Loading in 5 sec....

Closure Properties of DecidabilityPowerPoint Presentation

Closure Properties of Decidability

- 751 Views
- Updated On :

Closure Properties of Decidability. Lecture 28 Section 3.2 Fri, Oct 26, 2007. Closure Properties of Decidable Languages. The class of decidable languages is closed under Union Intersection Concatenation Complementation Star. Closure Under Union.

Related searches for

Download Presentation
## PowerPoint Slideshow about '' - starbuck

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Closure Properties of Decidable Languages

- The class of decidable languages is closed under
- Union
- Intersection
- Concatenation
- Complementation
- Star

Closure Under Union

- Theorem: If L1 and L2 are decidable, then L1L2 is decidable.
- Proof:
- Let D1 be a decider for L1 and let D2 be a decider for L2.
- Then build a decider D for L1L2 as in the following diagram.

Closure Under Union

- Theorem: If L1 and L2 are decidable, then L1L2 is decidable.
- Proof:
- Let D1 be a decider for L1 and let D2 be a decider for L2.
- Then build a decider D for L1L2 as in the following diagram.

Closure Properties of Recognizable Languages

- The class of recognizable languages is closed under
- Union
- Intersection
- Concatenation
- Star

Closure Under Union

- Theorem: If L1 and L2 are recognizable, then L1L2 is recognizable.
- Proof:
- Let R1 be a recognizer for L1 and let R2 be a recognizer for L2.
- Then build a recognizer R for L1L2 as in the following diagram.

Closure Under Union

- Theorem: If L1 and L2 are recognizable, then L1L2 is recognizable.
- Proof:
- Let R1 be a recognizer for L1 and let R2 be a recognizer for L2.
- Then build a recognizer R for L1L2 as in the following diagram.

Closure of Union

- In that diagram, we must be careful to alternate execution between R1 and R2.

Download Presentation

Connecting to Server..