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A Minimalistic BDD Library miniBDD miniBDD For teaching/learning purposes Designed for ease of use (there are more efficient libraries) only 556 lines of C++ (compare to cudd, which has 117k lines) D. Kroening: Computer-Aided Formal

  1. A Minimalistic BDD Library miniBDD miniBDD ◮ For teaching/learning purposes ◮ Designed for ease of use (there are more efficient libraries) ◮ only 556 lines of C++ (compare to cudd, which has 117k lines) D. Kroening: Computer-Aided Formal Verification (MT 2009) 1

  2. Data Structures ◮ A class for nodes ◮ With pointers to the two children ◮ With a reference counter ◮ The nodes are stored in a list of nodes in a BDD manager class ◮ The manager also contains: ◮ A list of the variables (with a label) ◮ The hash table for the nodes D. Kroening: Computer-Aided Formal Verification (MT 2009) 2

  3. The BDD Node Class class BDDnode { 1 class miniBDD mgr ∗ mgr ; 2 unsigned var , node number , re fe r en ce c ou nte r ; 3 BDD low , high ; 4 5 inline void add reference ( ) ; 6 void remove reference ( ) ; 7 } ; 8 There is also a (trivial) constructor. D. Kroening: Computer-Aided Formal Verification (MT 2009) 3

  4. The BDD Manager Class class miniBDD mgr { 1 public : 2 BDD Var( const std : : s t r i n g &l a b e l ) ; 3 4 inline const BDD &True ( ) ; 5 inline const BDD &False ( ) ; 6 7 protected : 8 typedef std : : l i s t < BDDnode > nodest ; 9 nodest nodes ; 10 11 v a r t a b l e e n t r y t { std : : s t r i n g l a b e l ; } ; struct 12 typedef std : : vector < var table entryt > v a r t a b l e t ; 13 v a r t a b l e t var table ; 14 . . . 15 There is also a constructor (which sets up True/False), and some methods to dump the node table. D. Kroening: Computer-Aided Formal Verification (MT 2009) 4

  5. The BDD Manager Class (Part II) class miniBDD mgr { 1 . . . 2 3 // t h i s i s our reverse − map for nodes 4 reverse keyt { struct 5 unsigned var , low , high ; 6 } ; 7 8 std : : map < reverse keyt , BDDnode ∗ > reverse map ; 9 10 // create a node ( consulting the reverse − map) 11 BDD mk( unsigned var , 12 const BDD &low , const BDD &high ) ; 13 } ; 14 D. Kroening: Computer-Aided Formal Verification (MT 2009) 5

  6. The Interface (Part I) class BDD { 1 public : 2 // Boolean operators on BDDs 3 BDD operator ! ( ) const ; 4 BDD operator ˆ( const BDD &) const ; 5 6 // copy operator 7 inline BDD & operator =( const BDD &); 8 9 protected : 10 class BDDnode ∗ node ; 11 } ; 12 There are more Boolean operators ( & , | , == ). This is essentially only one pointer, so copying is inexpensive. D. Kroening: Computer-Aided Formal Verification (MT 2009) 6

  7. The Interface (Part II) There are also some methods to obtain information about a BDD: class BDD { 1 public : 2 . . . 3 inline bool i s c o n s t a n t () const ; 4 inline bool i s t r u e () const ; 5 i s f a l s e () const ; inline bool 6 7 inline unsigned var () const ; 8 inline const BDD &low () const ; 9 inline const BDD &high () const ; 10 inline unsigned node number () const ; 11 . . . 12 } ; 13 D. Kroening: Computer-Aided Formal Verification (MT 2009) 7

  8. Using the Interface This produces: #include ”miniBDD . h” 1 y 2 int main () { 3 miniBDD mgr mgr ; 4 x 5 BDD f i n a l= 6 1 mgr . Var( ”x” ) & mgr . Var( ”y” ) ; 7 Warning: The mgr.Var(...) method doesn’t hash, so calling mgr.Var(”x”) twice will produce two different variables, both labelled ”x”. D. Kroening: Computer-Aided Formal Verification (MT 2009) 8

  9. Using the Interface You can look at the BDDs or the node table with: void DumpDot( std : : ostream &out ) const ; 1 void DumpTikZ( std : : ostream &out ) const ; 2 void DumpTable( std : : ostream &out ) const ; 3 This produces: # var low high y y 4 4 0 3 1 3 x x 3 3 2 − − − 3 2 x 0 1 0 1 0 1 4 1 y 0 3 D. Kroening: Computer-Aided Formal Verification (MT 2009) 9

  10. The Implementation of mk BDD miniBDD mgr : : mk( unsigned var , BDD low , BDD high ) { 1 i f ( low . node number()==high . node number ( ) ) 2 return low ; 3 4 reverse keyt reverse key ( var , low , high ) ; 5 reverse mapt : : c o n s t i t e r a t o r i t= 6 reverse map . find ( reverse key ) ; 7 8 i f ( i t != reverse map . end ( ) ) return BDD( it − > second ) ; 9 10 unsigned new number=nodes . back ( ) . node number+1; 11 nodes . push back ( 12 BDDnode( this , var , new number , low , high ) ) ; 13 reverse map [ reverse key]=&nodes . back ( ) ; 14 return BDD(&nodes . back ( ) ) ; 15 } 16 D. Kroening: Computer-Aided Formal Verification (MT 2009) 10

  11. The Implementation of apply BDD apply ( bool ( ∗ fkt )( bool x , bool y ) , 1 BDD x , BDD y) 2 { 3 miniBDD mgr ∗ mgr=x . node − > mgr ; 4 5 BDD u ; 6 7 i f (x . i s c o n s t a n t () && y . i s c o n s t a n t ( ) ) 8 u= BDD( fkt (x . i s t r u e () , y . i s t r u e ( ) ) ? 9 mgr − > true bdd : mgr − > false bdd ) ; 10 i f (x . var()==y . var ( ) ) else 11 u=mgr − > mk(x . var () , 12 apply ( fkt , x . low () , y . low ( ) ) , 13 apply ( fkt , x . high () , y . high ( ) ) ) ; 14 . . . 15 return u ; 16 } 17 D. Kroening: Computer-Aided Formal Verification (MT 2009) 11

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