Prove that the set of states expanded by algorithm A' is a subset of those examined by breadth-first search. Prove that more informed heuristics develop the same or less of the search space.

Q: Use a direct proof technique to prove the following theorems:   For all integers x and y, x2 + y2 −…

A:

Q: Prove the following problem fits the NP description. An integer set S and a time t are provided to…

A: Given problem involves determining whether a given integer set S has a subset whose product of its…

Q: Show that the language K = {(M) | M is a TM and does not accept (M)} is not Turing-recognizable.…

A:

Q: We say that a Turing machine is verbose on s if, at the completion of its computation on s, it…

A: Required : proof for undecidable by reduction.

Q: Write A greedy algorithm to find the maximal independent sets for matroids step by step.

A: A greedy algorithm to find the maximal independent sets for matroids step by step.

Q: Proposition H. The vertices reached in each call of the recursive method from the constructor are in…

A: The vertices reached in each iteration of the recursive procedure from the constructor must be in a…

Q: What is Warshall's algorithm? Obtain the transitive closure for the following diagraph [All steps…

A:

Q: Show that the language {M: M is a Turing machine with L(M) to be a finite set} is undecidable. You…

A: The given language is as following- FTM = { M | M is a TM and L(M) is finite} The  Properties of the…

Q: Need help in theoretical computer science Given the following language over the alphabet Σ = {a, b,…

A: Dynamic. We study dynamic learning of deterministic endless words automata. In our system, the…

Q: Prove that the language L = {a'b'c*d* ] j,k > 0} is countably infinite. Prove that the set of…

A: Answer is given below .

Q: Suppose (S, I) is a matroid, and suppose I' = { A' | S – A' contains some maximal A∈I }. Show that…

A:

Q: Prove The range of πk − πk+1 is the same as the range of (πk − πk+1)(Ik − Ik+1). More specifically,…

A: solution:

Q: Subject: Design analysis and algorithm     Please Solve this question and explain briefly

A: The objective of the question is to explain the 2-approximation algorithm for solving the Travelling…

Q: stablish that this problem is NP-complete.   Both S and t are whole numbers. Can we t-sum a subset…

A: The Subset Sum problem is the name for the issue you've just explained. Determine whether there is a…

Q: Let KCOMMONTM = { | M and N are Turing machines and |L(M) ^Ł(N)| ≥ k}. Show that KCOMMONTM is…

A: Given input <M,w> of , create input <M1,M2,1> for where M1 and M2 are such that L(M1)…

Q: Prove that the language L over {a,b,c}",given by L= {wcv: |w\a = [vl6} is recursive. You must…

A: The language Lover (a,b,c} *, given by L = {wev: [wla = [vlo} is recursive. A Turing machine that…

Q: The Well-Ordering Principle and (the theorem of) Mathematical In- duction (continued). This result…

A: The above question refers to the relationship between the Well-Ordering Principle (WOP) and the…

Q: Discrete mathematics applied to computer science: homework question. Let f : A → A be a function in…

A: Here is your solution :

Q: Find with proof every graph G for which ex(n, G) is defined for all positive integers n and there…

A: These question answer is as follows,

Q: Write an algorithm for addressing the subset-superset problem in string matching. That is, search a…

A: arr[] = {"catgc", "ctaagt", "gcta", "ttca", "atgcatc"} Initialize: temp[] = {"catgc", "ctaagt",…

Q: A* search with a heuristic which is admissible but not consistent is complete

A: Yes . A* complete when if the heuristics is not admissible.

Q: Show that the language L {w e {a,b}*: n(w) n(w) + 2} is not linear. %3D

A: Answer is given below:-

Q: Let A1, A2,..., An CU be n subsets of some universe U satisfying that A1 Ç A2 Ç A3 Ç .… Ç An. Prove…

A: The handwritten answer is to be solved below:

Q: A set S of logical connectives is said to be (logically) complete if each of ¬,∨, and ∧ can be…

A: Given: A set S of logical connectives is said to be (logically) complete if each of ¬,∨, and ∧ can…

Q: Prove A = { | M and M' are Turing machines and L(M) ∩ L(M') is empty } is not decidable.

A: Introduction:   Assume we have a D for A decider. We could use D to build the following decider for…

Q: Suppose I is a non empty regular language, over Σ, such that every w E L satisfies [w] = k, for some…

A: Given that, non-empty regular language L over the alphabet Σ such that every string w in L satisfies…

Q: Prove that the Independent Set Problem is NP-complete by showing it is polynomially reducible from…

A: There will be two parts: show that Independent Set (IS) is in NP show that IS is NP-Hard.

Q: [Undecidability and Reductions] OVERLAPPING = {{M, D) : | M is a Turing Machine and D is a DFA such…

A: A reduction from ATM to Overlapping is : Input : <M,w> Create a DFA D which accepts only one…

Q: Let L be a strict subset of LAc (i.e. L c LACC). Then L is ( always / sometimes / never ) decidable.

A: Defined the given statement always, sometimes or never

Q: Is it true that A* graph search with an admissible heuristic always returns an optimal solution in…

A: I have provided an answer to this question in step 2.

Q: P is the class of language that are decidable in polynomial time

A: ANSWER : Union: Let Li (i = 1, 2) be two languages in P and let Mi be a DTM that accepts Li in…

Q: Exercises Let I = {a,b}. Let A = {w•w*lw e I*}. Prove that A Sm A. D A is the language of…

A: Answer: I have given answer in the handwritten format

Q: Let SUBSET DFA = {{M1, M2) | M1 and M2 are DFAS and L(M,) C L(M2)}. a. Show that SUBSET DFA is…

A: given data   Let subset dfa = {(M1, M₂) M 1 and M 2 are df A and L (M1) ≤L (M2)   solution:   Show…

Q: 1. Reword the statement below as a theorem about graphs and then prove it. Assume that if A is a…

A: We use the pegionhole principle to explain this. In  mаthemаtiсs,  the  рigeоnhоle  рrinсiрle…

Q: Prove SAT (Satisfiability) true or false for (X v Y) ^ (~X v ~Y) in view of 'Theory of Computation'.

A: #include <bits/stdc++.h>using namespace std; const int MAX = 100000; vector<int>…

Q: Fix an integer n > 2 and consider the set P = {1,2, ..., n}. Define a partial order < on P such that…

A: Introduction

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A: Explained in the answer only

Q: 1-State the inverse and contrapositive of the statement “We leave whenever he comes”.  2-Let A,B…

A: Inverse means if two angles are not congruent then they do not have the same measure. Contrapositive…

Q: Let S be the set of all sentences in English Wikipedia as it existed on Feb 7, 2022 at midnight.…

A: S is a language that can be described using deterministic finite-state automaton. S is a language…

Q: Let L be any regular language over {a, b, c). Show how the Pumping Lemma can be used to demonstrate…

A:

Q: Graphs G and H are isomorphic if the nodes of G may be reordered so that it is identical to H. Let…

A: Graphs G and H are isomorphic if the nodes of G may be reordered so that it is identical to H. Let…

Q: Create and explain an exploration algorithm that could use the Generalized Voronoi Graph for mapping…

A: Exploration and mapping are principal essentials for independent robots working in at first obscure…

Q: For the undirected graph G shown in Example 9.1 and reproduced here for convenience, undertake…

A: By changing the procedure parameters to procedure BFT(s, K), where K is the search key and s is the…

Q: Make a maximal covering problem and formulate it. And Convert that problem into the set covering…

A: The Maximal Cover Location Question (MCLP) is a well-known optimisation question in operations…

Q: Let M be a FSM with n states. Let p and q be distinguishable states of M and let x be a shortest…

A: A finite deterministic automation M (transducer, Mealy machine, n M (transducer, Mealy machine,…

Q: Let A = {p, q, r, s} B = {r, t, v} C = {p, s, t, u} be subsets of S = {p, q, r, s, t, u, v, w}.…

A: The solution is given below for the above given question: