feat:summarize notes g

docs/Hardware/g_turingmachine.md

@@ -309,48 +309,32 @@ To tie things up, here we have learned how Turing machine works, and  its advant
 ## [Summary](https://www.youtube.com/watch?v=cmfDBAiogA0&t=3197s)
 [You may want to watch the post lecture videos here. ](https://youtu.be/p0plIDiBEj0)
 
-A Turing machine is a **theoretical** computing machine invented by Alan Turing in 1936, which is used to model the logic of any computer algorithm. Here are the key characteristics of a Turing machine:
-
-1. **Infinite Tape**: The Turing machine uses an infinite tape as its memory. This tape is divided into cells, each capable of holding a single symbol. This tape acts both as the device's memory and as a mechanism for moving data.
-
-2. **Read/Write Head**: The machine has a head that can read and write symbols on the tape and move the tape left or right one cell at a time. This allows the machine to modify its input data and to store the output data.
-
-3. **Finite Set of States**: Similar to a finite state machine, a Turing machine has a finite number of states. At any given moment, the machine is in one of these states.
-
-4. **Initial State**: The operation of a Turing machine begins from an initial state, which is predefined.
-
-5. **Transition Function**: This function dictates the behavior of the machine. It determines what the machine does based on its current state and the symbol it reads on the tape. Specifically, it tells the machine which symbol to write, which direction to move the tape (left, right, or stay), and what the next state should be.
-
-6. **Accepting and Rejecting States**: The Turing machine can have special states called accepting (or final) and rejecting states. Reaching an accepting state means the machine has successfully completed the computation and accepted the input. Reaching a rejecting state means the computation has finished but the input is not accepted.
-
-7. **Universality and Computability**: A Turing machine can simulate any other Turing machine. This concept, known as the universality of Turing machines, implies that any computational problem that can be solved by some algorithm can be solved by a Turing machine. This forms the basis for the Church-Turing thesis, which posits that the Turing machine can model any computation that can be performed by a "reasonable" computing device.
-
-8. **Non-determinism (in some variants)**: While the classical Turing machine is deterministic, there are variants like the non-deterministic Turing machine where the transition function allows for multiple possible actions from the same state with the same input symbol. This does not increase the computational power (in terms of what can be computed) but can affect the complexity and efficiency of the computation.
-
 The Turing machine remains a central object of study in the theory of computation and is fundamental in understanding what it means for a function to be computable. The concept of a universal Turing Machine is an *ideal abstraction*, since we can never create a machine with infinitely long tape. However, physically creating something that is "infinite" is not possible. We can only create a very long "tape" such that it appears "infinite" to some extent. 
 
-If we manage to create a physical manifestation of Universal Turing Machine, we need to ensure that this machine is **programmable**. A programmable machine is a device that can perform a sequence of operations or tasks according to a **set of instructions or software**. These instructions can be **changed**, allowing the machine to carry out different tasks at different times. The concept is <span class="orange-bold">central to the idea of computers and automation</span>. Here are the key characteristics of a programmable machine:
-
-1. **Hardware and Software Separation**: Programmable machines consist of both hardware (the physical components) and software (the instructions or programs). The software instructs the hardware on what tasks to perform and how to perform them. This separation allows the same hardware to perform different functions depending on the software it runs.
-
-2. **Memory for Storage**: These machines have memory where they can store the program instructions, operational data, and intermediate results. Memory might be volatile (such as RAM) or non-volatile (such as hard drives or flash memory).
-
-3. **Processing Unit**: A central processing unit (CPU) or processor executes the instructions provided by the software. It performs basic arithmetic, logic, controlling, and input/output operations as directed by the instructions.
-
-4. **Input/Output Mechanisms**: Programmable machines have ways to receive input and produce output. Inputs can be from keyboards, sensors, network connections, or other data sources. Outputs might be to displays, actuators, other machines, or network connections.
-
-5. **Programmability**: The defining feature of these machines is their programmability. They can be programmed to perform a wide range of tasks, from simple repetitive operations to complex algorithms involving decision-making and optimization.
+{:.note}
+The programmable machine is a manifestation of the Turing Machine concept, adapted for practical use in the physical world. It embodies the principles of computation formalized by Turing while overcoming theoretical constraints to enable real-world applications. Programmable machines form the basis of modern computing and are fundamental to various fields. Examples of programmable machines include desktop computers, laptops, smartphones, tablets, mainframes, servers, microcontrollers, washing machines, microwave ovens, robotics systems, drones, 3D printers, CNC machines, smart TVs, gaming consoles, ATMs, smart home devices, cars with programmable ECUs, and industrial automation systems.
 
-6. **Control System**: They often include a control system that manages the execution of the program, handling tasks such as fetching instructions, decoding them, executing them, and then handling the next instruction cycle.
 
-7. **Flexibility and Versatility**: Due to their programmability, these machines can adapt to different functionalities and requirements. This makes them versatile tools in numerous applications, from household appliances to complex industrial machinery.
+Here are the key points from this notes:
+1. **Turing Machine**: A **theoretical** computing machine invented by Alan Turing, which is used to model the logic of any computer algorithm. Main characteristics of a Turing Machine include: 
+   * **Infinite Tape**: Used as memory and mechanism for moving data. The tape is divided into cells, each capable of holding a single symbol.
+   * **Read/Write Head**: The head can read and write symbols on the tape and move the tape left or right **one** cell at a time. This allows the machine to **modify** its input data and to **store** the output data.
+   * **Finite Set of States**: At any given moment, the machine is in one of these states.
+   * **Initial State**: Predefined initial state.
+   * **Transition Function**: This function dictates the behavior of the machine. It determines **what** the machine does based on its current state and the symbol it reads on the tape. Specifically, it tells the machine which symbol to write, which direction to move the tape (left, right, or stay), and what the next state should be.
+2. **Universality and Computability**: A Turing machine can simulate any other Turing machine (**universality**) implies that any computational problem that can be solved by some algorithm can be solved by a Turing machine. This forms the basis for the Church-Turing thesis, which posits that the Turing machine can model any computation that can be performed by a "reasonable" computing device.
+3. **Programmable Machine**: A programmable machine is a device that can perform a sequence of operations or tasks according to a **set of instructions or software**. These instructions can be **changed**, allowing the machine to carry out different tasks at different times. The concept is <span class="orange-bold">central to the idea of computers and automation</span>. It is a **physical manifestation** of a Turing Machine. The key characteristics of a programmable machine are:
+   * **Hardware and Software Separation**: Programmable machines consist of both hardware (the **physical** components) and software (the **instructions** or programs). The software instructs the hardware on what tasks to perform and how to perform them. This <span class="orange-bold">separation</span> allows the same hardware to perform different functions depending on the software it runs.
+   * **Memory for Storage**: These machines have memory where they can **store** the program instructions, operational data, and intermediate results. Memory might be volatile (such as RAM) or non-volatile (such as hard drives or flash memory).
+   * **Processing Unit**: A central processing unit (CPU) or processor executes the instructions provided by the software. It performs basic arithmetic, logic, controlling, and input/output operations as directed by the instructions.
+   * **Input/Output Mechanisms**: Programmable machines have ways to receive input and produce output. Inputs can be from keyboards, sensors, network connections, or other data sources. Outputs might be to displays, actuators, other machines, or network connections.
+   * **Programmability**: A programmable machine is considered "programmable" because it can execute a wide variety of tasks based on a set of instructions, or a program, provided to it.
+   * **Control System**: They often include a control system that manages the execution of the program, handling tasks such as fetching instructions, decoding them, executing them, and then handling the next instruction cycle.
 
-8. **Automation Capability**: Programmable machines can automate processes. Automation can increase efficiency, reduce human error, and perform tasks that might be too complex, dangerous, or tedious for humans.
 
-Programmable machines form the basis of modern computing and are fundamental to various fields, including robotics, manufacturing, communications, and consumer electronics. Their development and enhancement continue to drive innovation across industries.
 
-### Instruction Set
 
+## Next Steps 
 The Turing machine's theoretical model of computation highlights the universal capability to execute any computable function, serving as a conceptual ancestor to modern programmable machines, which operate based on <span class="orange-bold">practical instruction sets</span>. These instruction sets provide the specific **commands** that programmable machines use to manipulate data and perform operations, embodying the abstract principles of the Turing machine in tangible, operational systems.
 
 {: .new-title}