4) Consider the system with the following input-output relation with x[n] and y[n] being input and output respectively. y[n] = Odd{x[n – 1]} Determine whether the system is memoryless, time invariant, linear, causal and stable.

Consider an airport management system. Each airport has a unique id (e.g. Montreal:YUL). Let us introduce the types AIRPORT and CITY . We also introduce variable airports that contains associations between airport id’s and their corresponding host cities. A possible state of the system is shown below:airports ={YUL → Montreal,LCY → London_UKLHR → London_UK,MIL → Milan,SFO → San_Francisco,SDQ → Santo_Domingo}1. (PROGRAMMING) Define global variable airports in Common LISP and populate it with the above data. Demonstrate that the variable indeed contains the ordered pairs as shown above.2. Provide a declaration of variable monitored that holds all airport id’s.3. What kind of variable is airports? Provide a formal definition together with any and all applicable properties.4. Describe what data structure you would deploy to model variable airports. Note that you may not use a Dictionary. Should this be an ordered or an unordered structure? Discuss.5. Provide a formal specification of the…

Solve the problem

Let = {0, 1} and consider the following languages 1. LBOUNDED = {(M, x) : M is a TM, x € Σ*, M never moves its pointer more than |x| tape symbols away from the left endmarker |} 2. LDEC = {(M): M is a TM, L(M) is decidable} For each language, determine whether it is decidable or undecidable. If it is decidable, give a decision procedure which decides it. If it is undecidable, you must use Rice's theorem, if applicable, or a mapping reduction, otherwise. [Hint: Given some input string x, you may assume that the number of possible instantaneous configurations of a TM where the pointer never moves more than |x| tape symbols away from the left endmarker is at most |T||*|. (²[+¹). (¹).]

Suppose we have two industrial control systems S1 and S2 that are workingconcurrently. We need to forbid some sequence of actions from taking placebetween the two systems. One such action is allowing S1 and S2 to be onat the same time. Consider the alphabet:Σ = {On(S1), On(S2), Off(S1), Off(S2)}A sequence of actions is a word over Σ∗.i. Convert the property on sequences given above into a language, andthen define an NFA that accepts it.ii. A second property is that S2 must power off after S1, but S2 mustpower on before S1. Define a language which captures this property(and this property only), and then define a NFA that accepts it.