1 / 11

Nondeterminism – Introduction

Nondeterminism – Introduction. Lecture 8 Section 1.2 Fri, Sep 7, 2007. Determinism. A finite automaton is deterministic because every move is forced. That is,  is a function . For every pair ( q , x )  Q   , there is exactly one q   Q such that ( q , x ) = q.

Patman
Download Presentation

Nondeterminism – Introduction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Nondeterminism – Introduction Lecture 8 Section 1.2 Fri, Sep 7, 2007

  2. Determinism • A finite automaton is deterministic because every move is forced. • That is,  is a function. • For every pair (q, x) Q, there is exactly oneqQ such that (q, x) = q.

  3. Nondeterminism • To make a nondeterministicfinite automaton, we relax the requirement that the image of (q, x) be unique. • (q, x) may have no image, one image, or more than one image. • We also allow  moves.

  4. Terminology • Deterministic finite automata are called DFAs. • Nondeterministic finite automata are called NFAs.

  5. The Language of an NFA • For a given input, an NFA may admit a multitude of computations. • If at least one computation ends in an accept state, then the input is accepted.

  6. Concatenation • Let A = {x | x contains an even number of a’s}. • Let B = {x | x contains an even number of b’s}. • Design NFAs that accept • AB • A B • A*

  7. Definition of an NFA • To define an NFA, we change the definition of the transition function .

  8. Relations and Functions • Given a relation from a set A to a set B, we may derive • A function from A to (B), or • A function from (A) to (B).

  9. Example • Let A = {2, 3, 4, 5}. • Let B = {6, 7, 8, 9}. • Let r be the relation defined by (a, b) r if a divides b. • Then r = {(2, 6), (2, 8), (3, 6), (3, 9), (4, 8)}.

  10. Example • Define f : A(B) by f(a) = {bB | a divides b}. • Then • f(2) = {6, 8} • f(3) = {6, 9} • f(4) = {8} • f(5) = 

  11. Example • Define g : (A) (B) by g(S) = {bB | a divides b for some aS} • Then, for example, • g({2}) = {6, 8} • g({2, 3}) = {6, 8, 9} • What is g()? g({4, 5})?

More Related