1. MARC: Developing Bioinformatics Programs Alex Ropelewski PSC-NRBSC Bienvenido Vélez UPR Mayaguez Reference: How to Think Like a Computer Scientist: Learning with Python 1 Essential Computing for Bioinformatics Computability The Nature of Computing

2. The following material is the result of a curriculum development effort to provide a set of courses to support bioinformatics efforts involving students from the biological sciences, computer science, and mathematics departments. They have been developed as a part of the NIH funded project “Assisting Bioinformatics Efforts at Minority Schools” (2T36 GM008789). The people involved with the curriculum development effort include: Dr. Hugh B. Nicholas, Dr. Troy Wymore, Mr. Alexander Ropelewski and Dr. David Deerfield II, National Resource for Biomedical Supercomputing, Pittsburgh Supercomputing Center, Carnegie Mellon University. Dr. Ricardo González Méndez, University of Puerto Rico Medical Sciences Campus. Dr. Alade Tokuta, North Carolina Central University. Dr. Jaime Seguel and Dr. Bienvenido Vélez, University of Puerto Rico at Mayagüez. Dr. Satish Bhalla, Johnson C. Smith University. Unless otherwise specified, all the information contained within is Copyrighted © by Carnegie Mellon University. Permission is granted for use, modify, and reproduce these materials for teaching purposes. Most recent versions of these presentations can be found at http://marc.psc.edu/http://marc.psc.edu/ Essential Computing for Bioinformatics

3. What is the Essence of Computing? Algorithmic Computational Function Input Information Output Information Computing is the study of Algorithms

4. The Computation Process 01101100 1010100 101… encode 01101100 1010100 101… compute Problem decode Solution ALGORITHM A single Procedure that can find a solution to every possible instance of a problem in a finite number of steps =

5. Some Fundamental Questions What is the nature of computation? What can be computed? What can be computed efficiently? How to build practical computing devices?

6. The Computation Process 01101100 1010100 101… encode 01101100 1010100 101… compute Problem decode Solution Integer An Algorithm can be thought of as an Integer Function

7. Computability All Integer Functions (IF) Computable Integer Functions (CF) IF ≟ CF Halting Problem IF ≠ CF Computable Integer Functions (CF)

8. The Halting Problem (Alan Turing 1936) Given a program and an input to that program, determine if the program will eventually stop when it is given that input. Compute Program P Input I P Halts on I? Cannot Build This Want to describe the set of computable functions? Can show any problem UNDECIDABLE show that its solution could be used to solve HP A CONTRADICTION!!

9. Mathematical Computers: The Turing Machine (1936) Alan Turing 01 01 FSM Infinite I/O TAPE 0/{1,0,R} 1/{0,1,R} Tape Head Turing demonstrated how to solve several problems using his computing model

10. Mathematical Computers: The Turing Machine (1936) Alan Turing 01 01 FSM Infinite TAPE 0/{1,0,R} 1/{0,1,R} FSM Infinite I/O TAPE Tape Head Turing demonstrated how to solve several problems using his computing model

11. FSM Sorting TM FSM Sorting TM FSM Sorting TM Ad-hoc Turing Machines FSM Sorting TM FSM Searching TM FSM Integrating TM Can we build a general purpose TM?

12. The Universal Turing Machine (UTM) Universal TM Coded TM MCoded Tape for M Capable of Emulating Every other TM Shown possible by Alan Turing (1936) BIG IDEA: INTEPRETATION!!! Software (flexible) Hardware (fast) The Paradigm for Modern General Purpose Computers

13. Church’s Thesis Alonso Church “ All the models of computation yet developed, and all those that may be developed in the future, are equivalent in power. ” “ Any realizable computing device can be simulated by a Turing machine ” Issues not considered: Size, Programmability, Performance But they must be considered if one is to build …

14. DataPaths PC ABR ALU AC Practical Universal Computers ( John) Von Neumann Architecture (1945) Program Data Memory Control Unit (FSM) CPU A CPU is a universal TM An interpreter of some programming language often called “machine code” status control This looks just like a TM Tape

15. "Computer Science is no more about computers than Astronomy is about telescopes" Final Word Edsger W. Dijkstra 1972 ACM Turing Award