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课程名称：泰米尔语中的计算理论 课程概述：本课程“自动机理论、语言与计算导论”旨在详细解释每种数学模型及其对应语言及可证明的等价性。计算理论主要包括三个重要分支：1）自动机理论 2）可计算性理论 3）复杂性理论。自动机理论涉及一些自动执行操作的数学模型，如编程机器。主要有四种数学模型：有限自动机（FA）、下推自动机（PDA）、线性有界自动机（LBA）和图灵机（TM）。每种模型根据其内存单元的不同而有所区别：FA没有外部内存单元，PDA具有堆栈作为内存单元，LBA有有限长度的带，TM则具有无限带。 每种模型解决的问题集被称为该模型所接受的语言，有限自动机解决的问题称为正规语言，其对应的语言表示称为正规文法；下推自动机接受的语言称为上下文无关语言；线性有界自动机接受的语言称为上下文相关语言；图灵机接受的语言称为无约束语言，因为图灵机具有无限内存和随机访问内存单元的能力。图灵机可等同于现代计算机，能够解决所有可以由计算机解决的问题。 可计算性理论验证问题是否可解决；如果可解决，复杂性理论则涉及图灵机可解决问题的算法复杂性。本课程主要集中于自动机理论（数学模型）及其语言。
The aim of this course "Introduction to Automata Theory, Languages and Computation" is to give a detailed working explanation regarding each Mathematical model, its corresponding languages, and their provable equivalence. "Theory of Computation" has three major subdivisions namely1) Automata Theory2) Computability Theory3) Complexity TheoryThe automata theory deals with some Mathematical models that perform some operations automatically like programming machines. There are four main Mathematical models namely, Finite Automata(FA), Push Down Automata(PDA), Linear Bound Automata(LBA), and Turing Machine(TM). Each Mathematical model differs based on its memory units as FA has no external memory unit, PDA has stack as a memory unit, LBA has finite length tape as a memory unit and TM has infinite tape as a memory unit.Based on the limitations in the memory unit each model solves a limited set of problems only. The set of problems solved by each model is grouped as languages accepted by the model. The problems solved by Finite Automata are called Regular Language and its corresponding language representation is called Regular Grammar. The language accepted by Push Down Automata is called Context Free Language, the language accepted by Linear Bound Automata is called Context Sensitive Language, and the language accepted by Turing Machine is called Un-Restricted language since Turing machines have unlimited memory and random access to the memory unit.Turing machines can be equated to modern computers, it can solve any problem that is solvable by computers. Computability theory deals with verifying whether the problem is solvable or not and If it is solvable complexity theory deals with the algorithmic complexity of problems that are solvable by Turing Machine.This course mainly deals with automata theory (Mathematical Models) and its languages.
