What is a Computer? computer: anything that is able to take a mathematically well-defined problem and perform a sequence of simple operations that will result in the solution to that problem. A computer can be mechanical, electrical, or even biological. (In fact, until the mid-1900 s, computers usually referred to people!) input: a way of coding your problem so that a computer can understand exactly what you are asking. output: the coding of the output to your problem. storage: space where you can keep information while you are working on the problem. algorithm: a mathematically precise description of the steps involved in finding the correct output for a given problem input.
The Beginning of the Computing Era Alan Turing, 1936: Developed the theory of computing, and was one of the first to use computing machines for serious application in code-breaking efforts during WWII. Claude Shannon, 1940: considered the Father of Information Theory. His MIT Thesis, An Algebra for Theoretical Genetics, developed the mathematical relationships for Mendelian genetics, and in the process also provided foundations for digital computing.
Progression of Computing Hardware Era Processor Input/Output Storage pre-1800 s stones, beads, paper, wheels, slides, people 1830 1930 gears&levers buttons none punch-cards 1940-50 s electromagnets wiring,printers tape vacuum tubes 1960 s transistors terminals, teletypes hard disk programming robots magnetic core 1970 s microprocessors graphics monitors floppy disk PC s punch-card decks RAM 1980 s integrated circuits internet CDs 1990 s VLSI WWW flash drives scanners instrumentation 2000 s optical Blackberries The Cloud nanochips iphones,ipads DNA
A Brief History of Automated Computing 1642/73: Pascal/Liebniz calculators 1832: Babbage s (unfinished) computing machine. 1938: Turing designed the (British) Bombe to help decode German communications. 1941: The Z3 (Konrad Zuse) the first programmable computer. 1946: ENIAC (J. Presper Eckert & John W. Mauchly) first fully electronic computer. 1959: The Integrated Circuit (Jack Kilby & Robert Noyce) 1971: Intel introduces the first microprocessor. 1976: Apple I (Steve Wozniak & Steve Jobs) the first affordable personal computer.
Moore s Law Proposed by Intel co-founder Gordon Moore in 1965, it states that computing power doubles roughly every 2 years. This prediction has been uncannily accurate in the half century since it was first made.
Turing Machine: The Simplest Computer Alan Turing in 1936 described the Turing Machine, even before the first programmable computer was constructed. His machine consists of: 1. A tape, which serves as input, output, and storage. 2. A processor, whose only job is to (a) Look at a specific location on the tape, and based on this... (b) Possibly change what was written on that tape, and... (c) Move to one of the two adjacent locations on the tape. 3. The Turing Machine will start with a given input written on the tape, one symbol per square, with all other tape squares blank ( ) and with the processor positioned on the leftmost square of the input. 4. The Turing Machine then moves back and forth across the tape, changing what is written on the tape as it sees fit in order to perform its computation. 5. When the computation is over the Turing Machine stops, and what is left on the tape will be the output for that instance of the problem.
How does the processor know what to do? The machine has a collection of instructions that determine what the computer will do when it is at a certain point of the computation. Each instruction is identified by an instruction label, and what the instruction does depends upon what symbol the processor is looking at on that square of the tape. This is given by an instruction list having entries that look like this: If you are... Then you should... (a) executing instruction I, (b) looking at symbol A; (c) write symbol B in that square, (d) move right (left) one square, (c) go to instruction J.
Example TAPE M Y P R O B L E M execute instruction "RtoO" PROCESSOR Instruction If executing instruction "RtoO" looking at symbol R: then change symbol to O move right execute instruction "LtoG" M Y P O O B L E M execute instruction "LtoG"
The Turing Machine always starts on the "START" instruction, and applies the same set of instructions over and over. That is, at every stage it will be asked to execute some instruction I. To do this it: 1. Looks at the symbol on the tape, and matches it with the symbol in the instruction list for instruction I. 2. Changes the symbol and moves right or left according the instruction in its list. 3. Executes the next instruction given by that instruction. Note that if no symbol is found in its instruction list that matches what it is looking at on the tape, the machine crashes. This should never happen! The Turing Machine stops when the "STOP" instruction is encountered. The output for the computation is whatever is left on the tape at the end of the computation.
An Example Turing Machine Let s construct a Turing Machine whose input is a sequence of A s and B s. The TM will go right across the input, changing each A to a P and each B to an Q. At the end of the input, it will turn around and go left over the input, changing each P to a Y and each Q to a Z. CURRENT NEXT INSTRUCT. SYMBOL SYMBOL MOVE INSTRUCT. START A P R START START B Q R START START L LEFT LEFT P Y L LEFT LEFT Q Z L LEFT LEFT L STOP The "START" instruction is executed when going right, and the "LEFT" instruction is executed when going left. Note that each instruction has in its list all of the symbols it might be seeing whenever that instruction is executed.
Using IDEAS to Run Your Turing Machine IDEAS Turing Machine will allow you to test and print all of your work when you are writing programs for your problems. 1. Put your instructions down in the IDEAS Turing Machine Instruction List, making sure that each row contains (a) the name of the instruction and what symbol you are looking for in the left two boxes, (b) what you write, where you move, and what the new instruction is in the right three boxes. 2. Push the Start button, and then the Step or Run button, to make your Turing Machine operate on the instruction list. 3. After you have performed your operations, push Show Record to obtain a copy of your instructions and computations for your records. 4. You can also save your Turing Machine by going to the File Save menu item.
Tips on Constructing Your Own Turing Machine 1. Figure out the sequence of steps it would take to solve your problem on a general input. Think about how these moves can be described in terms of moving back and forth across the Turing Machine tape and writing things on the tape. 2. You may use as many instructions as you need, and write whatever you want on the tape, to keep a record of where you are and what you are suppose to be doing during the operation of the Turing Machine. 3. Remember that the set of instructions you put down has to solve all inputs of the problem. Thus you cannot just write the instructions to solve one specific input sequence. 4. Remember to include the "START" instruction, since this is always the first one executed. 5. Be sure to add the appropriate instruction for every tape symbol you might see during your computation, so that your Turing Machine does not crash. 6. The only way you can avoid crashing or running forever is to make sure the Turing Machine always gets to an instruction that tells it to "STOP".
Example 2: An RNA-Polymerase Turing Machine The input to our problem will be any DNA sequence (list of A s, C s, G s, and T s), and the output will be the complementary mrna sequence (A U, C G, G C, T A), written in the same place as the original input. Example: If the tape had T GAT C written on it, then the output would be the letters ACUAG in the same place.
Example 3: A Transcription-Factor Turing Machine This particular Turing Machine will be the transcription factor for the particular promoter sequence AT on the genome. In particular, the input is again any DNA sequence, and the Turing Machine Deletes all letters up to and including the first occurrence of the sequence AT, or If it is unable to find AT anywhere in the sequence, it leaves the single symbol * on the tape. Example: If the tape had ACAAT T GAT C written on it, then the Turing Machine would leave T GAT C on the tape. If the tape had ACAAGT GAGC written on it, the Turing Machine would just leave * on the tape.
The Two Turing Machines RNA-polymerase Turing Machine: CURRENT NEXT INSTRUCT. SYMBOL SYMBOL MOVE INSTRUCT. START A U R START START C G R START START G C R START START T A R START START R STOP (AT) Transcription-Factor Turing Machine: CURRENT NEXT INSTRUCT. SYMBOL SYMBOL MOVE INSTRUCT. START A R CHECK START C R START START G R START START T R START START * R START CHECK A R CHECK CHECK C R START CHECK G R START CHECK T R STOP CHECK * R STOP
Example 4: A Transcription Turing Machine Here we combine the two Turing Machines to perform the entire transcription part of the Central Dogma. That is, the input is any DNA sequence, the Turing Machine will Delete all letters through the first occurrence of the promoter sequence AT, and then Transcribe the rest of the sequence as if you were producing the mrna sequence. (No terminator sequence.) Example: If the tape had ACAAT T GAT C written on it, then the Turing Machine would leave ACU AG (the complementary mrna corresponding to the remaining sequence T GAT C after the first occurrence of AT ) on the tape. Hint: Use the RNA-Polymerase and Transcription- Factor Turing Machines as subroutines. How?
The Turing Machine CURRENT NEXT INSTRUCT. SYMBOL SYMBOL MOVE INSTRUCT. START A R CHECK START C R START START G R START START T R START START * R STOP CHECK A R CHECK CHECK C R START CHECK G R START CHECK T R TRNSC CHECK * R STOP TRNSC A U R TRNSC TRNSC C G R TRNSC TRNSC G C R TRNSC TRNSC T A R TRNSC TRNSC R STOP
Example 5: A mrna Copier The input here is a sequence of A s and C s (we will only use two letters to make it simple) and the output is a copy of the mrna sequence immediately after the original sequence, with a blank in between. Example: If the tape had ACAACC written on it, then the Turing Machine would leave ACAACC UGUUGG on the tape.
Turing Machine CURRENT NEXT INSTRUCT. SYMBOL SYMBOL MOVE INSTRUCT. START A B R COPYU START C D R COPYG START R STOP COPYU A A R COPYU COPYU C C R COPYU COPYU R WRITU COPYG A A R COPYG COPYG C C R COPYG COPYG R WRITG WRITU U U R WRITU WRITU G G R WRITU WRITU U L BACK WRITG U U R WRITG WRITG G G R WRITG WRITG G L BACK BACK U U L BACK BACK G G L BACK BACK L BACK BACK A A L BACK BACK C C L BACK BACK B A R START BACK D C R START
Biology s Own Computer: The Central Dogma Biology Computer DNA suite of programs gene subroutine nucleotides bits codons instructions (or bytes) mrna storage polymerase ribosome trna processor transcription factor input protein output As a result, DNA is able to build proteins of an infinite amount of variety, which in turn make up the building blocks of everything an organism does.
A Visual Comparision TAPE PROCESSOR Turing Machine Central Dogma
A Translation Turing Machine A Turing machine can act like rrna and trna on an input of mrna to perform the translation of the Central Dogma. That is, it can decode the codon triples into amino acids (figuratively speaking), ending with a protein if a stop codon is found, or else just continuing to produce amino acids until the sequence ends. first second base third base U C A G base F S Y C U U F S Y C C L S A L S W G L P H R U C L P H R C L P Q R A L P Q R G I T N S U A I T N S C I T K R A M T K R G V A D G U G V A D G C V A E G A V A E G G The list of instructions for the Central Dogma Turing Machine is in the IDEAS Turing Machine module, under the file translator eg. The START Instruction is always executed when you are starting to read each codon, and thereafter the name of the instruction is the same as the sequence of letters that you have just seen (only lower case).
Making Computers Out of DNA DNA shows exciting promise to be the new generation of computers. They can, in theory, perform all of the operations a computer can, only on a molecular rather than merely microscopic level. It remains to find the technology to build and program these computers. The first DNA computer (1994): Adleman was able to get specially built 1-sided DNA strands to link together along complementary subsequences to solve the notoriously hard Traveling Salesman problem ( routing through a set of cities ). Unfortunately, it could only do so for up to 5 cities.
A Molecular Turing Machine (2004): Shapiro, Benenson, Gil, Ben-Dor, and Adar devised a complicated ribosome-like gadget ( Fokl enzyme ) that could read a 2- side strand of DNA comprised of a (coded) sequence of a s and b s, and tell whether there is an even number of a s. Even though the program is quite simple, this machine is capable of processing a sequence of any size. Other biological machines: Scientists are currently constructing artificial brains out of neurons, programmable biological sensors, nano-machines, and genetic circuit boards to perform complex computations both inside and outside an organism.