Description

Finite Automata. Finite Automaton. Input. String. Output. “Accept” or “Reject”. Finite Automaton. Transition Graph. initial state. accepting state. transition. state. Initial Configuration. Input String. Reading the Input. Input finished. accept. Rejection.

Transcripts

Limited Automata

Finite Automaton Input String Output âAcceptâ or âRejectâ Finite Automaton

Transition Graph starting state tolerating state move state

Initial Configuration Input String

Reading the Input

Input completed acknowledge

Rejection

Input completed reject

Another Rejection

reject

Another Example

Input completed acknowledge

Rejection Example

Input completed reject

Languages Accepted by FAs FA Definition: The dialect contains all data strings acknowledged by = { strings that convey to a tolerant state}

Example acknowledge

Example acknowledge

Example trap state acknowledge

Formal Definition Finite Automaton (FA) : set of states : info letters in order : move capacity : beginning state : set of tolerating states

Input Alphabet

Set of States

Initial State

Set of Accepting States

Transition Function

Transition Function

Extended Transition Function

Observation: if there is a stroll from to with mark then

Example: There is a stroll from to with name

Recursive Definition

Language Accepted by FAs For a FA Language acknowledged by :

Observation Language rejected by :

Example = { all strings with prefix } acknowledge

Example = { all strings without substring }

Example

Regular Languages Definition: A dialect is general if there is FA such that Observation: All dialects acknowledged by FAs shape the group of standard dialects

Examples of normal dialects: { all strings with prefix } { all strings without substring } There exist automata that acknowledge these Languages (see past slides).

There exist dialects which are not Regular: Example: There is no FA that acknowledges such a dialect (we will demonstrate this later in the class)

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