Autosave: 2024-09-13 19:00:03

zk/The_History_of_Computing_Swade.md

@@ -43,8 +43,8 @@ First three phases of digital electronic computers:
 | Term            | Definition                                                                                                                                                                  |
 | --------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
 | automatic       | can execute programs, process data and perform functions on its own once it has been started. Can monitor its own processes and make adjustments without human intervention |
-| general-purpose |                                                                                                                                                                             |
+| general-purpose | a computer designed to be able to solve a wide variety of problems and perform many different types of tasks as opposed to a computer built for a specific, limited purpose |
-| programmable    |                                                                                                                                                                             |
+| programmable    | the ability to change the operations a computer peforms without physically altering its hardware                                                                            |
 
 ## Mechanical calculating devices in the 17th century
 

zk/Turing_completeness.md

@@ -0,0 +1,39 @@
+---
+title: Turing_Completeness
+tags: [theory-of-computation, Turing]
+created: Friday, September 13, 2024
+---
+
+# Turing Completeness
+
+We know that a [Turing machine](Turing_machines.md) is a theoretical construct
+of a computer that:
+
+> contains mutable state, executes sequences of simple instructions that read
+> and write that state, and can pick different execution paths depending on the
+> state (via conditional branch instructions.)
+
+A Turing Complete (TC) system is a system that abides by, or can be reduced to,
+the above description.
+
+TC also serves as a _definition of computability_ and provides a formal basis
+for conceiving of computation at a theoretical level.
+
+All Turing Complete systems are functionally equivalent. This means they can
+simulate each other given enough time and memory. Similarly a TC system can in
+principle perform any computation that any other programmable computer can
+perform. This is true for _other_ TC systems and also those that are not TC
+however the inverse doesn't hold: a non-TC system cannot emulate a TS system.
+For instance a calculator cannot do what a TC smart phone can do. But a smart
+phone can act as a calculator.
+
+Completeness applies to the hardware of computers as well as their software.
+
+Turing Completeness is the theoretical basis of the practical concept of a
+"general-purpose computer": a general-purpose computer is such because it is
+TC - it can in theory compute anything that is computable.
+
+Most modern programming languages are Turing Complete in that they can, in
+theory, be used to compute anything that is computable.
+
+What about Universal Turing Machines eh?

zk/Turing_machines.md

@@ -1,19 +1,27 @@
 ---
 tags:
   - theory-of-computation
+  - Turing
 ---
 
 ## What is a Turing Machine?
 
-A Turing Machine consists of an infinitely long tape, that has been divided up
+Turing Machine is a machine that contains mutable state, executes sequences of
-into cells. Each cell can contain either a 1, a 0 or an empty space. Above one
+simple instructions that read and write that state, and can pick different
-cell of the tape is a head, which can either move left or right, and can read
+execution paths depending on the state (via conditional branch instructions.)
-the symbols written in the cells. The head is also capable of erasing symbols
-and writing new symbols into the cells.
 
-![Turing_machines_01.gif](Turing_machines_01.gif) The direction that the
+This is a general expression, it is typically expanded as follows.
-head moves, which values it erases, and which values it writes in, are dependent
+
-on a set of instructions provided to the machine.0
+The machine consists of an infinitely long tape, that has been divided up into
+cells. Each cell can contain either a 1, a 0 or an empty space. Above one cell
+of the tape is a head, which can either move left or right, and can read the
+symbols written in the cells. The head is also capable of erasing symbols and
+writing new symbols into the cells.
+
+![Turing_machines_01.gif](Turing_machines_01.gif)
+
+The direction that the head moves, which values it erases, and which values it
+writes in, are dependent on a set of instructions provided to the machine.
 
 Different sets of instructions can be divided into **states.** States are like
 sub-routines and can themselves feature as part of instructions.