10.1007/978-3-030-63799-6_8 ◽

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

Download Full-text

Incremental Construction and Maintenance of Minimal Finite-State Automata

Computational Linguistics ◽

10.1162/089120102760173652 ◽

2002 ◽

Vol 28 (2) ◽

pp. 207-216 ◽

Cited By ~ 26

Author(s):

Rafael C. Carrasco ◽

Mikel L. Forcada

Keyword(s):

Computational Linguistics ◽

Efficient Method ◽

Finite State Automaton ◽

Finite State Automata ◽

Construction Problem ◽

Finite State ◽

Single String ◽

Intersection Operation ◽

Incremental Construction ◽

Special Case

Daciuk et al. [Computational Linguistics 26(1):3–16 (2000)] describe a method for constructing incrementally minimal, deterministic, acyclic finite-state automata (dictionaries) from sets of strings. But acyclic finite-state automata have limitations: For instance, if one wants a linguistic application to accept all possible integer numbers or Internet addresses, the corresponding finite-state automaton has to be cyclic. In this article, we describe a simple and equally efficient method for modifying any minimal finite-state automaton (be it acyclic or not) so that a string is added to or removed from the language it accepts; both operations are very important when dictionary maintenance is performed and solve the dictionary construction problem addressed by Daciuk et al. as a special case. The algorithms proposed here may be straightforwardly derived from the customary textbook constructions for the intersection and the complementation of finite-state automata; the algorithms exploit the special properties of the automata resulting from the intersection operation when one of the finite-state automata accepts a single string.

Download Full-text

Artificial Intelligence and Machine Learning in Arrhythmias and Cardiac Electrophysiology

Circulation Arrhythmia and Electrophysiology ◽

10.1161/circep.119.007952 ◽

2020 ◽

Vol 13 (8) ◽

Author(s):

Albert K. Feeny ◽

Mina K. Chung ◽

Anant Madabhushi ◽

Zachi I. Attia ◽

Maja Cikes ◽

...

Keyword(s):

Artificial Intelligence ◽

Machine Learning ◽

Clinical Practice ◽

Patient Outcomes ◽

Cardiac Electrophysiology ◽

Recent Literature ◽

Human Capabilities ◽

Key Points ◽

Detection And Diagnosis

Artificial intelligence (AI) and machine learning (ML) in medicine are currently areas of intense exploration, showing potential to automate human tasks and even perform tasks beyond human capabilities. Literacy and understanding of AI/ML methods are becoming increasingly important to researchers and clinicians. The first objective of this review is to provide the novice reader with literacy of AI/ML methods and provide a foundation for how one might conduct an ML study. We provide a technical overview of some of the most commonly used terms, techniques, and challenges in AI/ML studies, with reference to recent studies in cardiac electrophysiology to illustrate key points. The second objective of this review is to use examples from recent literature to discuss how AI and ML are changing clinical practice and research in cardiac electrophysiology, with emphasis on disease detection and diagnosis, prediction of patient outcomes, and novel characterization of disease. The final objective is to highlight important considerations and challenges for appropriate validation, adoption, and deployment of AI technologies into clinical practice.

Download Full-text