Prove that the class of decidable languages is closed under union, concatenation and Kleene star. Solution: Closure under union. Let L 1 and L 2 be two decidable languages. By deﬁnition there are deciders M 1 and M 2 such that L(M 1) = L 1 and L(M 2) = L 2. We construct the following 2-tape Turing machine M: 1."On input x:

5. Show that decidable languages are closed under the following operations: a. Set Difference b. Kleene Closure c. Shuffle ; Question: 5. Show that decidable languages are closed under the following operations: a. Set Difference b. Kleene Closure c. Shuffle

Prove/disprove that the class of decidable (resp. partially decidable) languages is closed under symmetric difference. A symmetric difference of sets A and B is the set (A \ B) ∪ (B \ A). I know that the class of decidable languages is closed under symmetric difference, because it is closed under union, complement and intersection.

Solution: False. In fact, every language is the union of a countable set of regular languages, each containing a single string. Clusure under pairwise union does not imply closure under in nite union. T / F The set of decidable languages is closed under symmetric di erence. Recall, the sym-metric di erence operator is de ned as, L1 L2 = L1 \L2 ...

Suppose that C is the class of all objects that have some property (e.g. the property of being a decidable language). Also suppose that you have an operation · which takes two of these objects and returns another object (the number two is just an example). We say that C is closed under · when: given two objects x and y in C, applying the operator to them gives an object which is also in C: x ...

In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language. Equivalently, a formal language is recursive if there exists a total Turing machine (a Turing machine that halts for every given input) that ...

Constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory.The same first-order language with "=" and "" of classical set theory is usually used, so this is not to be confused with a constructive types approach.

Dec 29, 2011 · Recursive languages are closed under the following operations. That is, if L and P are two recursive languages, then the following languages are recursive as well: The last property follows from the fact that the set difference can be expressed in terms of intersection and complement.

Decidable languages--somebody's asking me a good question about closure properties of the class of decidable languages. Are they closed under intersection, union, and so on? Yes. And the decidable languages are also closed under complement. That should be something you should think about. But yes, that is true.