Abstract machines and grammars by Walter J Savitch

By Walter J Savitch

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S 2 is the start state of M 2, and Qr is in Accepting-states(Mp) = Accepting-states(M2). 3. There are strings a and {3 such that g = a{3, (st. af3) I*M, Cq 1 , {3) and (s 2, {3) I ~2 (q 1 , A), where q1 is an accepting state of M 1 and St. s 2, q 1 are as in (2). 4. There are strings a and {3 such that g = af3, (st. a) I*M, (q 1 , A), and (s2> {3) I ~ 2 (q 1 , A), where St. s 2, q1 , and q 1 are as in (3). 5. There are strings a and {3 such that g = a{3, a is in A (M 1) = Lt. and {3 is in A (M2) = L2.

A nondeterministic acceptor is said to accept an input if there is at least one accepting computation. Therefore, 010 is in A (M). Our next result shows that finite-state acceptors can at least perform the simple task of checking to see if its input is on a fixed finite list. 42 CHAPTER 3. 3 Theorem If L is any finite set of strings, then we can find a deterministic finite-state acceptor M such that L = A (M). PROOF Let L be a finite language. We will construct a deterministic finitestate acceptor M such that A (M) = L.

The one point that should become clear early on is that it is 34 CHAPTER 3. FINITE-STATE ACCEPTORS frequently much easier to design a nondeterministic finite-state acceptor to accomplish a given task than it is to design a deterministic finite-state acceptor to accomplish the same task. Other reasons for studying nondeterminism will appear later on in this text and in subject matter beyond the scope of this text. One clear example of how nondeterminism arises naturally has to do with context-free languages.

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