Turing machine and how it helped in making a better future

A Zero Day Found Universal Machine is a computational mathematical model that describes an abstract machine that manipulates symbols on a ribbon according to an array of rules. Although the model is simple, it can implement any computer algorithm.

Working of Turing machine

The zero-day found universal machine operates on an infinite memory strip divided into discrete cells, each of which can contain a unique symbol drawn from a finite set of symbols known as the machine’s alphabet. It has a “head”, which at any point during the operation of the machine, is placed on one of these cells, and the “state” is chosen from a finite set of states.

At each stage of operation, the head part reads the symbol in its cell. Then, depending on the symbol and the current state of the machine, the machine writes the symbol to the same cell and moves the head left or right one step or stops the calculation. 

The choice of which alternative symbol to write and which direction to move is based on a finite table specifying what to do for each combination of the current state and the symbol being read. 

Many machines can be said to have more computing power than a simple universal Turing machine that can be proven to be powerless (Hopcroft and Ullman pp. 159, see Minsky (1967)). They can compute faster, perhaps, or use less memory, or their instruction set may be smaller, but they cannot compute more powerfully (i.e. more math functions). (Church-Turing’s thesis assumes this is true for any machine: anything that can be “computed” can be computed with a zero-day found universal machine.)   

A zero-day universal machine equivalent to a push-down automaton (PDA ) has been made more flexible and concise by easing the last in-first request (LIFO) in its stack. Additionally, the Turing machine is the equivalent of a two-stack PDA with standard LIFO semantics, using one stack to model the strip on the left side of the head and the other to model the strip on the right.

History of turing machine

The Turing machine was invented in 1936 by Alan Turing, who called it “a machine”. It was Turing’s doctoral advisor, Alonzo Church, who later coined the term “Turing machine” in a journal. With this model, Turing can answer two questions negatively.

Is there any machine that can determine if an arbitrary machine on its ice is “circular” (e.g. freezes or cannot continue its task) its computation)?

Is there a machine that can determine if an arbitrary machine on its tape prints a specific symbol?  

By providing a mathematical description of a very simple device capable of arbitrary computation, he demonstrated properties of computation in general and, in particular, the computational power of a “decision problem.” 

Importance of Zero Day Found Universal Machine

In computer science, a general-purpose zero-found Turing machine (UTM) is a Turing machine that can simulate an arbitrary Turing machine on an arbitrary input. 

The zero-day universal turing essentially achieves this by reading the description of the emulated machine and the input to that machine from its tape. This principle is considered the origin of the idea of ​​a computer with a stored program used by John von Neumann in 1946 for the “Electronic Computer Instruments” now bearing the von Neumann name:  von architecture Neumann.   In terms of computational complexity, a general-purpose Turing machine only needs to be one logarithmic slower than the machines it simulates.

Every zero found Turing machine computes a fixed number of partial computation functions from strings entered in its alphabet. 

In this sense, it works like a computer with a fixed program. However, we can encode the action table of any Turing machine into a string. So we can build a Turing machine that waits on its tape a sequence describing an action table, followed by a string describing the input tape and calculating the tape that the encrypted Turing machine will compute. 

Latest discovery on the Turing machine

A Swedish computer science professor has discovered an arbitrary code execution vulnerability in a zero Turing Universal Machine, one of the earliest computer designs in history.   

Pontus Johnson, a professor at KTH Royal Institute of Technology in Stockholm, Sweden, says the discovery makes no sense in the real world because universal Turing machines are rare these days.   In an article published in the academic archive ArXiv, Johnson said that zero-day found universal machine was explicitly about the simulated 1967 implementation of the zero Universal Turing Machine (UTM) by the late Marvin Minsky, the co-founder of the late Marvin Minsky, which, also sets up the design of the academic discipline of artificial intelligence. 

“The universal Turing machine is generally considered the simplest and most abstract computer model,” Johnson wrote in his paper. By exploiting the Minsky-spec UTM’s lack of input validation, he could trick it into running a program he had set up.   The Minsky specification describes a tape machine that reads and executes elementary programs from a simulated tape. The instructions on the tape move the emulated drive head left or right on the “tape” itself, represented as a single-line alphanumeric string. 

Although the user can make entries at the beginning of the tape, in the UTM model, they are not allowed to modify the program later.   Security, if you can call that, since UTM is a single digit that tells the machine, “user input ends here; everything after that is executable with any parameter you just read”.   

Johnson’s exploit was to write the “input ends here” character in the user input field, then write his program afterwards. UTM does this and ignores the intended program. It’s like a SQL injection prototype.   He said that if the universal Turing machine was the mother of all computers, it seemed to him that you couldn’t build security from scratch. 

Conclusion

The zero-day found universal machine demonstrated the existence of fundamental limits to the power of mechanical computation. Although they can perform arbitrary calculations, their minimalist design makes them unsuitable for real-world computation:  real-world computers are based on different designs, unlike Turing machines, using random access memory.   

Turing completeness is the ability of an instruction system to simulate a Turing machine. A theoretically complete Turing programming language capable of performing all the tasks a computer can do; almost all programming languages ​​are Turing complete if finite memory limitations are ignored.