RegexComplementBlowup.png


Summary

Description
English: Regular expression over the alphabet { 0, 1, S, E } whose complement expression has a length of about 2 32 . "e" denotes the empty string. The example has been constructed from Thm.4.1, p.332 of: Wouter Gelade and Frank Neven (2008) " Succinctness of the Complement and Intersection of Regular Expressions " in Proc. 25th Ann. Symp. on the Theoretical Aspects of Computer Science (STACS) , pp. 325–336
Date
Source Own work
Author Jochen Burghardt
Ascii source
(e+(0+1+S+E)(e+(0+1+S+E)(e+(0+1+S+E)(e+(0+1+S+E)(e+(0+1+S+E))))))
+       
(e+(0+1)(e+(0+1)(e+(0+1)(e+(0+1))))) (S+E) (0+1+S+E)*
+       
(0+1)(0+1)(0+1)(0+1)(0+1) (0+1+E) (0+1+S+E)*

+       

(0+1+S+E)* S ( (e+(0+1+S+E)(e+(0+1+S+E)(e+(0+1+S+E)(e+(0+1+S+E))))) (S+E) + (0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E) (0+1+S) ) (0+1+S+E)*

+       

(0+1+S+E)* E ( (e+(0+1+S+E)(e+(0+1+S+E)(e+(0+1+S+E)(e+(0+1+S+E))))) (S+E) + (0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E) (0+1+E) ) (0+1+S+E)*

+       

(0+1+S+E)* (0+1+S) 

+       

( (0+1)* + (0+1+S+E)* E (0+1)* ) 0 (0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E) 1 (0+1+S+E)*                  
+       
( (0+1)* + (0+1+S+E)* E (0+1)* ) 1 (0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E)(0+1+S+E) 0 (0+1+S+E)*

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8 February 2021