2.2-2.3 - CSC4510 AUTOMATA 2.2 Accepting the Union...

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1 CSC4510 AUTOMATA 2.2 Accepting the Union, Intersection, or Difference of Two Languages 2.3 Distinguishing One String from Another Accepting the Union, Intersection, or Difference of Two Languages Suppose that L 1 and L 2 are languages over Given an FA that accepts L 1 and another that accepts L 2 , we can construct one that accepts L 1 L 2 . The same approach works for L 1 L 2 and L 1 L 2 . If x  *, then knowing whether x L 1 and whether x L 2 is enough to determine whether x L 1 L 2. 2
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2 Theorem: Suppose M 1 = ( Q 1 , , q 1 , A 1 , 1 ) and M 2 = ( Q 2 , , q 2 , A 2 , 2 ) are FAs accepting L 1 and L 2 . Let M = ( Q , , q 0 , A , ) be defined as follows: Q = Q 1 Q 2 q 0 = ( q 1 , q 2 )   (( p , q ), ) = ( 1 ( p , ), 2 ( q , )) Then, if : 1. A = {( p , q ) | p A 1 or q A 2 }, M accepts L 1 L 2. 2. A = {( p , q ) | p A 1 and q A 2 }, M accepts L 1 L 2. 3. A = {( p , q ) | p A 1 and q A 2 }, M accepts L 1 L 2.
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