By James L. Hein
ISBN-10: 0867204974
ISBN-13: 9780867204971
This article deals scholars a delicately built and whole advent to the formal good judgment utilized in common sense programming languages and automated reasoning platforms. the writer comprises many illustrative examples to support scholars snatch suggestions. huge workout units stick to each part to instantly toughen ideas because the scholar is brought to them. Many first-class tables and illustrations are incorporated to additional aid scholars conceptualize grammars and transitions.
Read Online or Download Theory of Computation: An Introduction (Jones and Bartlett Books in Computer Science) PDF
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Extra info for Theory of Computation: An Introduction (Jones and Bartlett Books in Computer Science)
Sample text
2. Suppose we have a function f : N -- N defined by f(x) = 2x + 1. Describe each of the following sets, where E and 0 denote the even and odd natural numbers, respectively. a. range(f). b. f(E). c. f(O). d. fP(E). e. f-P(O). 3. Evaluate each of the following expressions. a. 1j. b. 17. c. 1J. d. 11. 4 Languages 37 4. Evaluate each of the following expressions. a. 15 mod 12. b. -15 mod 12. c. 15 mod (-12). d. -15 mod (-12). 5. Let f : H,6 -ý 6 be defined by f(x) = 2x mod 6. Find the image and the pre- image for each of the following sets.
C. 0. d. (0). e. ((a), 01. 5. For each collection of sets, find the smallest set A such that the collection is a subset of power(A). a. {(a), {b, c). b. ((a), (0)). c. ((a), H{affl. d. ((a), 11b)), (a, b)). 6. Show that power(A r) B) = power(A) r) power(B) by proving that each side is a subset of the other side. 7. Is power(A u B) = power(A) u power(B)? 8. Give a proof or a counterexample for each of the following statements. a. An(BuA)=Ar)B? b. A-(BrmA)=A-B? c. Ar-(BuC)=(AuB)n(AuC)? d. A®A=A? 9.
For example, the infinite language {anb I n >_0) can be described by the grammar * S---*b I aS. To derive the string anb, we would use the production S -- aS repeatedly-n times to be exact-and then stop the derivation by using the production S --) b. The production S -4 aS allows us to say "IfS derives w, then it also derives aw. A production is called recursive if its left side occurs on its right side. For example, the production S -- aS is recursive. A production S --- a is indirectly recursive ifS derives a sentential form that contains S.