Question: 9 . [ 3 marks ] A set S of n positive integers is said to be splittable if it can be partitioned into two

9.[3 marks] A set S of n positive integers is said to be splittable if it can be partitioned
into two subsets such that the sum of the elements in each subset is the same. For example, S ={3,7,8,9,11} is splittable since we have can form disjoint subsets S1={3,7,9} and S2={8,11} such that S1 S2= S and the sum of each subset is the same (19).
Prove that the following language is decidable with a high-level algorithmic description: {S | S is a set of positive integers that is splittable}.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Programming Questions!

Q:

An absorber is to recover 99 percent of the ammonia in the air-ammonia stream fed to it, using water as the absorbing liquid. The ammonia content of the air is 20 mole percent. Absorber temperature...

Q:

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Q:

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Q:

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Q:

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

Q:

(iii) Now express your decision rule instead using only the quantities p(Ck), p(Cj ), p(x|Ck), p(x|Cj ), and relate it to the diagram above. [2 marks] (iv) If the classifier decision rule assigns...

Q:

Numerical Methods (a) Floating point representation: (i) If a single-precision floating point number is added to a double-precision floating point number, what can we say about the expected and...

Q:

= 2 2 2 2 = Let 3DIV = { S is a set of positive integers and S can be partitioned into 3 subsets all having the same sum } For example {1, 2, 3, 6, 8, 9, 10, 12 } E 3DIV because 2 + 3 + 12 = 8 +9=1 +...

Q:

Written in Java Consider the Subset Sum Problem, formally defined as: Subset Sum (SS): INPUT: a list S[O...n-1) of n positive integers, and a target integer t2 0. OUTPUT: TRUE and a set of indices AS...

Q:

A seismic probe bores itself into the seabed, going as deep as it can before running out of fuel. This takes about five minutes. It rotates its spiral drill head at rate R(t) that follows a...

Q:

2. (a). [3 marks] In how many ways can the symbols a,b,c,d,e,e,e,e,e be arranged so that no e is adjacent to another e? (b). 13 marks] With n a positive integer, evaluate the following sum. (Hint:...

Q:

The frame of an organization focuses on providing harmony between the needs of the organization and the needs of people. Select one: O a. structural O b. symbolic c. human resources O d. political

Q:

Griz Gear Inc. has $50,000 in debt and $80,000 in equity and does not want the debt to equity ratio to increase, nor can it issue new stock at this time. The firm has net income of $13,000, employs a...

Q:

f a company overstates its ending balance of inventory in Year 1 and it reports inventory correctly in Year 2 , which one of the following is true?Cost of goods sold is overstated in Year 1 . Net...

Q:

Afully amortizing mortgage loan is made for $100,000 at 6 percent interest for 20 years. a. Calculate the monthly payment for a CPM loan. b. Assume the loan is repaid at the end of 8 years. What will...