notes15 Decidability and Recognizability

notes15 Decidability and Recognizability - CS 373: Theory...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CS 373: Theory of Computation Gul Agha Mahesh Viswanathan Fall 2010 1 1 High-Level Descriptions of Computation High-Level Descriptions of Computation Instead of giving a Turing Machine, we shall often describe a program as code in some programming language (or often pseudo-code) 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 ... High-Level 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 self-terminating representations Example: encoding a graph. (1,2,3,4)((1,2)(2,3)(3,1)(1,4)) encodes the graph 1 2 3 4 High-Level 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 High-Level 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

Page1 / 7

notes15 Decidability and Recognizability - CS 373: Theory...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online