This paper investigates what happens to the solution space if a requirement is added to use a new technology. It formally proves that adding such a requirement would actually reduce the size of the solution space, since it is the emergence of the technology what expands the solution space, not the requirement to use it. The formal proof is supported by a toy example. DOI: http://dx.doi.org/10.1016/j.procs.2015.03.053

1. CSER 2015 March 18-19, 2015 1
On the Evolution of Solution Spaces Triggered by
Emerging Technologies
By
Alejandro Salado and Roshanak Nilchiani
13th Annual Conference on Systems Engineering Research (CSER)
March 18, 2015
Stevens Institute of Technology
Hoboken, NJ
www.stevens.edu/sse/CSER2015org

2. CSER 2015 March 18-19, 2015 2
A year ago… Put your logo
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3. CSER 2015 March 18-19, 2015 3
According to literature…
Adding a new requirement results in…
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A. Salado, R. Nilchiani, and D. Verma, “A formal theory of requirements engineering: stakeholder needs, system requirements, solution spaces, and requirements’ qualities,” unpublished.
Expand solution
space
Open new
regions of
solution space
Enable better
solutions
More cost
Less solutions

4. CSER 2015 March 18-19, 2015 4
Two theorems… Put your logo
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Theorem 13:
A requirement cannot expand the solution space.
Proof: Using the inclusion of intersection theorem in set theory 𝐴 ∩ 𝐵 ⊆ 𝐴 ∧ 𝐵, then 𝐶𝑆𝑆𝐸𝑇 ⊆
𝐶𝑆𝑆𝐸𝑇 .
QED.
Theorem 14:
A system requirement reduces the solution space.
Proof: Using Definition 15, system requirements do not overlap and are applicable to the system. Consequently, the
inclusion of intersection theorem in set theory can be reworded as 𝐴 ∩ 𝐵 ⊂ 𝐴 ∧ 𝐵, i.e., since B does not overlap A and A
does not overlap B, or in other words 𝐴 ⊄ 𝐵 and 𝐵 ⊄ 𝐴, then 𝐴 ∩ 𝐵 cannot be equal to A or B. Consequently, adding a
system requirement reduces the compliant space.
QED.
A. Salado, R. Nilchiani, and D. Verma, “A formal theory of requirements engineering: stakeholder needs, system requirements, solution spaces, and requirements’ qualities,” unpublished.

5. CSER 2015 March 18-19, 2015 5
Question from the audience
What if… you add a requirement to use a technology that did not
exist at the time of writing the initial set of requirements?
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Would the solution space not be expanded then?
NO

6. CSER 2015 March 18-19, 2015 6
What is a solution space? Put your logo
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DSYSTEMS VALID SYSTEMS
COMPLIANT
SYSTEMSDESIGNED/EXPLORED
SYSTEMS

7. CSER 2015 March 18-19, 2015 7
What is a solution space? Put your logo
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DSYSTEMS VALID SPACE
COMPLIANT
SPACEDESIGN SPACE
A. Salado and R. Nilchiani, “A mathematical justification for increasing the size of the solution space to improve the probabilities of designing compliant and affordable systems,” unpublished.

8. CSER 2015 March 18-19, 2015 8
Back to the original question Put your logo
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TIME
What if… you add a requirement to use a technology that did not
exist at the time of writing the initial set of requirements?

9. CSER 2015 March 18-19, 2015 9
What can happen? Put your logo
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New
technology New
stakeholder
need
New
requirement
1
3
2 4

10. CSER 2015 March 18-19, 2015 10
Case 1: T/-/- Put your logo
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Theorem 1: An emerging technology that is able to support satisfaction of a given set of stakeholder needs, but
that does not create new stakeholder needs for those stakeholders, increases the size of the valid space.
Proof: Using Definition 12 in [3],
𝑉𝑆𝑆𝑁 𝑖
𝑇1 = 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇1
; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1
= 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇0
; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1 ∪ 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0
; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1
= 𝑉𝑆𝑆𝑁 𝑖
𝑇0 + 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0
; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1 ⊃ 𝑉𝑆𝑆𝑁 𝑖
𝑇0
QED.
Theorem 2: An emerging technology that is able to support satisfaction of a given set of stakeholder needs, but
that does not create new stakeholder needs for those stakeholders, increases the size of the compliant space if new
system requirements are not added to the requirement set.
Proof: Using Definition 12 in [3],
𝐶𝑆 𝑅 𝑖
𝑇1 = 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇1
; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1
= 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇0
; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1 ∪ 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0
; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1
= 𝐶𝑆𝑆𝑁 𝑖
𝑇0 + 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0
; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1 ⊃ 𝐶𝑆 𝑅 𝑖
𝑇0
QED
A FORMAL PROOF…

11. CSER 2015 March 18-19, 2015 11
A practical, simple example Put your logo
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STAKEHOLDER
NEEDS
SYSTEM
REQUIREMENTS
TECHNOLOGIES
n1 - Read a book during night at home
n2 - Get a warm feeling.
r1 - Provide more than 1000 lux.
r2 - Provide warm temperature light.
T1 – Standard bulb.
T2 – Low consumption white bulb.
T3 – Low consumption yellow bulb.

12. CSER 2015 March 18-19, 2015 12
A practical, simple example Put your logo
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Technology n1 n2 r1 r2 #𝑉𝑆𝑆𝑁 𝑖
#𝐶𝑆 𝑅 𝑖
Standard bulb Y Y Y Y Y Y
Low consumption white bulb Y N Y N N N
Low consumption yellow bulb Y Y Y Y Y Y
2 2
n1 - Read a book during night at home
n2 - Get a warm feeling.
r1 - Provide more than 1000 lux.
r2 - Provide warm temperature light.

13. CSER 2015 March 18-19, 2015 13
Case 1: T/-/- Put your logo
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Technology n1 n2 r1 r2 #𝑉𝑆𝑆𝑁 𝑖
#𝐶𝑆 𝑅 𝑖
Standard bulb Y Y Y Y Y Y
Low consumption white bulb Y N Y N N N
Low consumption yellow bulb Y Y Y Y Y Y
Yellow LED Y Y Y Y Y Y
Green LED Y N Y N N N
Old (T0) 2 2
New (T1) 3 3
n1 - Read a book during night at home
n2 - Get a warm feeling.
r1 - Provide more than 1000 lux.
r2 - Provide warm temperature light.

14. CSER 2015 March 18-19, 2015 14
Case 2: T/-/r Put your logo
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Technology n1 n2 r1 r2 r3 #𝑉𝑆𝑆𝑁 𝑖
#𝐶𝑆 𝑅 𝑖
Standard bulb Y Y Y Y N Y N
Low consumption white bulb Y N Y N N N N
Low consumption yellow bulb Y Y Y Y N Y N
Yellow LED Y Y Y Y Y Y Y
Green LED Y N Y N Y N N
Old (T0) 2 2
New (T1) 3 1
n1 - Read a book during night at home
n2 - Get a warm feeling.
r1 - Provide more than 1000 lux.
r2 - Provide warm temperature light.
r3 - Use LED technology.

15. CSER 2015 March 18-19, 2015 15
Case 3: T/n/- Put your logo
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Technology n1 n2 n3 r1 r2 #𝑉𝑆𝑆𝑁 𝑖
#𝐶𝑆 𝑅 𝑖
Standard bulb Y Y N Y Y N Y
Low consumption white bulb Y N N Y N N N
Low consumption yellow bulb Y Y N Y Y N Y
Yellow LED Y Y N Y Y N Y
Green LED Y N N Y N N N
Color adaptive based on sensing Y Y Y Y N Y N
Old (T0) 3 3
New (T1) 1 3
n1 - Read a book during night at home
n2 - Get a warm feeling.
n3 - Adapt the color temperature of the light according to the feelings of a reader.
r1 - Provide more than 1000 lux.
r2 - Provide warm temperature light.

16. CSER 2015 March 18-19, 2015 16
Case 4: T/n/r Put your logo
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Technology n1 n2 n3 r1 r2 r3 #𝑉𝑆𝑆𝑁 𝑖
#𝐶𝑆 𝑅 𝑖
Standard bulb Y Y N Y - N N N
Low consumption white bulb Y N N Y - N N N
Low consumption yellow bulb Y Y N Y - N N N
Yellow LED Y Y N Y - N N N
Green LED Y N N Y - N N N
Color adaptive based on sensing Y Y Y Y - Y Y Y
Old (T0) 3 3
New (T1) 1 1
n1 - Read a book during night at home
n2 - Get a warm feeling.
n3 - Adapt the color temperature of the light according to the feelings of a reader.
r1 - Provide more than 1000 lux.
r2 - Provide warm temperature light. (deleted)
r3 - Adapt temperature to reader emotion.

17. CSER 2015 March 18-19, 2015 17
Wrapping up Put your logo
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If a NEW technology does NOT change the stakeholder needs…
…then adding a requirement reduces the compliant space
FORMAL PROOF + PRACTICAL EXAMPLE
What about obsolescence?