SpaceSearch: A Library for Building and Verifying Solver-Aided - PowerPoint PPT Presentation

SpaceSearch: 
 A Library for Building and Verifying Solver-Aided Tools Konstantin Steven S. 
 Stefan Emina Michael Zachary Weitz Lyubomirsky Heule Torlak D. Ernst Tatlock

Reduction

SMT Reduction

SMT Reduction

SpaceSearch Reduction SMT

The Border Gateway Protocol

The Border Gateway Protocol ISP ISP

The Border Gateway Protocol ISP ISP ISP ISP ISP

The Border Gateway Protocol ISP ISP ISP ISP ISP

The Border Gateway Protocol ISP ISP ISP ISP ISP

The Border Gateway Protocol configure terminal router bgp 1 ISP neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 ISP ! prefix lists ip prefix-list outCustomer permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list outProvider permit ISP ISP

The Border Gateway Protocol configure terminal router bgp 1 ISP neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 ISP ! prefix lists ip prefix-list outCustomer permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list outProvider permit ISP ISP

The Border Gateway Protocol configure terminal router bgp 1 ISP neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 ISP ! prefix lists ip prefix-list outCustomer permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list outProvider permit ISP ISP

The Border Gateway Protocol configure terminal router bgp 1 ISP neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 ISP ! prefix lists ip prefix-list outCustomer permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list outProvider permit ISP ISP

The Border Gateway Protocol configure terminal router bgp 1 ISP neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 ISP ! prefix lists ip prefix-list outCustomer permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list outProvider permit ISP ISP

The Border Gateway Protocol configure terminal router bgp 1 ISP neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 ISP ! prefix lists ip prefix-list outCustomer permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list outProvider permit ISP ISP

The Border Gateway Protocol ISP ISP ISP configure terminal router bgp 1 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 ! prefix lists ip prefix-list ISP outCustomer permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list outProvider permit

Specification Spec 
 Holds Bagpipe Bagpipe configure terminal router bgp 1 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 Spec 
 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou permit Violation Configuration

Specification Spec 
 Holds Bagpipe Bagpipe configure terminal router bgp 1 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 Spec 
 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou permit Violation Configuration

Bagpipe ∀ t:trace( ), check( , t) configure terminal router bgp 1 Specification Spec 
 Holds configure terminal router bgp 1 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 Spec 
 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou permit Violation Configuration

Bagpipe ∀ t:trace( ), check( , t) configure terminal router bgp 1 ∞ Specification Spec 
 Holds configure terminal router bgp 1 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 Spec 
 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou permit Violation Configuration

Bagpipe ∀ t:trace( ), check( , t) configure terminal router bgp 1 ∞ [OOPSLA’16] Reduce Specification fin ∀ t:initTrace( ), check( , t) Spec 
 configure terminal router bgp 1 Holds configure terminal router bgp 1 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 Spec 
 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou permit Violation Configuration

Bagpipe ∀ t:trace( ), check( , t) configure terminal router bgp 1 ∞ [OOPSLA’16] Reduce Specification fin ∀ t:initTrace( ), check( , t) Spec 
 configure terminal router bgp 1 Holds configure terminal router bgp 1 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 Spec 
 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou permit Violation Configuration

Bagpipe ∀ t:trace( ), check( , t) configure terminal router bgp 1 ∞ [OOPSLA’16] Reduce Specification fin ∀ t:initTrace( ), check( , t) Spec 
 configure terminal router bgp 1 Holds Reduce ? configure terminal router bgp 1 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 Spec 
 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou permit Violation Configuration SMT

∀ t:initTrace( ), check( , t) configure terminal router bgp 1 neighbor 8.212.226.20

∀ t:initTrace( ), check( , t) configure terminal router bgp 1 neighbor 8.212.226.20 initTrace( ) configure terminal router bgp 1

∀ t:initTrace( ), check( , t) configure terminal router bgp 1 neighbor 8.212.226.20 { t:initTrace( ) | ¬check( , t) } initTrace( ) configure terminal configure terminal router bgp 1 router bgp 1

∀ t:initTrace( ), check( , t) configure terminal router bgp 1 neighbor 8.212.226.20 { t:initTrace( ) | ¬check( , t) } initTrace( ) configure terminal configure terminal router bgp 1 router bgp 1 search( ) = None

SpaceSearch Interface empty = singleton(a) = a union( , ) =

SpaceSearch Interface empty = singleton(a) = a union( , ) = f(a) a a bind(S,f) = U x:S f(x) = bind( , ) = f(b) b b

SpaceSearch Interface empty = search( ) = None a singleton(a) = search( ) = Some a a union( , ) = f(a) a a bind(S,f) = U x:S f(x) = bind( , ) = f(b) b b

Bagpipe ∀ t:trace( ), check( , t) configure terminal router bgp 1 ∞ Reduce fin Specification ∀ t:initTrace( ), check( , t) Spec 
 configure terminal router bgp 1 Holds configure terminal router bgp 1 Spec 
 neighbor 8.212.226.20 remote-as 2 neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou Violation permit Configuration

Bagpipe ∀ t:trace( ), check( , t) configure terminal router bgp 1 ∞ Reduce fin Specification ∀ t:initTrace( ), check( , t) Spec 
 configure terminal router bgp 1 Holds Reduce search( 
 configure terminal router bgp 1 Spec 
 neighbor 8.212.226.20 remote-as 2 bind(initTraceSpace( ), ( λ t. neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 configure terminal router bgp 1 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou Violation permit if check( , t) 
 Configuration then empty 
 else singleton(t))) = None

Bagpipe ∀ t:trace( ), check( , t) configure terminal router bgp 1 ∞ Reduce fin Specification ∀ t:initTrace( ), check( , t) Spec 
 configure terminal router bgp 1 Holds Reduce search( 
 configure terminal router bgp 1 Spec 
 neighbor 8.212.226.20 remote-as 2 bind(initTraceSpace( ), ( λ t. neighbor 172.16.254.1 remote-as 3 neighbor 95.112.23.51 remote-as 4 configure terminal router bgp 1 ! prefix lists ip prefix-list outC permit 0.0.0.0/0 le 32 ip prefix-list outPeer permit 8.212.226.0/24 le p prefix-list ou Violation permit SMT if check( , t) 
 Configuration Extract ? then empty 
 else singleton(t))) = None

Meet

Meet ∀ x y. (x /\ y) ⟺ ¬(¬x \/ ¬y) De Morgan's Law

Meet ∀ x y. (x /\ y) ⟺ ¬(¬x \/ ¬y) De Morgan's Law (let ((x ( symbolic-bool )) (y ( symbolic-bool )))