1. CVC4 for Sygus Comp 2017 CVC4 is an SMT solver
Fourth generation of Cooperating Validity Checker (CVC, CVC Lite, CVC3, CVC4)
Supports many theories:
Linear arithmetic, bitvectors, UF, datatypes, arrays, sets, strings, …
Supports quantified formulas
Two approaches for refutation-based synthesis in SMT [Reynolds et al CAV 15]
Counterexample-Guided  Instantiation (CEGQI) for single invocation properties
Techniques Enumerative Syntax-guided synthesis (SyGuS) in DPLL(T)
 …and (limited) hybrid approaches that combine the two

2. Refutation-Based Synthesis in SMT
f.x.P(f,x) +
Negated Synthesis Conjecture
(+ syntactic restrictions R)

3. Refutation-Based Synthesis in SMT
f.x.P(f,x) +
SMT Solver
SMT Solver or
Counterexample
Guided
-Instantiation
Enumerative
SyGuS
unsat
unsat
f = lx.t1
f = lx.t2

4. CVC4 for Sygus Comp 2017 Enumerative Enumerative SyGuS SyGuS
With
Syntactic
Restrictions
+ I/O Symmetry
Breaking
CEGQI + reconstruction
CEGQI
(trivially)
Hybrid
approaches
Enumerative
SyGuS
(using default restrictions)
Counterexample
Guided
-Instantiation
Without
Syntactic
Restrictions
Input/Output Examples
Single
Invocation
Conjectures
Partially Single
Invocation
Conjectures
Other Second-Order
Synthesis
Conjectures

5. Input/Output Examples
CVC4 for Sygus Comp 2017
GENERAL
PBE
With
Syntactic
Restrictions
CLIA
INV
Without
Syntactic
Restrictions
Input/Output Examples
Partially Single
Invocation
Conjectures
Other Second-Order
Synthesis
Conjectures
Single
Invocation
Conjectures

6. What’s new this Year For enumerative SyGuS approach (all tracks):
Key optimizations for the q.f. datatypes procedure to reduce #terms
Improvements to symmetry breaking for search space pruning
For INV track:
Custom grammar construction
E.g. include constants occurring in conjecture into grammar
Improved use of templates
For PBE track:
New approaches to I/O example conjectures inspired by [Alur et al TACAS2017]
Decision tree learning for ite-solutions for PBE Bit-Vectors
Sequencing algorithm for concat-solutions for PBE Strings

7. PBE Strings Algorithm R:
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D”

8. PBE Strings Algorithm R:
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
Enumerate
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …

9. PBE Strings Algorithm R:
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match

10. PBE Strings Algorithm R: f=lx.++(“Dr”,…)
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,…)

11. PBE Strings Algorithm R: f=lx.++(“Dr”,“_”,…)
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,“_”,…)

12. PBE Strings Algorithm R: f=lx.++(“Dr”,“_”,substr(x,0,1),…)
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,“_”,substr(x,0,1),…)

13. PBE Strings Algorithm R:
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,“_”,substr(x,0,1),substr(x,1,1),…)

14. PBE Strings Algorithm R:
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
…no enumerated value
is prefix!
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,“_”,substr(x,0,1),substr(x,1,1),…)

15. PBE Strings Algorithm R: f=lx.++(“Dr”,“_”,…)
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
Backtrack
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,“_”,…)

16. PBE Strings Algorithm R: f=lx.++(“Dr”,“_”,x,…)
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,“_”,x,…)

17. PBE Strings Algorithm R: f=lx.++(“Dr”,“_”,x,”_”,…)
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,“_”,x,”_”,…)

18. PBE Strings Algorithm R: f=lx.++(“Dr”,“_”,x,”_”,substr(x,0,1))
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D” x
“_”
“Dr”
substr(x,0,1)
substr(x,1,1)
substr(x,0,2)
substr(“Dr”,0,1) …
Match
f=lx.++(“Dr”,“_”,x,”_”,substr(x,0,1))

19. PBE Strings Algorithm R: f=lx.++(“Dr”,“_”,x,”_”,substr(x,0,1))
fStr := x | “_” | “Dr”| ++(fStr,fStr)
substr(fStr,fInt,fInt)
fInt := 0 | 1 | +(fInt,fInt)
f.x. x=“Alice”  f(x)=“Dr_Alice_A”  x=“Bob”  f(x)=“Dr_Bob_B”  x=“Carl”  f(x)=“Dr_Carl_C”  x=“David”  f(x)=“Dr_David_D”
f=lx.++(“Dr”,“_”,x,”_”,substr(x,0,1))
 Return