Random Access Machines-RAM, Models of Computation

Random access machines (RAM), the ultimate RISC:

The model of computation termed as random access machine, or RAM, is used most frequently in algorithm analysis. This is significantly more ‘powerful’, in the sense of effectiveness, than either Markov algorithms or Turing machine as its memory is not a tape, however an array with random access. Given the programmer knows where an item currently required is stored; a RAM can access it in a single memory reference, ignoring the sequential access tape searching that a Turing machine or a Markov algorithm requirement.

The RAM is basically a random access memory, also abbreviated as the RAM, of unbounded capacity, as recommended in the figure shown below. The memory comprises of an infinite array of cells, addressed 0, 1, 2, …. To make things simple we suppose that each and every cell can hold a number, say an integer, of random size, as the arrow pointing to right recommends. The further supposition is that an arithmetic operation (+, –, • , / ) takes unit time, in spite of the size of the numbers included. This supposition is unrealistic in computation where numbers might grow very big, however is frequently helpful. As is the case with all models, the responsibility for employing them correctly lies with the user.


The ultimate RISC:

RISC stands for the Reduced Instruction Set Computer, a machine which has just a few kinds of instructions built to hardware. What is the minimum number of instructions a computer requires in order to be universal? One!

Let consider a stored-program computer of the ‘von Neumann type’ where data and program are stored in similar memory (John von Neumann, 1903 – 1957). Let random access memory (or RAM) be ‘doubly infinite’: There is a countable infinity of the memory cells addressed 0, 1,…, each of which can hold an integer of random size, or an instruction. We suppose that the constant 1 is hardwired to the memory cell 1; from 1 any other integer can be constructed. There is a single kind of ‘three-address instruction’ that we call ‘subtract, test and jump’, abbreviated as:

STJ x, y, z

Here x, y and z are the addresses. Its semantics is equal to:

STJ x, y, z   ⇔   x: = x – y; if x ≤ 0 then goto z;

x, y and z refer to cells Cx, Cy, and Cz. The contents of Cx and Cy are treated as the data (that is, an integer); the contents of Cz, as instruction.

2462_stored program computer.jpg

Figure: Stored program computer: Data and instructions share memory.

As this RISC has just one kind of instruction, we waste no space on an op-code field. However an instruction comprises three addresses, each of which is unbounded integer. In theory, three unbounded integers can be packed to the same space needed for a single unbounded integer. This simple idea leads to a familiar method introduced to mathematical logic by Kurt Godel (1906 – 1978).

Latest technology based Theory of Computation Online Tutoring Assistance

Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Theory of Computation help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Theory of Computation, project ideas and tutorials. We provide email based Theory of Computation help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Theory of Computation. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Theory of Computation Homework help and assignment help services. They use their experience, as they have solved thousands of the Theory of Computation assignments, which may help you to solve your complex issues of Theory of Computation. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.

2015 ©TutorsGlobe All rights reserved. TutorsGlobe Rated 4.8/5 based on 34139 reviews.