cs215 wiki: Top/RegularLanguages

Read /TheGeneralIdea before reading this.

Regular languages are languages that can be decided by finite automata -- computers with a finite number of states.

What is a finite automaton? In class we drew examples using diagrams (graphs where the nodes are states and edges are transitions).

Examples of regular languages:

{0,1}*
{x | x is a string of zeros and ones, x ends in a zero}
{x | x is a string of roman alphabet characters, x ends in a "abracadabra"}
{x | x is a string of zeros and ones, x has an odd number of ones}
{x | x is the binary representation of an integer that is a multiple of 3} (challenge problem)
{x | x is a word in the 2004 Mirriam-Webster dictionary}

Formally, how to define a finite automaton?

Finite set S of states
Finite alphabet Σ
Set A of accept states, A ⊆ S
Start state s₀ ∈ S
Transition function δ : S × Σ → S (See Chapter 0 of /Sipser for mathematical notation.)

[Did not formally define how a finite automaton computes.]

Examples of non-regular languages: