Finite Automata and Regular Operations

q = Haven't seen any symbols of the pattern q0 = Have just seen a 0 q00 = Have just seen 00 q001 = Have seen the entire pattern 001

Union = Takes all the strings in both A and B and lumps them together into one language Concatenation = Attaches a string from A in front of a string from B in all possible ways Star = Attaches any number of strings in A together to get a string in the new language Intersection = Finds the common strings between A and B

Start state = The initial state of the finite automaton Accept state = The state that indicates the input string is accepted Transition = The movement from one state to another based on the input symbol Binary operation = An operation that takes two languages as input

<p>Assign a state to each possibility = Determine the start state Assign the transitions = Represent the information as a finite list of possibilities Set the accept states = Skip over all 1s Set the start state = Note that you may have just seen the first of the three symbols</p> Signup and view all the answers

<p>Regular language = A language that can be recognized by a finite automaton Formal language = A language defined by a set of rules and strings Language acceptance = The process of determining whether a string belongs to a language Unary operation = An operation that takes a single language as input</p> Signup and view all the answers

<p>States = To represent possibilities Transitions = To determine the next state based on the input symbol Start state = To indicate where to begin the recognition process Accept states = To determine whether to accept or reject the input string</p> Signup and view all the answers

<p>State = A node in the diagram that represents a possible situation Transition = An arrow that connects two states based on the input symbol Edge = A connection between two states in the diagram Vertex = A point in the diagram that represents a state</p> Signup and view all the answers

<p>Pattern recognition = The process of identifying a pattern in the input string State assignment = The process of assigning states to possibilities in the pattern Transition assignment = The process of assigning transitions between states based on the input symbol Accept state identification = The process of identifying the accept state in the finite automaton</p> Signup and view all the answers

<p>Skip over all 1s = Initially ignore all 1s in the input string Note that you may have just seen the first of the three symbols = Recognize the first 0 in the pattern 001 Go back to skipping over 1s = Reject the input string if a 1 is seen after a single 0 Continue scanning until you see a 1 = Accept the input string if the entire pattern 001 is seen</p> Signup and view all the answers

<p>Union = A U B = {good, bad, boy, girl} Concatenation = A ∩ B = {goodboy, goodgirl, badboy, badgirl} Star = A* = {&quot;, good, bad, goodgood, goodbad, badgood, badbad,...} Intersection = A ∩ B = {good, bad}</p> Signup and view all the answers

<p>Finite automaton = A machine that recognizes a regular language Formal language = A set of strings that can be recognized by a finite automaton Regular language = A language that can be recognized by a finite automaton State transition diagram = A graphical representation of a finite automaton</p> Signup and view all the answers

<p>Determine the start state = To set the initial state of the automaton Assign the transitions = To specify how the automaton moves from one state to another Represent the information as a finite list of possibilities = To identify the possible states of the automaton Set the accept states = To determine when to accept the input string</p> Signup and view all the answers

<p>Start state = Specifies the initial situation in the automaton Accept state = Indicates whether the input string is accepted or rejected Transition = Determines the next state based on the input symbol State assignment = Specifies the possible situations in the automaton</p> Signup and view all the answers

<p>States = To store information about the input string Transitions = To determine the next step in the recognition process Start state = To begin the recognition process Accept states = To signal the end of the recognition process</p> Signup and view all the answers

<p>Language acceptance = The process of determining whether a string is in a language Formal language recognition = The process of designing a finite automaton to recognize a language Finite automaton design = The process of creating a finite automaton to recognize a language State transition diagram = A graphical representation of a finite automaton</p> Signup and view all the answers

<p>Recognize the first 0 in the pattern 001 = Identify the first symbol of the pattern Reject the input string if a 1 is seen after a single 0 = Discard the input string if it does not match the pattern Accept the input string if the entire pattern 001 is seen = Confirm that the input string is in the language Continue scanning until you see a 1 = Search for the remaining symbols in the pattern</p> Signup and view all the answers

<p>Q = set of states Σ = alphabet of input symbols δ = transition function q<del>0</del> = initial state</p> Signup and view all the answers

<p>r<del>0</del> = q<del>0</del> = machine starts in the start state δ(r<del>i</del>,w<del>i</del>+1) = r<del>i</del>+1 = machine goes from state to state according to the transition function r<del>n</del> ∈F = machine accepts its input if it ends up in an accept state w<del>1</del>w<del>2</del>··· w<del>n</del> = input string of symbols</p> Signup and view all the answers

<p>A = language recognized by the finite automaton M M accepts w = finite automaton M accepts input string w w ∈ A = input string w belongs to language A M recognizes A = finite automaton M recognizes language A</p> Signup and view all the answers

<p>Pretending to be the automaton = start getting an input string of symbols Remember whether the number of 1s seen so far is even or odd = keep track of this information as you read new symbols Flip the answer if you read a 1 = update the state based on the input symbol Leave the answer as is if you read a 0 = no change in the state based on the input symbol</p> Signup and view all the answers

<p>Q = used to define the states of the automaton Σ = used to define the input alphabet δ = used to define the transition between states F = used to define the accept states</p> Signup and view all the answers

<p>A = language consisting of all strings with an odd number of 1s M accepts w = finite automaton M accepts input string w w ∈ A = input string w belongs to language A M recognizes A = finite automaton M recognizes language A</p> Signup and view all the answers

<p>r<del>0</del>,r<del>1</del>,…,r<del>n</del> = sequence of states δ(r<del>i</del>,w<del>i</del>+1) = r<del>i</del>+1 = transition from one state to another r<del>n</del> ∈F = machine ends up in an accept state w = w<del>1</del>w<del>2</del>··· w<del>n</del> = input string of symbols</p> Signup and view all the answers

<p>E1 = finite automaton recognizing language A alphabet {0,1} = input alphabet of the finite automaton language A = consisting of all strings with an odd number of 1s state transition diagram = visual representation of the finite automaton</p> Signup and view all the answers