An Introduction to Formal Languages and Automata by Linz Peter

Author:Linz, Peter [Linz, Peter]
Language: eng
Format: epub
Publisher: Jones & Bartlett Learning
Published: 2011-02-14T00:00:00+00:00

and define such that

if and only if

and

In this, we also require that if a = λ, then pj = pl. In other words, the states of are labeled with pairs (qi, pj), representing the respective states in which M1 and M2 can be after reading a certain input string. It is a straightforward induction argument to show that

with qr ε F1 and Ps ε F2 if and only if

and

Therefore, a string is accepted by if and only if it is accepted by M1 and M2, that is, if it is in L (M1) L (M2)= L1 L2.

The property addressed by this theorem is called closure under regular intersection. Because of the result of the theorem, we say that the family of context-free languages is closed under regular intersection. This closure property is sometimes useful for simplifying arguments in connection with specific languages.

Example 8.7

Show that the language

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