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Results tagged with fl.formal-languages
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user 5183
formal languages, grammars, automata theory
7
votes
Accepted
What kind of language is needed to recognize an ordered list? [multihead automata, apparently]
It sounds like what you are looking for are multihead automata (in your case, 1-way 2-head deterministic finite automata should suffice). I'm not really an expert on these, but google turns up some in …
- 2,530
13
votes
Accepted
Is the Set of all Primitive Words a Prime Language?
The answer is yes. Suppose we have a factorization $Q = A\cdot B$.
One easy observation is that $A$ and $B$ must be disjoint (since for $w\in A\cap B$ we get $w^2\in Q$). In particular, only one of …
- 2,530
7
votes
Accepted
The number of states of local automata
Since you say that $T_w:=\{\delta(q,w):q\in Q\}$ should have at most one element, I'll assume that you use the version of DFA where $\delta$ can be partial. Then this is a counterexample: $X=\{a,b\}, …
- 2,530
25
votes
Accepted
Why is non-determinism (Push-down automata) necessary?
I'm not quite sure which flavour of "why" you are looking for. One reason for the increase in power when allowing nondeterminism can be seen in the following example:
Let $L$ be the set of palindrome …
- 2,530
11
votes
Accepted
Measurable language which is not $\omega$-regular
A simple class of examples can be found by considering singleton languages $\{w\}$. These are measurable (Let $C_n(w)$ be the set of words agreeing with $w$ up to the $n$-th letter, then $\{w\}$ is th …
- 2,530