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Results tagged with automata
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user 8955
Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques
0
votes
If L is regular, so is $L-\{λ\}$?
Another option here is to obtain a regular expression for $L$, then transform it into a regex for $L - \{\lambda\}$. To do so, let’s define a function $D(R)$ (for “delambda”) that takes in a regex $R$ …
- 10.6k
3
votes
1
answer
20
views
Directly constructing a DFA for the Kleene star of a language given as a DFA?
The regular languages are closed under Kleene star. One common way to prove this is to define a construction that, given a DFA or NFA for a regular language $L$, produces a new NFA whose language is $ …
- 10.6k
3
votes
Accepted
What does it mean for a language to be sparse?
Pick some alphabet $\Sigma$, and in particular focus on the “interesting” case where $|\Sigma| \ge 2$. Then $|\Sigma^n|$, the number of possible strings of length $n$, is equal to $|\Sigma|^n$. In oth …
- 10.6k
10
votes
2
answers
1k
views
Why is it undecidable whether two finite-state transducers are equivalent?
I find this result striking, since it is decidable whether two finite-state automata are equivalent to one another. …
- 10.6k
2
votes
is {w in {0,1}* | #0(w) = #1(w)} a regular language?
No, this language isn't regular. @MJD has a great intuitive explanation for this in the comments: determining whether a string is in this language requires tracking the relative numbers of 0s and 1s, …
- 10.6k