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- Fill out the table for executing the polynomial-time dynamic programming algorithm for deciding whether the string 1001 is in the context-free language generated by the following CFG. Fill the table completely—do not stop the algorithm early. (Note: This CFG is not quite in Chomsky Normal Form since A appears on the right-hand side of a rule, but the same algorithm still works.) A → BC | CC B → BA | 0 C → AB | BB | 1Mathematical Logic First-order or predicate logic. Show that the sum relation, {(m,n,p)|p=m+n}, is not definable on (N; ∙). Hint: Consider an automorphism of (N; ∙) that interchanges two primes. Where N is the set of natural numbers. Please be as clear as possible. Show and explain all the steps. Thank you very much.In "Computing Machines and Intelligence," the English mathematician Alan Turing (1912-1954) wrote, "If each man had a definite set of rules of conduct by which he regulated his life, he would be a machine, but there are no such rules, so men cannot be machines." Using what you now know about Logic, determine whether this statement make sense and explain. Construct a truth table for Turing's statement and determine if this statement is a tautology.
- 1. The notion of a verifier is central to the definition of the complexity class NP. However, we can consider the idea of a verifier independent of ideas from complexity theory. Recall that a verifier for a language L is an TM V such that L = {w | V accepts <w, c> for some c}. Prove that ATM, the acceptance language for Turing machines, has a verifier even if we add the extra condition that the verifier is a decider. Note that the verifier need not run in polynomial time. We are not asking for a polynomial-time verifier. 2. Let L be a context-free language. Prove that L is NP-Complete if and only if P = NP. 3. For a string w, let w_rev be the string w reversed. For any language A, Let reverse(A) = { w_rev| w is in A}. For which of the following classes of languages is closed under the reverse operation. In other words, for which classes is it true that for every language A in the class, reverse(A) is also in the class. Context-Free languages(Closed or Not Closed) Nonregular…Prolog Depth-first based on the graph search template is not memory efficient because it keeps all active branches while searching for a goal. A more efficient search for graphs looks at one path only and exploits the Prolog built-in backtracking mechanism. Create a file searches.pl and incrementally add to it the following. arc(a, b). arc(a, f). arc(b, c). arc(b, d). arc(b, e). arc(f, g). arc(f, i). arc(i, j). arc(i, k). arc(j, e). arc(j, m). goal(d). goal(i). goal(m). (a) Implement dfs/2 (depth-first search) – this strategy takes a single path 1 as input and then expands that path with a new node until the goal is found, in which case the solution is returned in the second argument. Query your program with: ?- dfs([a], X). for each file in Tests and check you find the right solution.Computer Science Show that the language L is regular. show your work, i am trying to learn this.
- Computer Science State whether the languages over binary strings below are Regular, Context-Free or Turing-recognizable. Use the simplest type. Explain. {ww^r} where w^r is the reverse of string w. And {ww} for any binary string w And {w : w is not a palindrome}Show that a language is decidable. Show that {M | M is a DFA whose language is empty} is decidable Hint: Check if M has a path from the initial state to some final state. If it does not, then L(M) is empty. A graph exploration algorithms such as depth first search or breadth first search can be used to check if there is a path from the initial state to some final state.consider the block problem. please solve it with explanations artificial intelligence
- Develop a Turing machine for the language L={w∈{0,1}∗ ||w|isoddandwcontainsatleastone1}. This means that the Turing machine should accept all strings over {0, 1} of odd length that contain at least one 1. Show the state transition diagram in addition to your defi- nition of the Turing machine. Show the working of your Turing machine on the strings “0010”, “00101”, and “000”.1.Let Σ = {a, b, c} and f : Σ∗ → Σ ∗ the function that for input w yields the string obtained by duplicating each a. E.g. f(baaca) = baaaacaa. Prove that if L is a regular language, then so is {f(w) | w ∈ L}. [Hint: Use induction on regular expressions.] 2.Assume given a non-basic language K . Find an infinite collection of basic languages, all different, whose intersection (i.e. the strings that are in at least one of them) is not basic. Hint: This problem is dual to the previous one. But in place of the union of trivial finite languages, consider here the intersection of trivial co-finite languages.Can you help me with this problem because I am struggling, can you explain it step by step in detail leading up to the solution so I know how you did it. Thank you so much. Question that I really need help with:A useless state in a Turing machine is one that is never entered on any input string. Consider the problem of determining whether a Turing machine has any useless states. Formulate this problem as a language and show that it is undecidable.