Algorithms, Computer Systems, and Programming Languages
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1 overview Algorithms, Computer Systems, and Programming Languages CSC121, Introduction to Computer Programming what is a computational process? what is an algorithm? what is a computer? brief overview of computer organization computer processing as a discrete state machine assembly language programming high-level language programming the landscape of computational problems Computational Processes a computational process denotes a collection of rules, or a sequence of operations or transformations whereby some resulting information is derived from a set of initial or given information and conditions. Algorithm an algorithm is a plan for directing a computational process. algorithms should satisfy these conditions each of the steps must be clearly and precisely defined. each step must be effective (for the agent executing the process) the steps must be ordered properly the process must terminate at some point 1
2 Devising an Algorithm Computer Systems (1) Creating an algorithm is a process that involves these considerations: a) what is the result? (specifications for the task, process, answer, or product) b) what do I know? (information that is given or input into the computational process) c) how do I derive (a) from (b)? (modifications, transformations, steps required to produce (a)) Today s ge ne ration of compute r s ys te ms are automated, programmable, electronic digital processing machines. electronic digital programmable automated Computer Systems (2) Computer Systems (3) A computer system is an electronic digital data processing machine. A computer system is comprised by software that directs the processing performed by hardware. data symbolic representation of information process a sequence of states during which the data are modified in prescribed ways program a set of instructions that direct the process software programs program a set of instructions that direct a process hardware devices that make up the physical system of the computer 2
3 Hardware Hardware Hardware denotes the devices that comprise the computer system processor CPU main memory secondary memory and I/O subsystem auxiliary memory input/output devices Processor System main memory stores both data and instructions used for processing bus provides interconnections central processing unit: manages the instruction-execution cycle Instruction-Execution Cycle fetching the next instruction decoding (or interpreting) that instruction executing what the instruction prescribes 3
4 Memory Secondary Memory and I/O information (data) is stored in uniform-sized units each unit has a unique address that identifies it reading from memory copy data from a memory location non-destructive writing to memory moving and replacing data in a memory location destructive 13 Secondary memory nonvolatile storage cheaper, mass storage Input/Output devices input--translates human-readable forms of information to machine-readable data output-- translates machine-readable data to human-readable forms 14 Discrete State Machine Digital computers... may be classified amongst the 'discrete state machines. These are the machines which move by sudden jumps or clicks from one quite definite state to another. These states are sufficiently different for the possibility of confusion between them to be ignored. Turing, Computing Machinery and Intelligence (1951) Capturing a Discrete State the current values of any data objects specified for the process the status of the processor temporary values and flags stored there the status of input and output operations the address of the next executable instruction in the program 4
5 Software computer programs are commonly called software each machine instruction in a program typically corresponds to a type of operation that the computer s processor can perform the set of possible processor or machine instructions is called the processor or machine language Assembly Language Programming assembly language programs contain symbolic instructions representing elements of some machine language instruction each instruction typically has a mnemonic for the operation code literals or labels for the operands Assembly Language Programming Assembly Language Programming Some operands are literals e.g., ADD 3 [ACC ß ACC + 3] where ACC denotes the Accumulator Some operands are labels signifying indirection (indirect codes) e.g., ADD LOC 1024 [ACC ß ACC + value(loc 1024)] Labels may function as constants. literals or values that may change from time to time, but are fixed or static for the current execution of the program variables. these denote values that are dynamic, that is, may change in the course of processing pointers (handles). these denote values that are the address of other locations containing values 5
6 Assignments Conditional Processing Putting a data value into memory is called (algorithmica lly) an assignment ACC ß 3 In Python (and most programming languages), it is written in this form name = value where name is a symbolic label and value expresses some data value is the capability of the processor to choose between alternative actions based on evaluating current data 22 Conditional Processing is made possible at the processor level by branch instructions Conditional Processing is made possible at the processor level by branch instructions unconditional branch (jump) change the address of the next instruction to the one indicated in the branch instruction conditional branch (jump) if some condition is true, then change the address of the next instruction to the one indicated in the branch instruction 6
7 Subroutines Assembly Language Programming library program units that can be linked with the main program Assembly Process Review: Assembly Language Programming instructions have a low-level of abstraction because they model the actual operations of the native processor instructions represent (nearly) a 1 1 relation with those of the corresponding machine language assembly language programs are not portable assembly languages are considered low-level programming languages 7
8 High-Level Programming Languages Advantages of High-Level Programming Languages High-Level Language (HLL) instructions are more abstract HLL instructions express higher-order operations single HLL instructions substitute for a sequence of low-level machine language instructions. In short, there is a 1 many relation between HLL instructions and machine language instructions HLL programs are portable to other processors provided a suitable means of translation programmer is relieved of many implementation details in performing tasks HLLs are designed to be more compatible with the way we think and solve problems HLL programs can be adapted more easily for a variety of computer systems and modified more easily for different functions HLL programs are more concise Trans lating HLL Programs interpreters decode and execute programs one instruction at a time translation on the fly emulates the way the processor functions compilers analyze and translate the entire HLL source program to produce an executable machine language version like a prepared text translation Some computational problems have solutions, but these solutions cannot be computed effectively because we lack the practical means to do so some problems may be solvable when we have faster processors or greater memory capacities for others, we will never have the resources to effectively compute them with current solutions or algorithms Example: the traveling salesperson problem 8
9 The brute-force solution for the traveling salesperson problem (TSP) has a factorial growth rate Computer scientists often describe the behavior of algorithms using a notation called Big O this denotes the upper bound for the worst-case performance of an algorithm TSP = O(N!), for N cities (or nodes) Suppose that we had hardware that was capable of analyzing one million individual paths or trips per second. N = 10 solution < 4 seconds N = 100 solution = approximately centuries Problems with algorithms like for TSP are said to be intractable there is another class of problems that are not solvable example: The Halting Problem Suppose that we created a program that could analyze any other program. Specifically, analyze an input program with a specific set of input data Our program must be able to determine whether the input program will halt i.e., complete its task An effective solution has two possibilities: Yes, the input program terminates or No, the input program never terminates or halts Alan Turing demonstrated that the Halting Problem was unsolvable in 1936 headed the group at Bletchley Park that cracked the Enigma Machine in WWII developed the ACE computer in 1946 introduced what is now called the Turing Test to determine whether a machine could be considered intelligent 9
10 undecidable problems: problems for which there can be no effective algorithm intractable problems: these are decidable but have no practical algorithmic solutions tractable problems: these are both decidable and have algorithms that are or would be practical to implement review what is a computational process? what is an algorithm? what is a computer? brief overview of computer organization computer processing as a discrete state machine assembly language programming high-level language programming the landscape of computational problems 10
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