This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CS 373: Theory of Computation Gul Agha Mahesh Viswanathan Fall 2010 1 1 HighLevel Descriptions of Computation HighLevel Descriptions of Computation Instead of giving a Turing Machine, we shall often describe a program as code in some programming language (or often pseudocode) Possibly using high level data structures and subroutines Inputs and outputs are complex objects, encoded as strings Examples of objects: Matrices, graphs, geometric shapes, images, videos, ... DFAs, NFAs, Turing Machines, Algorithms, other machines ... HighLevel Descriptions of Computation Encoding Complex Objects Everything finite can be encoded as a (finite) string of symbols from a finite alphabet (e.g. ASCII) Can in turn be encoded in binary (as modern day computers do). No special t symbol: use selfterminating representations Example: encoding a graph. (1,2,3,4)((1,2)(2,3)(3,1)(1,4)) encodes the graph 1 2 3 4 HighLevel Descriptions of Computation We have already seen several algorithms, for problems involving complex objects like DFAs, NFAs, regular expressions, and Turing Machines For example, convert a NFA to DFA; Given a NFA N and a word w , decide if w L ( N ); ... All these inputs can be encoded as strings and all these algorithms can be implemented as Turing Machines Some of these algorithms are for decision problems, while others are for computing more general functions All these algorithms terminate on all inputs 2 HighLevel Descriptions of Computation Examples: Problems regarding Computation Some more decision problems that have algorithms that always halt (sketched in the textbook) On input h B,w i where B is a DFA and w is a string, decide if B accepts w . Algorithm: simulate B on w and accept iff simulated B accepts On input h B i where B...
View Full
Document
 Fall '08
 Viswanathan,M

Click to edit the document details