Master Theory of Computation: Models, Properties, and Equivalences

In summary, This course on Theory of Computation covers various models of computation and their properties. These include regular languages models such as finite state machines, recursive and recursively enumerable sets models such as turing machines, and context-free languages models such as grammars. Properties such as closure, decidability, and minimality are also discussed. The course also explores the concepts of FSMs, grammars, regular expressions, and turing machines and their practical applications. Additionally, the course touches on the topics of decidability and computability, and their relevance in solving problems such as TSP and boolean satisfiability. Overall, this course provides a theoretical basis for understanding how things are done on a computer.
  • #1
heman
361
0
I am taking this course this semester and i don't have enough idea about what this is all about...like i want to have a clearcut view in mind like how this coyrse helps...please i appreciate your comments..


Syllabus runs as::
Theory of Computation
Course Contents:
Models of computation -- classification, properties and equivalences.

Regular languages models: finite state machines (deterministic and non-deterministic), regular grammars, regular expressions, equivalence of deterministic and non-deterministic machines and of the three models. Properties: closure, decidability, minimality of automata, iteration theorems.

Recursive and recursively enumerable sets models: turing machines, grammars, recursive functions, their equivalence. Church's thesis. Properties: closure, decidability, undecidablity/non-computability, notion of reductions.

Context-free languages models: grammars (including different normal forms), pushdown automata, and their equivalence. Properties: closure, iteration theorems, parsing.
 
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  • #2
Its about how things are done on a computer...with a theoretical basis.
FSMs- are like graph theory...however each node represents a configuration or state of your environment. Each link from node to node represents how one goes from state to state. You write up a transition table normally to describe the FSM (eg current state, transition symbol/alphabet, new state). Simplest example is to create an ATM describe all the configurations or state, and the transitions are the button pressing. You'll learn the DFA and nDFA in class.

Grammars and regular expressions are the types of strings and grammaes that you can store on a computer. Minimality is the lowest # of states that a given FSM can be changed into(a transformation that makes it equivalent to the lowest).

Turing Machine or Tape: is the universal language...all languages and algorithms can be stored as a turing machine. Decidability is the process of deciding whether an algorithm will terminate. And Computability is the study if it can be done PvsNP(polynomial time or nonpolynomial). examples of NP are TSP-travelling salesman problem, boolean satisfiability, and some other various math like given a set of # {xi} can you find a subsum = n. Also if you prove one NP problem to be P or !P then the entire collection of NP problems will follow suit.

CFL: just various methods to store language/computer language. Like Parse trees...if you ever scripted in website language or computing language or a scripted for AI or openInventor...imagine how they store the commands
 
  • #3




The Master Theory of Computation course covers a wide range of topics that are essential for understanding the fundamental principles of computation. It introduces various models of computation such as finite state machines, turing machines, and grammars, and explores their properties and equivalences. This course helps in developing a clear understanding of the different types of languages and their corresponding models of computation.

By studying the properties of these models, students will gain insights into the capabilities and limitations of different computing systems. This knowledge is crucial for designing efficient algorithms and solving complex problems in computer science and other related fields.

Moreover, understanding the concepts of decidability, undecidability, and non-computability is crucial for identifying the limits of what can and cannot be computed. This course also introduces the concept of reductions, which is a powerful tool for proving undecidability and solving difficult problems by reducing them to simpler ones.

In summary, the Master Theory of Computation course provides a strong foundation for understanding the principles of computation and their applications in various fields. It is an essential course for any student pursuing a career in computer science or related fields, as it equips them with the necessary knowledge and skills to tackle complex problems and develop efficient computing systems. I hope this helps in giving you a better understanding of the course and its significance.
 

1. What is the Master Theory of Computation?

The Master Theory of Computation is a branch of computer science that studies the fundamental principles and models of computation. It focuses on understanding the capabilities and limitations of different computational models and their relationships to each other.

2. What are some properties of computational models?

Some properties of computational models include their computational power, efficiency, determinism, and expressiveness. These properties help us understand the capabilities of different models and their potential applications.

3. What are some examples of computational models?

Some examples of computational models include Turing machines, finite automata, pushdown automata, and lambda calculus. These models have different levels of computational power and are used to solve different types of problems.

4. What is the importance of studying computational models?

Studying computational models allows us to understand the fundamental principles of computation and how different models can be used to solve problems. It also helps us develop new algorithms and techniques for solving complex problems.

5. How are computational models related to each other?

Computational models are related to each other through equivalences, which establish the computational equivalence of different models. For example, Turing machines and lambda calculus are equivalent in their computational power, meaning that they can solve the same types of problems.

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