Comparison with real machines Turing machine

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1 comparison real machines

1.1 limitations of turing machines

1.1.1 computational complexity theory
1.1.2 concurrency
1.1.3 interaction







comparison real machines

a turing machine realisation in lego


it said turing machines, unlike simpler automata, powerful real machines, , able execute operation real program can. neglected in statement that, because real machine can have finite number of configurations, real machine nothing linear bounded automaton. on other hand, turing machines equivalent machines have unlimited amount of storage space computations. however, turing machines not intended model computers, rather intended model computation itself. historically, computers, compute on (fixed) internal storage, developed later.


there number of ways explain why turing machines useful models of real computers:



one way in turing machines poor model programs many real programs, such operating systems , word processors, written receive unbounded input on time, , therefore not halt. turing machines not model such ongoing computation (but can still model portions of it, such individual procedures).



an experimental prototype of turing machine


limitations of turing machines
computational complexity theory

a limitation of turing machines not model strengths of particular arrangement well. instance, modern stored-program computers instances of more specific form of abstract machine known random-access stored-program machine or rasp machine model. universal turing machine rasp stores program in memory external finite-state machine s instructions . unlike universal turing machine, rasp has infinite number of distinguishable, numbered unbounded registers —memory cells can contain integer (cf. elgot , robinson (1964), hartmanis (1971), , in particular cook-rechow (1973); references @ random access machine). rasp s finite-state machine equipped capability indirect addressing (e.g. contents of 1 register can used address specify register); rasp s program can address register in register-sequence. upshot of distinction there computational optimizations can performed based on memory indices, not possible in general turing machine; when turing machines used basis bounding running times, false lower bound can proven on algorithms running times (due false simplifying assumption of turing machine). example of binary search, algorithm can shown perform more when using rasp model of computation rather turing machine model.


concurrency

another limitation of turing machines not model concurrency well. example, there bound on size of integer can computed always-halting nondeterministic turing machine starting on blank tape. (see article on unbounded nondeterminism.) contrast, there always-halting concurrent systems no inputs can compute integer of unbounded size. (a process can created local storage initialized count of 0 concurrently sends both stop , go message. when receives go message, increments count 1 , sends go message. when receives stop message, stops unbounded number in local storage.)


interaction

non-interactive computing can simulated turing machine. in days of computing common use computer batch processing, i.e., non-interactive tasks series of jobs processed given input data.


however, external input , output communication of real computers, enable interactivity, cannot modeled turing machine. is, because turing machine requires input available on tape, no further input or change of input during course of computation possible.


in practical terms, turing machine capable model computation happens inside real computer, not capable model behaviour of whole computer, turing machine cannot model real computer s communication capability used interaction. example, not possible model computer representing web server turing machine tm1 , computer representing web client turing machine tm2, , connecting tm1 , tm2 simulate web transactions between web server , client.


given above example, 1 might argue still possible model web server , web client single turing machine. true, however, misses point turing machine cannot model behaviour of individual computer alone. composability of individual computers larger computing system not possible individual turing machines.







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