Type equation here.

Learning a Meta-Solver for Syntax-Guided Program SynthesisXujie Si*, Yuan Yang*, Hanjun Dai, Mayur Naik, Le Song (*equal contribution)

University of Pennsylvania & Georgia Institute of Technology Contact: {xsi,mhnaik}@cis.upenn.edu; {yyang754, hanjundai}@gatech.edu; lsong@cc.gatech.edu

Logical Spec !"X OR Y AND Z

Grammar #"s -> d1 OR d1 | d1 AND d1d1 -> X OR Y | d2 OR d2d2 -> ......

Task 1

Logical Spec !$X XOR Y OR (X AND Z)

Grammar #$s -> d1 XOR d1d1 -> d2 AND d2 | d2 OR d2

| d2 XOR d2d2 -> ......

Task 2

• Global graph embedding:

• Embedding of production rules

d1 -> X OR Y | d2 AND d2

d1_OR

d1_AND

==>

ℎ('")

......

GRAPH

EMBED

• Global graph embedding:

• Embedding of production rules

d1_AND

d1_OR==>

ℎ('$)

......

GRAPH

EMBED

d1 -> d2 AND d2 | d2 OR d2| d2 XOR d2

d1_XOR

S

d1

X

d1

YOR

?

)(*+")

d1_OR

d1_AND

Context vector ,*

Embedding matrix -./

⊙

1 2* ℎ('" , )(*+"))

d1

~d2

OR

d2OR

S

d1 d1

AND

?

)(*+")

Context vector ,*

XOR

d2 d2

Embedding matrix -./

⊙d1_AND

d1_OR

d1_XOR

1 2* ℎ('" , )(*+"))

~

d1

XORd2 d2

𝑟𝑒𝑤𝑎𝑟𝑑 =∑6∈89∪;8<[𝑓 𝑏 ≡ 𝜙 𝑏 ]

|𝐵E ∪ ;𝐵6|

METAL: Meta-Learning Framework

Experimental ResultsChallenges

Syntax-Guided Program Synthesis

Representation learning and transfer learning of structured data with rich semantics remain open problems. Our work addresses two fundamental challenges in this area:

q How to learn a neural representation of both syntax and semantic constraints?

q How to learn a transferable policy for program synthesis tasks with different syntax G and semantic 𝝓?

Cryptographic circuits synthesis

Synthesize programs using a grammar adaptive policy network

Jointly learn the representation of syntax and semantics

ℎHIJK = 𝑎𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒( 𝐹(ℎPI , 𝑒P,H) P∈S(H) )

Learn embedding via message passing

𝐹 ℎI, 𝑒 = 𝜎(𝑊IVWℎI)

𝜋 𝑓 𝜙, 𝐺 =ZI[K

|\|

𝜋 𝑎I ℎ 𝐺 , Τ(I^K))

Learning to solve from scratch(overall: 214)

Meta-learning enables faster solving(train/test: 150/64)

o Collected 214 circuit synthesis tasks from the 2017 SyGuS Competition

o Compared with one baseline solver and two state-of-the-art solvers

o Code and data are available at: https://github.com/PL-ML/metal

EUSolver

CVC4

Esym

Learnedsolver

Visualization ofsolved tasks

The syntax-guided program synthesis (SyGuS) problem aims to find a function f that meets both syntactic and semantic constraints:• syntactic constraint: a context-free grammar G describing the

syntax that captures the candidate implementations of f.• semantic constraint: a logical formula 𝝓 that captures the

desired functionality of f.

Countermeasure Synthesis

Original circuit[Morioka & Satoh, CHES 2002]

Buffered circuit [Ghalaty et al, DATE 2014][Endo et al, IEEE TVLSI, 2014]

Synthesized countermeasure

Countermeasure Synthesis

Original circuit[Morioka & Satoh, CHES 2002]

Buffered circuit [Ghalaty et al, DATE 2014][Endo et al, IEEE TVLSI, 2014]

Synthesized countermeasure

𝜙 (vulnerable)

𝑓(s

ide

chan

nel f

ree)

Semantic Constraint∀𝑖𝑛b, … , 𝑖𝑛d

𝜙(𝑖𝑛b, … , 𝑖𝑛d) ≡ 𝑓(𝑖𝑛b, … , 𝑖𝑛d)

Grammar (Syntactic Constraint)S -> d1 XOR d1 | d1 AND d1d1 -> d2 AND d2 | NOT d2d2 -> …d3 -> in0 | … | in7

Graph construction objective:o Capture the syntax structure and property

(e.g. rule order invariance, symmetry)o Capture the semantic constraint by its ASTo Enable information exchange by shared tokens

Global nodeNon-terminalsTerminals

Graph Representation !(#, %)

Typed ASTAST edgeGlobal link

Logical Spec #X OR Y AND Z

Grammar %s -> d1 OR d1 | d1 AND d1d1 -> X | Y | d2 OR d2d2 -> ......

XX d2

<spec>

OR

AND

Y Z

X

S

S_OR S_AND

d1

NT_DNT_D

AND_DAND_DOR_DOR_D

YX

d1TNT_D

d1_or

d2

NT_D

OR_D

OR_DT_DT_D

X

Y

Z

AND

OR

X_D

<spec>

OR

AND

Y Z

X

S

NI_DNI_D

YXd2

OR_D

OR_D

T_DT_D

X

Y

Z

AND

OR

<spec>

OR

Y Z

X

S

S_OR

d1

NI_DNI_D

AND_D

AND_DOR_DOR_D

YX

d1T

NI_D

d1_or

d2

NI_D

OR_D

OR_D

T_DT_D

X

Y

Z

OR

<spec>

OR

AND

Y Z

X

S

S_OR S_AND

NI_DNI_D

AND_D

AND_DOR_DOR_D

d1_or

d2

NI_D

OR_D

OR_D

X

Y

Z

AND

OR

......

S_OR S_AND

d1

AND_D

AND_DOR_DOR_D

d1T

NI_D

d1_or

NI_D

S_AND

AND

AND

d1

YX

d1T

NI_D

T_DT_D

Repeat ' times

• Global graph embedding:

• Node embeddings:

Output

......

s

d1

z

• Embed production rules

s -> d1 OR d1| d1 AND d1

S_OR

S_AND

==>

ℎ(!)

......One step of message

passing update

Policy network is built in an auto-regressive way

A2C is used for model training, reward is the passing ratio of accumulated examples.

𝑏: counter example ;𝐵6: samples near b

Side Channels

Input CryptographicAlgorithm Output

PowerConsumption Faulty

OutputsEM

Emissions

Timing DesignDetailsSound Heat

What can we observe?

01101001101100101110

10011011011000101110

10010000011001001110

side channels leaking secrets

SyGuS Solver

End-user Programming

Code Optimization

Intelligent Tutor

Code Auto-completion

Data Transformation