Synthia: a Generic and Flexible Data Structure Generator (Long Version)

M.-A. Plourde, S. Hallé
Marc-Antoine Plourde and Sylvain Hallé
Université du Québec à Chicoutimi
CANADA
A Generic And Flexible Data
Structure Generator
CRSNG
NSERC
synthia
synthia

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Generating "synthetic" inputs

Generating "synthetic" inputs
script

synthia
synthia
Enter Synthia
A Java library to facilitate the generation of
synthetic objects of various kinds
Intended to be reusable from one scenario to the
next
Provides high-level abstractions of common
functionalities

Pickers
The library is centered on the concept of Picker; it
is an interface deﬁning a method called pick.
P
picker
interface Picker<T> {
public T pick();
}
pick? t

Some built-in Pickers
Random integer in interval [m,n]
[m,n]
42
42
42
¼
42
p
λ
42
3
Uniform ﬂoat in interval [0,1]
Integer in Poisson distribution of parameter λ
Integer in Gaussian distribution N(0,1)
Biased coin ﬂip with probability p

Some built-in Pickers
Random integer in interval [m,n]
[m,n]
42
42
42
¼
42
p
λ
42
3
Uniform ﬂoat in interval [0,1]
Integer in Poisson distribution of parameter λ
Integer in Gaussian distribution N(0,1)
Biased coin ﬂip with probability p
seed

Seedable Pickers
[m,n]
Pseudo-random pickers implement an interface
called Seedable, whose method setSeed can be
used to set the starting seed of the algorithm.
setSeed(42)
Each Seedable picker guarantees to generate the
same objects in the same order for a given starting
seed.

Other built-in Pickers
[a,b,c,d]
Playback outputs objects by iterating on a
predeﬁned list, optionally looping around.
Constant is a special Playback producing a single
value.
c
list of objects
loop
value

Resettable and Duplicable Pickers
Pickers implement two other interfaces, each
deﬁning a single additional method.
Duplicable: method duplicate creates a copy of
the current picker and places the new copy in
current internal state of the original
Resettable: method reset puts a picker back into
the state it was at construction
This is also true of Seedable (i.e. pseudo-random)
pickers!

P
A picker can be instantiated by giving
references to other picker instances.
The picker calls these other pickers to
decide how to generate its own
objects.
Graphically, this results in a "wiring diagram" of
interconnected pickers.
Wiring diagram

Tick
s δ
For example: the Tick picker is parameterized by
two pickers producing numbers.

Tick
s δ
start value increment

0 1
0, 1, 2, 3, 4, 5, ...
Tick
s δ

42 1
7, 8, 9, 10, 11, 12, ...
[0,10]
Tick
s δ

0 [1,2]
0, 1, 3, 4, 6, 7, ...
Tick
s δ

http://www.retrolinear.com/services/analog-synth-restoration.aspx
"Pickers parameterized by other pickers": powerful
concept making Synthia very ﬂexible to generate
objects following various patterns.
Wiring diagram
Similar in nature
to synthesizers of
the 1970s, with
modules connected
by patch cables!

Create list/set/array of given size with
objects from upstream picker
Other built-in Pickers
Freeze ﬁrst value of upstream picker
Scramble ordering of objects from upstream
picker
Enumerate tuples with all combinations of
elements from upstream pickers
Pick element from list with probabilities
{ a,b,c,d }
[a,b,c,d]

Geometric Pickers
2D point in Cartesian coordinates (x,y)
2D point in polar coordinates (r,θ)
Sides of a triangle of unit perimeter
Polyomino of given size
r θ
x y
b 1
m 2
Aﬀine transform mx+b

Behavioral pickers
Some pickers produce objects following a complex
sequence, useful to simulate the "behavior" of some
component. The possible sequences can be deﬁned
using...
Markov
chain
Behavior
tree
Formal
grammar

P p m Knit interleaves objects produced by
multiple instances of a picker P to form
a single sequence of objects
Behavioral pickers
P P P
a
b
c
d
e
f
g
h
i a h d e i b f g
c
p m
42 42
1 2 3

A Java code example
r θ
HyperspherePicker h = new HyperspherePicker(r, a);

r θ
[1,2]
42
RandomInteger r = new RandomInteger(1, 2);
A Java code example

r θ
b 0
m 2π
[1,2]
42
AffineTransformFloat a =
new AffineTransformFloat(f, 2*PI, 0);
A Java code example

r θ
b 0
m 2π
42
[1,2]
42
RandomFloat f = new RandomFloat().setSeed(42);
A Java code example

r θ
b 0
m 2π
42
[1,2]
42
for (int i = 0; i < 100; i++) {
Utilities.print(System.out, h.pick());
}
A Java code example

for (int i = 0; i < 100; i++) {
Utilities.print(System.out, h.pick());
}
r θ
b 0
m 2π
42
[1,2]
42
A Java code example

r θ
π/6
s δ
42
[0, ,π, ]
π/2
π/2
3
s δ
/6
1
[0,1]
42
RandomFloat f1 = new RandomFloat().setSeed(42);
RandomFloat f2 = new RandomFloat().setSeed(40);
AffineTransformFloat af =
new AffineTransformFloat(f1, 2, 1);
Freeze<Float> r = new Freeze<Float>(af);
Choice<Double> a = new Choice<Double>(f2)
.add(0d, 0.25).add(PI / 2, 0.25)
.add(PI, 0.25).add(3*PI / 2, 0.25);
HyperspherePicker hp =
new HyperspherePicker(radius, angle);
A Java code example

Other examples
s δ
-1 10-4
x y
1000
s δ
0 .1
s δ
0 k
1
0
0

Other examples
11.205.232.45 - - [26-Oct-1985 01:21:00 EDT 0] "GET J0.html HTTP/2" 200 1000
11.130.222.207 - - [26-Oct-1985 01:21:04 EDT 0] "GET Xv.html HTTP/2" 200 1000
11.130.222.207 - - [26-Oct-1985 01:21:09 EDT 0] "GET 9y.html HTTP/2" 200 1000
11.16.2.198 - - [26-Oct-1985 01:21:17 EDT 0] "GET Xv.html HTTP/2" 200 1000
11.130.222.207 - - [26-Oct-1985 01:21:27 EDT 0] "GET t0.html HTTP/2" 200 1000
45.86.208.44 - - [26-Oct-1985 01:21:29 EDT 0] "GET b7.html HTTP/2" 200 1000
10.112.251.183 - - [26-Oct-1985 01:21:34 EDT 0] "GET b7.html HTTP/2" 200 1000

Other features
Since Synthia can generate inputs for a system, it is
natural to use it in a software testing context. The
library offers a few features for this purpose:
Test input shrinking: generate inputs that violate a
condition, and automatically find "smaller" inputs
that also violate it
Object mutation: special pickers receive objects
and apply a "modification" to them
Monkey testing: generate sequences of actions
sent to a reactive system
Provenance tracking: explain the origins of a value
generated by a wiring diagram

Explainability
We point to a part of a result produced by a picker,
and Synthia can provide an explanation for it.

Explainability
[1,2]
42
s δ [0,1,-1]
x y
4
x ≠ y
0

Explainability
[1,2]
42
s δ [0,1,-1]
x y
4
x ≠ y
0
[(2,-1),(3,0),(4,1),(5,-1)]

[1,2]
42
s δ [0,1,-1]
x y
4
x ≠ y
0
[(2,-1),(3,0),(4,1),(5,-1)]
Explainability

1∘1
1
3
3
3
1
[0,1,-1] 3
1
1
0
2 2
1
1
-1
[1,2]
42
s δ [0,1,-1]
x y
4
x ≠ y
0
[(2,-1),(3,0),(4,1),(5,-1)]
Explainability

Automatic shrinking
Pickers implementing the Shrinkable interface can
produce a picker returning "smaller" objects.
interface Shrinkable<T> extends Picker<T> {
public Shrinkable<T> shrink(T t);
}
P
t
shrink( )
t P'
t'
t' t

Automatic shrinking
Pickers implementing the Shrinkable interface can
produce a picker returning "smaller" objects.
P
1
shrink( )
t1
t1
P
2
shrink( )
t2
t2
...
shrink( )
tn-1
P
n
tn

Grammar-based shrinking
Synthia can interact with a reactive component by
producing sequences of actions following a
grammar (or Markov chain, behavior tree).
<S> := <number> <op> <number> <inop> ;
<inop> := <op> <number> <inop> | = ;
<number> := <integer> <digit> <rest> | <integer> ;
<integer> := <nzdigit> <rest> ;
<rest> := <digit> <rest> | ε ;
<digit> := 0 | <nzdigit> ;
<nzdigit> := 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 ;
<op> := + | − | × | ÷ ;
A sequence leading to a failure can be
automatically shrunk and still follow the grammar.

Eat your own dog food
Public disclosure: the authors of Synthia use
Synthia themselves!
Examples:
Test Suite Generation for Boolean Conditions with
Equivalence Class Partitioning, FormaliSE 2022
Boolean formulas
A Modular Runtime Enforcement Model using Multi-
Traces, FPS 2021
Behavioral sequences of events
Automated Repair of Layout Bugs in Web Pages with
Linear Programming, ICWE 2021
Web pages with injected layout faults

Code examples
Synthia comes with many detailed code examples
highlighting its features.
https://liﬂab.github.io/synthia/javadoc

Conclusion
Many other features left uncovered: picker
duplication, object mutation, value enumeration,
etc.
Many other data types not showcased: graphs,
complex Java objects, etc.
Simple and "clean" set of abstract interfaces allow
a modular and versatile design.
Used in computer experiments in multiple scientiﬁc
publications
https://github.com/liﬂab/synthia

Synthia: a Generic and Flexible Data Structure Generator (Long Version)

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