The Regular Operations

















What are the Arithmetic Operations?

	addition
	subtraction
	multiplication
	division
	etc

What types of objects do the Arithmetic Operations operate on?

	integers
	real numbers
	etc


What are the Regular Operations?

	union
	concatenation
	star

What types of objects do the Regular Operations operate on?

	languages


What's the union of languages A and B?

	A = {a, b}
	B = {x, y, z}

	A union B = 


What's the concatenation of languages A and B?

	A = {a, b}
	B = {x, y, z}

	A concat B = 


What's the star of language A?

	A = {a, b}

	A* = 

















What does it mean to say the set of integers is Closed under addition?

	when you add two integers you get an integer

Is the set of integers closed under subtraction?

Is the set of integers closed under multiplication?

Is the set of integers closed under division?

















What does it mean to say the set of Regular Languages is closed under Union?

	if A1 and A2 are regular languages, A1 union A2 is regular

How do you show (A1 union A2) is regular?

	given machine M1 that recognizes A1, and M2 that recognizes A2
	construct machine M from M1 and M2 that recognizes (A1 union A2)

Can you build a machine that recognizes (A1 intersect A2)?

Can you build a machine that recognizes the complement of A1?

Is the set of Regular Languages closed under Concatenation?

Is the set of Regular Languages closed under Star?