Can a Turing machine decide an infinite language?
Yes, a Turing machine can decide that langauge: it just looks at the first character and accepts or rejects without even needing to look at the rest of the string.
What are Turing recognizable languages?
A language is “Turing-Recognizable” iff there exists a Turing Machine such that. when encountering a string in that language, the machine terminates and accepts that string; when encountering a string not in that language, the machine either terminates and rejects that string or doesn’t terminate at all.
Is every language Turing Recognisable?
Every regular language is Turing-decidable and therefore Turing acceptable / recognisable (but note that Turing acceptable does not imply Turing decidable). Suppose you are given a DFA D such that L = L(D).
Is it true that every infinite Turing recognizable language has an infinite decidable subset?
(b) (10 points) If E enumerates an infinite language, then A is infinite. [This proves that every infinite Turing recognizable set has an infinite decidable subset.]
Is every finite language computable?
According to wikipedia, every finite set is computable. Definition: set S⊂N is computable if there exists an algorithm which defines in finite time if a given number n is in Set.
Are all finite languages Turing decidable?
If A is finite, it is decidable because all finite languages are decidable (just hardwire each of the strings into the TM). If A is infinite, a TM M that decides A operates as follows.
How do you know if a language is Turing recognizable?
Recognizable Language A Turing machine M recognizes language L if L = L(M). We say L is Turing-recognizable (or simply recognizable) if there is a TM M such that L = L(M). Decidable Language A Turing machine M decides language L if L = L(M) and M halts on all inputs.
How do you prove a language is Turing recognizable?
Prove that the language it recognizes is equal to the given language and that the algorithm halts on all inputs. To prove that a given language is Turing-recognizable: Construct an algorithm that accepts exactly those strings that are in the language. It must either reject or loop on any string not in the language.
Is there a language that is not Turing recognizable?
After a lot of searching I came to the conclusion that yes, there are languages that are not even Turing Recognisable, but I can’t get good examples which are simple to understand.
Are there infinite decidable languages?
2 Answers. No, there are many infinite languages that are decidable. One trivial example is the language {n € N | a^n} , i.e. the language of words that only contain the letter “a”. This language can be matched by the regular expression a* .
Is the subset of a Turing recognizable language Turing recognizable?
No, finite languages don’t have subsets which aren’t Turing recognizable. However, infinite languages (Turing recognizable or not) always have subsets which are not Turing recognizable, simply because they have uncountably many subsets, but there are only countably many Turing recognizable languages.
Is an infinite language regular?
The Wikipedia entry for Regular language states that the all finite languages are regular and that infinite languages are not regular because they cannot be recognized by a finite automaton because the finite automaton has access to a finite quantity of memory.