VISUALIZATION OF MATHEMATICAL MODELS

Pradip Peter Dey et al

Some static and dynamic visualization of mathematical models are linked to this page for considerations in understanding computational aspects of these models. Static visualizations are often found in books and journals and therefore they are not emphasized here. The examples of dynamic visualizations (or animations) shown here are a part of an ongoing effort in visualization of all major mathematical models of computation.

Dynamic Visualization of Turing Machines

Logically speaking, the class of Turing Machines is the most powerful class of computing machines. Any problem that can be solved computationally can be solved by a Turing Machine. Thus, computability means Turing computability. Dynamic visualization of Turing Machines can be seen following the links given below.
   
  Dynamic Visualization of a Turing Machine for  
    L1  = {   aba*    } = {    ab, aba, abaa, abaaa, abaaaa, abaaaaa, . . . .  } is 
    demonstrated with an input. Compare this with the static visualization given below. 

 

Dynamic Visualization of a Turing Machine for
L2 = {   anbnan : n > 0   } = {   aba, aabbaa, aaabbbaaa, aaaabbbbaaaa, . . .   }
Please try   aabbaa   as an input to this Turing Machine.   It accepts any string with equal number of a's b's and a's that is, a string with the pattern anbnan, where n > 0. aabbaa will be accepted by this machine; but aabbaaaaa will not be accepted.

 

Static Visualization of Turing Machines

Static Visualizaion of a Turing Machine can be seen following the link given below where a Turing Machine for L1 = {   aba*   } = {   ab, aba, abaa, abaaa, abaaaa, abaaaaa, . . . .  } is demonstated with an input.
 
Static Visualization of a Turing Machine

For questions and comments, please contact:

             Dr. Pradip Peter Dey   
             School of Engineering, Technology  and Media
             National University
             3678 Aero Court, San Diego, CA 92123
             U.S.A.
             Phone: (858) 309-3421
             Fax (858) 309-3420    
             Email:  pdey@nu.edu 



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