part-1
Abstract
The parallelism and concurrency, the original desirable nature of computer over the decades. The multicore computing is the recent industrial trends to provide that 'multitasking nature' in users hand. This article is about these trends of multicore, multiproessor computing, explained by the idea of Turing Machine(TM) for giving the formal definition of those architectures. This exploses some real problems thats are coming in very near future to the multicore society and how the TM is suitable for applying as abstract mathematical model of the algorithmic computing.
Introduction
Turing machine is the most accepted formal model of algorithmic computer of the current generation. Though the most popular 1936 paper was primarily about the inability of the Turing machines to solve mathematical problems,Turing machines were adopted by theoretical computer scientists in the 1960s as a mode of solving all problems of computing.In this fifty years they present the turing thesis as `oracle'. They written many books, articles, created movies on Alan Turing, presented the turing machine best as ever invented machines.The students created and written many types of turing machines in their school assignments for getting more higher grades and so many things.In this paper, we presenting the turing machine in more different areas where the current technology is moving forward. For example, the multicore and multiprocessor systems are very popular today to provide the low cost parallel systems. To examine this different multiprocessor systems by formal mathematical definition of turing, we present Timed Turing machine and multiheaded turing machine in later portion of this paper. And, at the end we show that how the once so called powerful turing mechanism is facing so much problems to handle problem solving.
Computing Today
Multicore computing is a common industrial trend today for power effiecient HPC(High Performance Computing) from the end user systems to the high end commercial servers. Multiple number of control devices are working simultaneously over single or multiple memory tapes in those multicore systems. They are able to execute multiple tasks or threads concurrently. To examine this multicore systems mathematically we need some basic changes in the current turing machine topology. Thus we present different new architectures of the Turing Machine in the next and analyse them.
Timed Turing Machine is 8-tuple
M =
whose components have the following meanings:
Q: The finite set of states of the finite control.
Σ :The finite set of input symbols.
Γ :The complete set of tape symbols;
δ :The transition function. The arguments of δ(q, X) are a state q and a tape
symbol X. The value of δ(q, X), if it is defined, is a triple (p,Y,D), where:
B : The blank symbol.
F : The set of final or accepting states,a subset of Q.
T : The atomic operational time over tape by a control device.
Part-2 coming soon. In that part we will discuss about the SMPs with the TTM and the problems currently our computing society is getting suffered.