Post machine simulates Turing machine:
Assume that the TM M encompass the alphabet A = {0, 1, <, > }, where the angular brackets are employed to delimit the finite part of the tape which initially includes the input and later gets expanded to delimit the part of the tape which has been visited so far. Assume that the M’s transition function be of form f: Q x A -> Q x A x {L, R}.
We sketch the design of Post machine P which simulates M utilizing the alphabet B = {0, 1, <, >, #}. The fundamental idea is straight-forward, the details are complicated and will be skipped.
Let consider a configuration where M is in the state q and presently reads the (bold) symbol x of the tape:
M: < B y x z C>, with y, x, z ∈ A and B, C ∈ A*. That is, we focus attention on what occurs to x and to its two neighbor symbols y to left and z to the right, and merely carry all along the remaining parts of the tape, B and C.
In this configuration, M performs either a move-right transition q, x -> q’ x’ R or move-left transition q, x -> q’ x’ L
Post machine P’s state space comprises a subspace that is in 1-to-1 correspondence with the state space Q of TM M. Devoid of danger of confusion; we call this subspace Q and select its states with similar label as the corresponding state of M. When referring to a state q, the context will make it apparent whether we signify the state qM of M or qP of P. P’s state space comprises additional states, to be introduced as required, as in general a single transition of M needs a sequence of transition s of P.M’s configuration: state q, tape < B y x z C > is modeled as P’s configuration: state q, tape x z C > < B y
The encoding is practically forced, as P should inspect the similar symbol x as M does, however the only symbol it can examine is at the head of queue. Since M executes a transition q, x -> q’ x’ R or q, x -> q’ x’ L, P should be programmed to convert its queue in a corresponding manner. First try, that doesn’t quite work.
The easy case, that is, a move-right transition q, x -> q’ x’ R:
M: q, < B y x z C > becomes q’, < B y x’ z C > P: q, x z C > < B y becomes q’, z C > < B y x’
The single P transition attains accurately the needed transformation.
The cumbersome case, a move-left transition q, x -> q’ x’ L:
M: q, < B y x z C > becomes q’, < B y x’ z C> P: q, x z C > < B y should become q’, y x’ z C > < B
P’s transformation needs a complete rotation of queue in order to get the tail symbol to the head of queue. The rotation is possible when there is a distinguished symbol # which tells us when to stop. Therefore, the tentative encoding employed so far fails for a move-left transition and should be corrected.
Accurate encoding of M’s configuration in P’s configuration: Place a marker # two slots to left of the scanned symbol x. ‘To the left’ is interpreted in a circular manner, as when head and tail were glued altogether, and therefore # appears as next-to-last symbol in the queue.
M’s configuration: state q, tape < B y x z C > is modeled as
P’s configuration: state q, tape x z C > < B # y
Simulating the move-right transition q, x -> q’ x’ R:
M: q, < B y x z C > becomes q’, < B y x’ z C > P: q, x z C > < B # y becomes q’, z C > < B y # x’
Unluckily, this former ‘easy case’ has become more complex, as the consecutive pair # y should be permuted to y #. This can be attained by using auxiliary states and complete rotation.
Simulating the move-left transition q, x -> q’ x’ L, focus on two neighboring symbols to the left of scanned symbol x:
M: q, < B y z x C > becomes q’, < B y z x’ C > P: q, x C > < B y # z becomes q’, z x’ C > < B # y
Again, the consecutive pair # y should be permuted to y #, attained by using auxiliary states and complete rotation.
Two more cases should be considered, if M’s read or write head is placed at either end of tape visited so far, on a symbol <or>, and probably extends the visited part. In sum up, the design of a PM which simulates a random TM is theoretically straightforward once one mastered the acrobatics of the P’s queue rotations.
Therefore, we have completed cycle TM ≥ MA ≥ PM ≥ TM which verifies the computational equivalence of such three universal models of the computation.
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.
A large range of products means much more investment in terms of equipment in both fixed and working capital and larger sales attempts that all push up the cost of production and sales.
tutorsglobe.com thalamus assignment help-homework help by online position of flower tutors
www.tutorsglobe.com offers The Cost of Prototyping homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
We proffer sought-after Opera Assignment Help at the most rational prices and ensure plagiarism free solutions every time.
Superposition of Harmonic Oscillations tutorial all along with the key concepts of Superposition of two harmonic oscillations of same frequency along same line, Uniform Circular Motion and SHM, Vector Addition, Oscillations in two dimensions
tutorsglobe.com investment function assignment help-homework help by online aggregate demand tutors
the magnetic field tutorial all along with the key concepts of fields due to magnets, electric field to define magnetic field, field due to currents, force on a current in a magnetic field, magnetic flux density, torque on a rectangular coil and biot-savart law
other properties of liquids tutorial all along with the key concepts of vaporization, differences between evaporation and boiling, trouton's rule, liquid crystals and liquid crystal phases
the meaning of television is “to see from a distance” .the 1st illustration of actual television was provided through j.l.baird in uk (united kingdom) and c.f.jenkins in us (united states) around 1927.
tutorsglobe.com reactions of electron transport assignment help-homework help by online electron transport chain tutors
Structure and Function of Membranes tutorial all along with the key concepts of Structure of Membranes, Functions of Membranes, Movement of Water through Membranes, Water Potential, Osmosis and Turgor
Types and Functions of Proteins tutorial all along with the key concepts of Protein Composition, Protein and their Functions, Enzyme Reaction and Denaturation, Antibodies, Contractile Proteins, Hormonal Proteins, Structural Proteins
www.tutorsglobe.com offers electronic configuration of atoms homework help, electronic configuration of atoms assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
Fungi morphology tutorial all along with the key concepts of Unicellular Forms, Yeast, Slime Moulds, Cellular type, Plasmodial type, Filamentous Forms and Pseudoparenchymatous Forms
tutorsglobe.com difference between chemical and nuclear reactions assignment help-homework help by online nuclear reaction tutors
1952445
Questions Asked
3689
Tutors
1475371
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!