6 votes 6 votes I'm so confused what happens when you concatenate/MUL Epsilon ε with any input symbol? What is ε.a = ? and what is ε.0 = ? what is ε.1= ? Theory of Computation theory-of-computation finite-automata regular-expression + – iarnav asked Aug 11, 2017 iarnav 3.3k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes Epsilon can be considered almost like 1 in mathematics. €.a=a €.1=1 €.0=0 Sandeep shahu answered Aug 12, 2017 selected Oct 9, 2020 by iarnav Sandeep shahu comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes ϵ is the empty string. Concatenation of empty string with non empty string is the string itself. ϵ.a=a. ϵ =a Surya Dhanraj answered Aug 11, 2017 Surya Dhanraj comment Share Follow See all 8 Comments See all 8 8 Comments reply Vivek Jain commented Aug 11, 2017 reply Follow Share and what about phi(Ǿ) ? 0 votes 0 votes iarnav commented Aug 11, 2017 reply Follow Share Thank you! 0 votes 0 votes just_bhavana commented Aug 11, 2017 reply Follow Share Concatenation of any string with $\phi$ is $\phi$ itself. 2 votes 2 votes stblue commented Aug 11, 2017 reply Follow Share ya there is confusion, what epsilon is, if its null then concatenation will be null, if its A= {$\epsilon$}, then A.anything = anything. 0 votes 0 votes mohit kumar 5 commented Aug 11, 2017 reply Follow Share @ just_bhavana can you please explain, how can you Concatenate any string with ϕ. As ϕ is language with no string. 0 votes 0 votes just_bhavana commented Aug 11, 2017 reply Follow Share For concatenation consider two sets A and B. The concatenation a.b exists if there is an element 'a' such that 'a' $\epsilon$ A and an element 'b' such that 'b' $\epsilon$ B. Now, suppose one of the sets is empty i.e. consider A = $\phi$ which means there is no element in a that can be concatenated to element(s) of set B, which itself makes the concatenation of A and B to be an empty set. So, concatenation of any string with ϕ is ϕ itself. 5 votes 5 votes mohit kumar 5 commented Aug 11, 2017 reply Follow Share just_bhavana Thank you i got it :) 1 votes 1 votes jiminpark commented Dec 29, 2021 reply Follow Share @just_bhavana maam, Does this mean L.ϕ = ϕ. L = ϕ ? I am assuming something like this, but is this diagram is correcrt then above does not seem to be correct but I have seen on stackoverflow that the above statement holds true . Can you please guide. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes To generalize it lets consider r to be any regular expression. 1) r.ε=r=ε.r 2) But r + ε != a if ε does not belong to the language of r i.e. L(r) r + ε = r if ε belongs to the language i.e. L(r) ankit_chahal answered Aug 11, 2017 ankit_chahal comment Share Follow See all 0 reply Please log in or register to add a comment.