Finite State Models

The University of Nottingham School of Computer Science and IT LECTURE 3 numeric PRELIMINARIES PART 1 Overview Sets, Relations and Functions Strings and Languages Sets, Relations and Functions A primed(p) is a collection of objects with no repetition. The simplest way to chance upon a station is by listing its elements. If a strict is expound using a defining property, the description should intelligibly place the objects and the universe of discourse: A = {x | x ? ? ? x < 10} Important notation for sets: ?, a?A, a?A A?B, A?B, A?B, A=B, A?B, A?B, A\B, A×B ?(A) or 2A, A or Ac , ?A what does this notation pixilated? what do these notations mean? For all sets A, B, and C in the universe U the pastime set properties hold: Associative uprightness: (A ? B) ? C = A ? (B ? C) (A ? B) ? C = A ? (B ? C) Commutative faithfulness: A?B=B?A A?B=B?A Complement law: A ? Ac = U A ? Ac = ? 1 Dr. Dario Landa-Silva The University of Nottingham School of Com puter Science and IT Idempotency law: A?A=A A?A=A identity element law: A??=A A?U=A slide fastener law: A?U=U A??=? engagement law: De Morgans law: (Ac)c = A (A ? B)c = Ac ? Bc (A ? B)c = Ac ? Bc Distributive law: A ? (B ? C) = (A ? B) ? (A ? C) A ? (B ? C) = (A ? B) ? (A ? C) A set |A| is express to be finite if A contains a finite cast of elements. A set |A| is said to be infinite if A contains an infinite number of elements. The set A is said to be d calculable or enumerable is there is a way to list of the elements of A. more than formally, A set A is enumerable or countable is A is finite or if there is a bijection f:A??+. Example. The following sets are countable: explain wherefore? A = {x | y ? ?+ ? x = 2?y+1} = {3, 5, 7, 9, 11, 13, 15,} B = {(x,y) | x,y ? A} = {(3,3),(3,5),(5,3),(3,7),(5,5),(7,3),(3,9),(5,7),(7,5)} A relation R is a subset of A × B where A is the domain and B is the cut back of R. If the domain is the same as the range, A = B, so R is a relation on the! set A. Properties of transaction: 2 Dr....If you want to get a full essay, order it on our website: BestEssayCheap.com

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