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1 Lecture 21 Regular languages review –Several ways to define regular languages –Two main types of proofs/algorithms Relative power of two computational.

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Presentation on theme: "1 Lecture 21 Regular languages review –Several ways to define regular languages –Two main types of proofs/algorithms Relative power of two computational."— Presentation transcript:

1 1 Lecture 21 Regular languages review –Several ways to define regular languages –Two main types of proofs/algorithms Relative power of two computational models proofs/constructions Closure property proofs/constructions –Language class hierarchy Applications of regular languages

2 2 Defining regular languages

3 3 Three definitions LFSA –A language L is in LFSA iff there exists an FSA M s.t. L(M) = L LNFA –A language L is in LNFA iff there exists an NFA M s.t. L(M) = L Regular languages –A language L is regular iff there exists a regular expression R s.t. L(R) = L Conclusion –All these language classes are equivalent –Any language which can be represented using any one of these models can be represented using either of the other two models

4 4 Two types of proofs/constructions

5 5 Relative power proofs These proofs work between two language classes and two computational models The crux of these proofs are algorithms which behave as follows: –Input: One program from the first computational model –Output: A program from the second computational model that is equivalent in function to the first program

6 6 Closure property proofs These proofs work within a single language class and typically within a single computational model The crux of these proofs are algorithms which behave as follows: –Input: 1 or 2 programs from a given computational model –Output: A third program from the same computational model that accepts/describes a third language which is a combination of the languages accepted/described by the two input programs

7 7 Comparison L 1 intersect L 2 L1L1 L2L2 LFSA M3M3 M1M1 M2M2 FSA’s LNFA LFSA NFA’s FSA’s L L M M’

8 8 Language class hierarchy All languages over alphabet  RE REC regular H H ?

9 9 Three remaining topics Myhill-Nerode Theorem –Provides technique for proving a language is not regular –Also represents fundamental understanding of what a regular language is Decision problems about regular languages –Most are solvable in contrast to problems about recursive languages Pumping lemma –Provides technique for proving a language is not regular

10 10 Review Problems We will cover one example of converting a regular expression into an NFA We will work on a new closure property proof –regular languages are closed under language reversal

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